NOORUL ISLAM COLLEGE OF ENGG,
Kumaracoil
DEPARTMENT OF ECE
2 MARKS & QUESTION- ANSWERS
EC 1302- Digital Signal Processing
Class: S5 ECE (A&B)
Prepared by : G.Sofia, Lecturer/ECE
Electronics & Communication Engineering.
Digital Signal Processing
S5ECE A&B
1. What is a continuous and discrete time signal?
Ans:
Continuous time signal: A signal x(t) is said to be continuous if it is defined for all time t.
Continuous time signal arise naturally when a physical waveform such as acoustics wave
or light wave is converted into a electrical signal. This is effected by means of
transducer.(e.g.) microphone, photocell.
Discrete time signal: A discrete time signal is defined only at discrete instants of time.
The independent variable has discrete values only, which are uniformly spaced. A
discrete time signal is often derived from the continuous time signal by sampling it at a
uniform rate.
2. Give the classification of signals?
Ans:
Continuous-time and discrete time signals
Even and odd signals
Periodic signals and non-periodic signals
Deterministic signal and Random signal
Energy and Power signal
3. What are the types of systems?
Ans:
Continuous time and discrete time systems
Linear and Non-linear systems
Causal and Non-causal systems
Static and Dynamic systems
Time varying and time in-varying systems
Distributive parameters and Lumped parameters systems
Stable and Un-stable systems.
4. What are even and odd signals?
Ans:
Even signal: continuous time signal x(t) is said to be even if it satisfies the condition
x(t)=x(-t) for all values of t.
Odd signal: he signal x(t) is said to be odd if it satisfies the condition x(-t)=-x(t) for all t.
In other words even signal is symmetric about the time origin or the vertical axis, but odd
signals are anti-symmetric about the vertical axis.
5. What are deterministic and random signals?
Ans:
Deterministic Signal: deterministic signal is a signal about which there is no certainty
with respect to its value at any time. Accordingly we find that deterministic signals may
be modeled as completely specified functions of time.
Random signal: random signal is a signal about which there is uncertainty before its
actual occurrence. Such signal may be viewed as group of signals with each signal in the
ensemble having different wave forms
.(e.g.) The noise developed in a television or radio amplifier is an example for random
signal.
6. What are energy and power signal?
Ans:
Energy signal: signal is referred as an energy signal, if and only if the total energy of the
signal satisfies the condition 0ltElt . The total energy of the continuous time signal x(t)
is given as
E=limT x2 (t)dt, integration limit from –T/2 to +T/2
Power signal: signal is said to be powered signal if it satisfies the condition 0ltPlt .
The average power of a continuous time signal is given by
P=limT 1/T x2(t)dt, integration limit is from-T/2 to +T/2.
7. What are the operations performed on a signal?
Ans:
Operations performed on dependent variables:
Amplitude scaling: y (t) =cx (t), where c is the scaling factor, x(t) is the continuous time
signal.
Addition: y (t)=x1(t)+x2(t)
Multiplication y (t)=x1(t)x2(t)
Differentiation: y (t)=d/dt x(t)
Integration (t) = x(t)dt
Operations performed on independent variables
Time shifting
Amplitude scaling
Time reversal
8. What are elementary signals and name them?
Ans:
The elementary signals serve as a building block for the construction of more complex
signals. They are also important in their own right, in that they may be used to model
many physical signals that occur in nature.
There are five elementary signals. They are as follows
Unit step function
Unit impulse function
Ramp function
Exponential function
Sinusoidal function
9. What are the properties of a system?
Ans:
Stability: A system is said to be stable if the input x(t) satisfies the condition(t) Mx<
and the out put satisfies the condition y(t) My< for all t.
Memory: A system is said to be memory if the output signal depends on the present and
the past inputs.
Invertibility: A system is said to be invertible if the input of the system con be recovered
from the system output.
Time invariance: A system is said to be time invariant if a time delay or advance of the
input signal leads to an identical time shift in the output signal.
Linearity: A system is said to be linear if it satisfies the super position principle
i.e.) R(ax1(t)+bx2(t))=ax1(t)+bx2(t)
10. What is memory system and memory less system?
Ans:
A system is said to be memory system if its output signal at any time depends on the past
values of the input signal. circuit with inductors capacitors are examples of memory
system..
A system is said to be memory less system if the output at any time depends on the
present values of the input signal. An electronic circuit with resistors is an example for
memory less system.
11. What is an invertible system?
Ans:
A system is said to be invertible system if the input of the system can be recovered from
the system output. The set of operations needed to recover the input as the second system
connected in cascade with the given system such that the output signal of the second
system is equal to the input signal applied to the system.
H-1{y(t)}=H-1{H{x(t)}}.
12. What are time invariant systems?
Ans:
A system is said to be time invariant system if a time delay or advance of the input signal
leads to an idenditical shift in the output signal. This implies that a time invariant system
responds idenditically no matter when the input signal is applied. It also satisfies the
condition
R{x(n-k)}=y(n-k).
13. Is a discrete time signal described by the input output relation y[n]= rnx[n] time
invariant.
Ans:
A signal is said to be time invariant if R{x[n-k]}= y[n-k]
R{x[n-k]}=R(x[n]) / x[n] x[n-k]
=rnx [n-k] ---------------- (1)
y[n-k]=y[n] / n n-k
=rn-kx [n-k] -------------------(2)
Equations (1) Equation(2)
Hence the signal is time variant.
14. Show that the discrete time system described by the input-output relationship y[n]
=nx[n] is linear?
Ans:
For a sys to be linear R{a1x1[n]+b1x2[n]}=a1y1[n]+b1y2[n]
L.H.S:R{ a1x1[n]+b1x2[n] }=R{x[n]} /x[n] a1x1[n]+b1x2[n]
= a1 nx1[n]+b1 nx2[n] -------------------(1)
R.H.S: a1y1[n]+b1y2[n]= a1 nx1[n]+b1 nx2[n] --------------------(2)
Equation(1)=Equation(2)
Hence the system is linear
15. What is SISO system and MIMO system?
Ans:
A control system with single input and single output is referred to as single input single
output system. When the number of plant inputs or the number of plant outputs is more
than one the system is referred to as multiple input output system. In both the case, the
controller may be in the form of a digital computer or microprocessor in which we can
speak of the digital control systems.
16. What is the output of the system with system function H1 and H2 when connected in
cascade and parallel?
Ans:
When the system with input x(t) is connected in cascade with the system H1 and H2 the
output of the system is
y(t)=H2{H1{x(t)}}
When the system is connected in parallel the output of the system is given by
y(t)=H1x1(t)+H2x2(t).
17. What do you mean by periodic and non-periodic signals?
A signal is said to be periodic if
x(n+N)=x(n)
Where N is the time period.
A signal is said to be non-periodic if
x(n+N) x(n) .
18.Determine the convolution sum of two sequences x(n) = {3, 2, 1, 2} and
h(n) = {1, 2, 1, 2}
Ans: y(n) = {3,8,8,12,9,4,4}
19.Find the convolution of the signals
x(n) = 1 n=-2,0,1
= 2 n=-1
= 0 elsewhere.
Ans: y(n) = {1,1,0,1,-2,0,-1}
20.Detemine the solution of the difference equation
y(n) = 5/6 y(n-1) – 1/6 y(n-2) + x(n) for x(n) = 2n u(n)
Ans: y(n) = -(1/2)n u(n) + 2/3(1/3)n u(n)+8/5 2nu(n)
21.Determine the response y(n), n>=0 of the system described by the second order
difference equation
y(n) – 4y(n-1) + 4y(n-2) = x(n) – x(n-1) when the input is x(n) = (-1)n u(n) and the
initial condition are y(-1) = y(-2)=1.
Ans:y(n) = (7/9-5/3n)2n u(n) +2/9(-1)n u(n)
22. Differentiate DTFT and DFT
DTFT output is continuous in time where as DFT output is Discrete in time.
23.Differentiate between DIT and DIF algorithm
DIT – Time is decimated and input is bi reversed format output in natural order
DIF – Frequency is decimated and input is natural order output is bit reversed
format.
24. How many stages are there for 8 point DFT
8
25 How many multiplication terms are required for doing DFT by expressional
method and FFT method
expression –n2 FFT N /2 log N
26. Distinguish IIR and FIR filters
27. Distinguish analog and digital filters
Analog digital
Constructed using active or
passive components and it is
described by a differential
equation
Consists of elements like adder,
subtractor and delay units and it is
described by a difference equation
Frequency response can be
changed by changing the
components
Frequency response can be
changed by changing the filter
coefficients
It processes and generates
analog output
Processes and generates digital
output
Output varies due to external
conditions
Not influenced by external
conditions
28. Write the expression for order of Butterworth filter?
The expression is N=log ( /€) 1/2/log (1/k) ½
29. Write the expression for the order of chebyshev filter?
N=cosh-1( /e)/cosh-1(1/k)
30. Write the various frequency transformations in analog domain?
LPF to LPF:s=s/ c
LPF to HPF:s= c/s
LPF to BPF:s=s2xlxu/s(xu-xl)
LPF to BSF:s=s(xu-xl)?s2=xlxu. X=
31. Write the steps in designing chebyshev filter?
1. Find the order of the filter.
2. Find the value of major and minor axis.
3. Calculate the poles.
FIR IIR
Impulse response is finite
They have perfect linear phase
Impulse Response is infinite
They do not have perfect linear
phase
Non recursive Recursive
Greater flexibility to control the
shape of magnitude response
Less flexibility
4. Find the denominator function using the above poles.
5. The numerator polynomial value depends on the value of n.
If n is odd: put s=0 in the denominator polynomial.
If n is even put s=0 and divide it by (1+e2)1/2
32. Write down the steps for designing a Butterworth filter?
1. From the given specifications find the order of the filter
2 find the transfer function from the value of N
3. Find c
4 find the transfer function ha(s) for the above value of c by su s by that value.
33. State the equation for finding the poles in chebyshev filter
sk=acos¢k+jbsin¢k,where ¢k=
/2+(2k-1)/2n)
34. State the steps to design digital IIR filter using bilinear method
Substitute s by 2/T (z-1/z+1), where T=2/ (tan (w/2) in h(s) to get h (z)
35. What is warping effect?
For smaller values of w there exist linear relationship between w and .but for
larger values of w the relationship is nonlinear. This introduces distortion in the
frequency axis. This effect compresses the magnitude and phase response. This
effect is called warping effect
36. Write a note on pre warping.
The effect of the non linear compression at high frequencies can be compensated.
When the desired magnitude response is piecewise constant over frequency, this
compression can be compensated by introducing a suitable rescaling or prewar
ping the critical frequencies.
37. Give the bilinear transform equation between s plane and z plane
s=2/T (z-1/z+1)
38. Why impulse invariant method is not preferred in the design of IIR filters other
than low pass filter?
In this method the mapping from s plane to z plane is many to one. Thus there ire
an infinite number of poles that map to the same location in the z plane, producing
an aliasing effect. It is inappropriate in designing high pass filters. Therefore this
method is not much preferred.
39. By impulse invariant method obtain the digital filter transfer function and the
differential equation of the analog filter h(s) =1/s+1
H (z) =1/1-e-Tz-1
Y/x(s) =1/s+1
Cross multiplying and taking inverse lap lace we get,
D/dt(y(t)+y(t)=x(t)
40. What is meant by impulse invariant method?
In this method of digitizing an analog filter, the impulse response of the resulting
digital filter is a sampled version of the impulse response of the analog filter. For
e.g. if the transfer function is of the form, 1/s-p, then
H (z) =1/1-e-pTz-1
41. What do you understand by backward difference?
One of the simplest methods of converting analog to digital filter is to
approximate the differential equation by an equivalent difference equation.
d/dt(y(t)/t=nT=(y(nT)-y(nT-T))/T
42. What are the properties of chebyshev filter?
1. The magnitude response of the chebyshev filter exhibits ripple either in the stop
band or the pass band.
2. The poles of this filter lies on the ellipse
43. Give the Butterworth filter transfer function and its magnitude characteristics for
different orders of filter.
The transfer function of the Butterworth filter is given by
H (j ) =1/1+j ( / c) N
44. Give the magnitude function of Butterworth filter.
The magnitude function of Butterworth filter is
|h(j )=1/[1+( / c)2N]1/2 ,N=1,2,3,4,….
45. Give the equation for the order N, major, minor axis of an ellipse in case of
chebyshev filter?
The order is given by N=cosh-1(((10.1 p)-1/10.1 s-1)1/2))/cosh-1 s/ p
A= (μ1/N-μ-1/N)/2Ωp
B=Ωp (μ1/N+ μ-1/N)/2
46. Give the expression for poles and zeroes of a chebyshev type 2 filters
The zeroes of chebyshev type 2 filter SK=j s/sink k, k=1….N
The poles of this filter xk+jyk
xk= s k/ s2+ k2
yk= s k/ s2+ k2 k=acos k
47. How can you design a digital filter from analog filter?
Digital filter can de designed from analog filter using the following methods
1. Approximation of derivatives
2. Impulse invariant method
3. Bilinear transformation
48. write down bilinear transformation.
s=2/T (z-1/z+1)
49. List the Butterworth polynomial for various orders.
N Denominator polynomial
1 S+1
2 S2+.707s+1
3 (s+1)(s2+s+1)
4 (s2+.7653s+1)(s2+1.84s+1)
5 (s+1)(s2+.6183s+1)(s2+1.618s+1)
6 (s2+1.93s+1)(s2+.707s+1)(s2+.5s+1)
7 (s+1)(s2+1.809s+1)(s2+1.24s+1)(s2+.48s+1)
50. Differentiate Butterworth and Chebyshev filter.
Butterworth dampimg factor 1.44 chebysain Hd(n)
Convert the infinite duration sequence Hd(n) to h(n)
Take Z transform of h(n) to get H(Z)
56. What are advantages of FIR filter?
Linear phase FIR filter can be easily designed .
Efficient realization of FIR filter exists as both recursive and non-recursive
structures.
FIR filter realized non-recursively stable.
The round off noise can be made small in non recursive realization of FIR filter.
57. What are the disadvantages of FIR FILTER
The duration of impulse response should be large to realize sharp cutoff filters.
The non integral delay can lead to problems in some signal processing
applications.
58. What is the necessary and sufficient condition for the linear phase characteristic of
a FIR filter?
The phase function should be a linear function of w, which inturn requires
constant group delay and phase delay.
59. List the well known design technique for linear phase FIR filter design?
Fourier series method and window method
Frequency sampling method.
Optimal filter design method.
60. Define IIR filter?
The filter designed by considering all the infinite samples of impulse response are
called IIR filter.
61. For what kind of application , the antisymmetrical impulse response can be used?
The ant symmetrical impulse response can be used to design Hilbert transforms
and differentiators.
62. For what kind of application , the symmetrical impulse response can be used?
The impulse response ,which is symmetric having odd number of samples can be
used to design all types of filters ,i.e , lowpass,highpass,bandpass and band reject.
The symmetric impulse response having even number of samples can be used
to design lowpass and bandpass filter.
63.What is the reason that FIR filter is always stable?
FIR filter is always stable because all its poles are at the origin.
64.What condition on the FIR sequence h(n) are to be imposed n order that this filter
can be called a liner phase filter?
The conditions are
(i) Symmetric condition h(n)=h(N-1-n)
(ii) Antisymmetric condition h(n)=-h(N-1-n)
65. Under what conditions a finite duration sequence h(n) will yield constant group
delay in its frequency response characteristics and not the phase delay?
If the impulse response is anti symmetrical ,satisfying the condition
H(n)=-h(N-1-n)
The frequency response of FIR filter will have constant group delay and not the
phase delay .
66. State the condition for a digital filter to be causal and stable?
A digital filter is causal if its impluse response h(n)=0 for n<0.
A digital filter is stable if its impulse response is absolutely summable ,i.e,
¥
½h(n)½< ¥
n=-¥
67. What are the properties of FIR filter?
1.FIR filter is always stable.
2.A realizable filter can always be obtained.
3.FIR filter has a linear phase response.
68. When cascade from realization is preferred in FIR filters?
The cascade from realization is preferred when complex zeros with absolute
magnitude less than one.
69. What are the disadvantage of Fourier series method ?
In designing FIR filter using Fourier series method the infinite duration impulse
response is truncated at n= ± (N-1/2).Direct truncation of the series will lead to fixed
percentage overshoots and undershoots before and after an approximated discontinuity in
the frequency response .
70. What is Gibbs phenomenon?
OR
What are Gibbs oscillations?
One possible way of finding an FIR filter that approximates H(ejw)would be to
truncate the infinite Fourier series at n= ± (N-1/2).Abrupt truncation of the series
will lead to oscillation both in pass band and is stop band .This phenomenon is
known as Gibbs phenomenon.
71. What are the desirable characteristics of the windows?
The desirable charaterstics of the window are
1.The central lobe of the frequency response of the window should contain
most of the energy and should be narrow.
2.The highest side lobe level of the frequency response should be small.
3.The sides lobes of the frequency response should decrease in energy
rapidly as w tends to p .
72. Compare Hamming window with Kaiser window.
Hamming window Kaiser window
1.The main lobe width is equal to8p/N
and the peak side lobe level is –41dB.
2.The low pass FIR filter designed will
have first side lobe peak of –53 dB
The main lobe width ,the peak side lobe
level can be varied by varying the
parameter a and N.
The side lobe peak can be varied by
varying the parameter a.
73.What is the necessary and sufficient condition for linear phase characteristics in
FIR filter?
The necessary and sufficient condition for linear phase characteristics in FIR filter
is the impulse response h(n) of the system should have the symmetry property,i.e,
H(n) = h(N-1-n)
Where N is the duration of the sequence .
74.What are the advantage of Kaiser widow?
1.It provides flexibility for the designer to select the side lobe level and N .
2. It has the attractive property that the side lobe level can be varied
continuously from the low value in the Blackman window to the high value in the
rectangle window .
75.What is the principle of designing FIR filter using frequency sampling method?
In frequency sampling method the desired magnitude response is sampled and a linear
phase response is specified .The samples of desired frequency response are defined as
DFT coefficients. The filter coefficients are then determined as the IDFT of this set of
samples.
76.For what type of filters frequency sampling method is suitable?
Frequency sampling method is attractive for narrow band frequency selective
filters where only a few of the samples of the frequency response are non-zero.
77.What is meant by autocorrelation?
The autocorrelation of a sequence is the correlation of a sequence with its shifted
version, and this indicates how fast the signal changes.
78.Define white noise?
A stationary random process is said to be white noise if its power density
spectrum is constant. Hence the white noise has flat frequency response spectrum.
SX(w) = x
2, - w
79.what do you understand by a fixed-point number?
In fixed point arithmetic the position of the binary point is fixed. The bit to the right
represent the fractional part of the number & those to the left represent the integer part.
For example, the binary number 01.1100 has the value 1.75 in decimal.
80.What is the objective of spectrum estimation?
The main objective of spectrum estimation is the determination of the power
spectral density of a random process. The estimated PSD provides information about the
structure of the random process which can be used for modeling, prediction or filtering of
the deserved process.
81.List out the addressing modes supported by C5X processors?
1. Direct addressing
2. Indirect addressing
3. Immediate addressing
4. Dedicated-register addressing
5. Memory-mapped register addressing
6. Circular addressing
82.what is meant by block floating point representation? What are its advantages?
In block point arithmetic the set of signals to be handled is divided into blocks. Each
block have the same value for the exponent. The arithmetic operations with in the block
uses fixed point arithmetic & only one exponent per block is stored thus saving memory.
This representation of numbers is more suitable in certain FFT flow graph & in digital
audio applications.
83.what are the advantages of floating point arithmetic?
1. Large dynamic range
2. Over flow in floating point representation is unlike.
84.what are the three-quantization errors to finite word length registers in digital filters?
1. Input quantization error 2. Coefficient quantization error 3. Product quantization
error
85.How the multiplication & addition are carried out in floating point arithmetic?
In floating point arithmetic, multiplication are carried out as follows,
Let f1 = M1*2c1 and f2 = M2*2c2. Then f3 = f1*f2 = (M1*M2) 2(c1+c2)
That is, mantissa is multiplied using fixed-point arithmetic and the exponents are
added.
The sum of two floating-point number is carried out by shifting the bits of the mantissa
of the smaller number to the right until the exponents of the two numbers are equal and
then adding the mantissas.
86.What do you understand by input quantization error?
In digital signal processing, the continuous time input signals are converted into digital
using a b-bit ACD. The representation of continuous signal amplitude by a fixed digit
produce an error, which is known as input quantization error.
87.List the on-chip peripherals in 5X.
The C5X DSP on-chip peripherals available are as follows:
1. Clock Generator
2. Hardware Timer
3. Software-Programmable Wait-State Generators
4. Parallel I/O Ports
5. Host Port Interface (HPI)
6. Serial Port
7. Buffered Serial Port (BSP)
8. Time-Division Multiplexed (TDM) Serial Port
9. User-Maskable Interrupts
88.what is the relationship between truncation error e and the bits b for representing a
decimal into binary?
For a 2's complement representation, the error due to truncation for both positive and
negative values of x is 0>=xt-x>-2-b
Where b is the number of bits and xt is the truncated value of x.
The equation holds good for both sign magnitude, 1's complement if x>0
If x<0, then for sign magnitude and for 1's complement the truncation error satisfies.
89.what is meant rounding? Discuss its effect on all types of number representation?
Rounding a number to b bits is accomplished by choosing the rounded result as the b
bit number closest to the original number unrounded.
For fixed point arithmetic, the error made by rounding a number to b bits satisfy the
inequality
-2-b 2-b
-----<=xt-x<= --------
2 2
for all three types of number systems, i.e., 2's complement, 1's complement & sign
magnitude.
For floating point number the error made by rounding a number to b bits satisfy the
inequality
-2-b<=E<=2-b where E=xt-x
--------
x
90.what is meant by A/D conversion noise?
A DSP contains a device, A/D converter that operates on the analog input x(t) to
produce xq(t) which is binary sequence of 0s and 1s.
At first the signal x(t) is sampled at regular intervals to produce a sequence x(n) is of
infinite precision. Each sample x(n) is expressed in terms of a finite number of bits given
the sequence xq(n). The difference signal e(n)=xq(n)-x(n) is called A/D conversion noise.
91.what is the effect of quantization on pole location?
Quantization of coefficients in digital filters lead to slight changes in their value. This
change in value of filter coefficients modify the pole-zero locations. Some times the pole
locations will be changed in such a way that the system may drive into instability.
92.which realization is less sensitive to the process of quantization?
Cascade form.
93.what is meant by quantization step size?
Let us assume a sinusoidal signal varying between +1 and -1 having a dynamic range
2. If the ADC used to convert the sinusoidal signal employs b+1 bits including sign bit,
the number of levels available for quantizing x(n) is 2b+1. Thus the interval between
successive levels
q= 2 =2-b
--------
2b+1
Where q is known as quantization step size.
94.How would you relate the steady-state noise power due to quantization and the b bits
representing the binary sequence?
Steady state noise power
Where b is the number of bits excluding sign bit.
95.what is overflow oscillation?
The addition of two fixed-point arithmetic numbers cause over flow the sum exceeds
the word size available to store the sum. This overflow caused by adder make the filter
output to oscillate between maximum amplitude limits. Such limit cycles have been
referred to as over flow oscillations.
96.what are the methods used to prevent overflow?
There are two methods used to prevent overflow
1. Saturation arithmetic 2. Scaling
97.what are the two kinds of limit cycle behavior in DSP?
1.zero input limit cycle oscillations
2.Overflow limit cycle oscillations
98.Determine "dead band" of the filter
The limit cycle occur as a result of quantization effect in multiplication. The
amplitudes of the output during a limit cycle are confined to a range of values called the
dead band of the filter.
99.Explain briefly the need for scaling in the digital filter implementation.
To prevent overflow, the signal level at certain points in the digital filter must be
scaled so that no overflow occurs in the adder.
100.What are the different buses of TMS320C5X and their functions?
The C5X architecture has four buses and their functions are as follows:
Program bus (PB):
It carries the instruction code and immediate operands from program memory
space to the CPU.
Program address bus (PAB):
It provides addresses to program memory space for both reads and writes.
Data read bus (DB):
It interconnects various elements of the CPU to data memory space.
Data read address bus (DAB):
It provides the address to access the data memory space.
Part B
1. Determine the DFT of the sequence
x(n) =1/4, for 0<=n <=2
0, otherwise
Ans: The N point DFT of the sequence x(n) is defined as
N-1
x(k)= x(n)e-j2 nk/N K=0,1,2,3,…N-1
n=0
x(n) = (1/4,1/4,1/4)
X(k) = ¼ e-j2 k/3[1+2cos(2 k/3)] where k= 0,1,……….,N-1
2. Derive the DFT of the sample data sequence x(n) = {1,1,2,2,3,3}and compute the
corresponding amplitude and phase spectrum.
Ans: The N point DFT of the sequence x(n) is defined as
N-1
X(k)= x(n)e-j2 nk/N K=0,1,2,3,…N-1
n=0
X(0) = 12
X(1) = -1.5 + j2.598
X(2) = -1.5 + j0.866
X(3) = 0
X(4) = -1.5 – j0.86{5/2, -1/2-j1/2, -1/2, -1/2+j1/2}
6. Design an ideal low pass filter with a frequency response Hd(e jw) =1 for –
/2<=w<=
/2
0 otherwise
find the value of h(n) for N=11 find H(Z) plot magnitude response
a. Find h(n) by IDTFT
b. Convert h(n) in to a fine length by truncation
c. H(0)=1/2,
h(1)=h(-1)=0.3183
h(2)=h(-2)=0
h(3)=h(-3)= -0.106
h(4)=h(-4)=0
h(5)=h(-5)=0.06366
d. Find the transfer function H(Z) which is not realizable conver in to realizable by
multiplying by z-(N-1/2)
e. H’(Z) obtained is 0.06366-0.106z-2+.3183Z-4+.5Z-5+.3183Z-6-.106Z-8+0.06366Z-
10
f. Find H (e jw) and plot amplitude response curve.
7. Design an ideal low pass filter with a frequency response Hd(e jw) =1 for –
/4<=|w|<=
0 otherwise
find the value of h(n) for N=11 find H(Z) plot magnitude response
g. Find h(n) by IDTFT
h. Convert h(n) in to a fine length by truncation
i. H(0)=0.75
h(1)=h(-1)=-.22
h(2)=h(-2)=-.159
h(3)=h(-3)= -0.075
h(4)=h(-4)=0
h(5)=h(-5)=0.045
j. Find the transfer function H(Z) which is not realizable conver in to realizable by
multiplying by z-(N-1/2)
k. H’(Z) obtained is 0.045-0.075z-2 -.159 Z-3-0.22Z-4+0.75Z-5-.22Z-6 -0.159Z-7 -.
075Z-8+0.045Z-10
l. Find H (e jw) and plot amplitude response curve.
8. Design band pass filter with a frequency response Hd(e jw) =1 for –
/3<=|w|<=2
/3
0 otherwise
find the value of h(n) for N=11 find H(Z) plot magnitude response
m. Find h(n) by IDTFT
n. Convert h(n) in to a fine length by truncation
o. Find the transfer function H(Z) which is not realizable conver in to realizable by
multiplying by z-(N-1/2)
p. H’(Z) obtained Find H (e jw) and plot amplitude response curve.
9. Design band reject filter with a frequency response Hd(e jw) =1 for
/4<=|w|<=3
/4
0 otherwise
find the value of h(n) for N=11 find H(Z) plot magnitude response
q. Find h(n) by IDTFT
r. Convert h(n) in to a fine length by truncation
s. Find the transfer function H(Z) which is not realizable conver in to realizable by
multiplying by z-(N-1/2)
t. H’(Z) obtained Find H (e jw) and plot amplitude response curve.
10. Derive the condition of FIR filter to be linear in phase.
Conditions are
Group delay and Phase delay should be constant
And
And show the condition is satisfied
11Derive the expression for steady state I/P Noise Power and Steady state O/P Noise
Power.
Write the derivation.
12 Draw the product quantatization model for first order and second order filter
Write the difference equation and draw the noise model.
13 For the second order filter Draw the direct form II realization and find the scaling
factor S0 to avoid over flow
Find the scaling factor from the formula
1+r2
I= ---------------------------------------
(1-r2)(1-2r2cos2ø =r4)
14 Explain Briefly about various number representation in digital computer.
1 Fixed point
2 Floating point
3 Block floating point
Signed magnitude represenation
1’s Complement
2’s Complement
etc
15 Consider the transfer function H(Z)=H1(Z)H2(Z) where H1(Z) =1/1-a1Z-1
H2(z) =1/ 1-a2Z-1
Find the o/p Round of noise power Assume a1=0.5 and a2= 0.6 and find o.p
round off noise power.
Draw the round of Noise Model.
By using residue method find 01
By using residue method find 02
= 01 2+ 02 2
2 –2b (5.43)
Ans:__________________
12
16.Explain the architecture of DSP processor .
Diagram. & explanation.
17.Describe briefly the different methods of power spectral estimation?
1. Bartlett method
2. Welch method
3. Blackman-Tukey method
and its derivation.
18.what is meant by A/D conversion noise. Explain in detail?
A DSP contains a device, A/D converter that operates on the analog input x(t) to
produce xq(t) which is binary sequence of 0s and 1s.
At first the signal x(t) is sampled at regular intervals to produce a sequence x(n) is of
infinite precision. Each sample x(n) is expressed in terms of a finite number of bits given
the sequence xq(n). The difference signal e(n)=xq(n)-x(n) is called A/D conversion noise.
+ derivation.
19 onsider the transfer function H(Z)=H1(Z)H2(Z) where H1(Z) =1/1-a1Z-1
H2(z) =1/ 1-a2Z-1
Find the o/p Round of noise power Assume a1=0.7 and a2= 0.8and find o.p round
off noise power.
Draw the round of Noise Model.
By using residue method find 01
By using residue method find 02
= 01 2+ 02 2
20.Given X(k) = {1,1,1,1,1,1,1,1,} ,find x(n) using inverse DIT FFT algorithm.
WN
k = ej(2 /N)k
Find x(n)
21.Find the inverse DFT of X(k) = {3,4,5,6}
Ans: The inverse DFT is defined as
N-1
x(n)=(1/N ) x(k)ej2 nk/N n=0,1,2,3,…N-1
k=0
22. Explain various addressing modes of TMS processor.
Immediate.
Register
Register indirect
Indexed
& its detail explanation.
23 Derive the expression for steady state I/P Noise Variance and Steady state O/P
Noise Variance
Write the derivation.
24. Explain briefly the periodogram method of power spectral estimation?
Write the derivation with explanation.
25. Explain various arithmetic instruction of TMS processor.
All arithmetic instruction with explanation.
KEYWORDS:DIGITAL SIGNAL PROCESSING,DIGITAL SIGNAL PROCESSING QUESTION PAPER,DSP QUESTION PAPER,ANNA UNIVERSITY QUESTION PAPER,ANNA UNIVERSITY,ANNA UNIVERSITY CHENNAI,ANNA UNIVERSITY COIMBATORE,ANNA UNIVERSITY TRICHY,ANNA UNIVERSITY TIRUNELVELI,ANNA UNIVERSITY MADURAI,ANNA UNIVERSITY SYLLABUS,ANNA-UNIVERSITY RESULTS,ANNA UNIVERSITY DISTANCE EDUCATION,ANNA UNIVERSITY MBA-CENTRE FOR DISTANCE EDUCATION,ANNA UNIVERSITY SCHEDULE OF EXAMINATIONS,ANNA UNIVERSITY ADMISSION,ANNA UNIVERSITY COURSES,ANNA UNIVERSITY ACADEMIC,ANNA UNIVERSITY DEPARTMENTS,ANNA UNIVERSITY RESEARCH,ANNA UNIVERSITY MAIL,ANNA UNIVERSITY QUESTION PAPERS,ANNA UNIVERSITY COUNSELLING DATES,ANNA UNIVERSITY RE-EVALUATION RESULTS
Kumaracoil
DEPARTMENT OF ECE
2 MARKS & QUESTION- ANSWERS
EC 1302- Digital Signal Processing
Class: S5 ECE (A&B)
Prepared by : G.Sofia, Lecturer/ECE
Electronics & Communication Engineering.
Digital Signal Processing
S5ECE A&B
1. What is a continuous and discrete time signal?
Ans:
Continuous time signal: A signal x(t) is said to be continuous if it is defined for all time t.
Continuous time signal arise naturally when a physical waveform such as acoustics wave
or light wave is converted into a electrical signal. This is effected by means of
transducer.(e.g.) microphone, photocell.
Discrete time signal: A discrete time signal is defined only at discrete instants of time.
The independent variable has discrete values only, which are uniformly spaced. A
discrete time signal is often derived from the continuous time signal by sampling it at a
uniform rate.
2. Give the classification of signals?
Ans:
Continuous-time and discrete time signals
Even and odd signals
Periodic signals and non-periodic signals
Deterministic signal and Random signal
Energy and Power signal
3. What are the types of systems?
Ans:
Continuous time and discrete time systems
Linear and Non-linear systems
Causal and Non-causal systems
Static and Dynamic systems
Time varying and time in-varying systems
Distributive parameters and Lumped parameters systems
Stable and Un-stable systems.
4. What are even and odd signals?
Ans:
Even signal: continuous time signal x(t) is said to be even if it satisfies the condition
x(t)=x(-t) for all values of t.
Odd signal: he signal x(t) is said to be odd if it satisfies the condition x(-t)=-x(t) for all t.
In other words even signal is symmetric about the time origin or the vertical axis, but odd
signals are anti-symmetric about the vertical axis.
5. What are deterministic and random signals?
Ans:
Deterministic Signal: deterministic signal is a signal about which there is no certainty
with respect to its value at any time. Accordingly we find that deterministic signals may
be modeled as completely specified functions of time.
Random signal: random signal is a signal about which there is uncertainty before its
actual occurrence. Such signal may be viewed as group of signals with each signal in the
ensemble having different wave forms
.(e.g.) The noise developed in a television or radio amplifier is an example for random
signal.
6. What are energy and power signal?
Ans:
Energy signal: signal is referred as an energy signal, if and only if the total energy of the
signal satisfies the condition 0ltElt . The total energy of the continuous time signal x(t)
is given as
E=limT x2 (t)dt, integration limit from –T/2 to +T/2
Power signal: signal is said to be powered signal if it satisfies the condition 0ltPlt .
The average power of a continuous time signal is given by
P=limT 1/T x2(t)dt, integration limit is from-T/2 to +T/2.
7. What are the operations performed on a signal?
Ans:
Operations performed on dependent variables:
Amplitude scaling: y (t) =cx (t), where c is the scaling factor, x(t) is the continuous time
signal.
Addition: y (t)=x1(t)+x2(t)
Multiplication y (t)=x1(t)x2(t)
Differentiation: y (t)=d/dt x(t)
Integration (t) = x(t)dt
Operations performed on independent variables
Time shifting
Amplitude scaling
Time reversal
8. What are elementary signals and name them?
Ans:
The elementary signals serve as a building block for the construction of more complex
signals. They are also important in their own right, in that they may be used to model
many physical signals that occur in nature.
There are five elementary signals. They are as follows
Unit step function
Unit impulse function
Ramp function
Exponential function
Sinusoidal function
9. What are the properties of a system?
Ans:
Stability: A system is said to be stable if the input x(t) satisfies the condition(t) Mx<
and the out put satisfies the condition y(t) My< for all t.
Memory: A system is said to be memory if the output signal depends on the present and
the past inputs.
Invertibility: A system is said to be invertible if the input of the system con be recovered
from the system output.
Time invariance: A system is said to be time invariant if a time delay or advance of the
input signal leads to an identical time shift in the output signal.
Linearity: A system is said to be linear if it satisfies the super position principle
i.e.) R(ax1(t)+bx2(t))=ax1(t)+bx2(t)
10. What is memory system and memory less system?
Ans:
A system is said to be memory system if its output signal at any time depends on the past
values of the input signal. circuit with inductors capacitors are examples of memory
system..
A system is said to be memory less system if the output at any time depends on the
present values of the input signal. An electronic circuit with resistors is an example for
memory less system.
11. What is an invertible system?
Ans:
A system is said to be invertible system if the input of the system can be recovered from
the system output. The set of operations needed to recover the input as the second system
connected in cascade with the given system such that the output signal of the second
system is equal to the input signal applied to the system.
H-1{y(t)}=H-1{H{x(t)}}.
12. What are time invariant systems?
Ans:
A system is said to be time invariant system if a time delay or advance of the input signal
leads to an idenditical shift in the output signal. This implies that a time invariant system
responds idenditically no matter when the input signal is applied. It also satisfies the
condition
R{x(n-k)}=y(n-k).
13. Is a discrete time signal described by the input output relation y[n]= rnx[n] time
invariant.
Ans:
A signal is said to be time invariant if R{x[n-k]}= y[n-k]
R{x[n-k]}=R(x[n]) / x[n] x[n-k]
=rnx [n-k] ---------------- (1)
y[n-k]=y[n] / n n-k
=rn-kx [n-k] -------------------(2)
Equations (1) Equation(2)
Hence the signal is time variant.
14. Show that the discrete time system described by the input-output relationship y[n]
=nx[n] is linear?
Ans:
For a sys to be linear R{a1x1[n]+b1x2[n]}=a1y1[n]+b1y2[n]
L.H.S:R{ a1x1[n]+b1x2[n] }=R{x[n]} /x[n] a1x1[n]+b1x2[n]
= a1 nx1[n]+b1 nx2[n] -------------------(1)
R.H.S: a1y1[n]+b1y2[n]= a1 nx1[n]+b1 nx2[n] --------------------(2)
Equation(1)=Equation(2)
Hence the system is linear
15. What is SISO system and MIMO system?
Ans:
A control system with single input and single output is referred to as single input single
output system. When the number of plant inputs or the number of plant outputs is more
than one the system is referred to as multiple input output system. In both the case, the
controller may be in the form of a digital computer or microprocessor in which we can
speak of the digital control systems.
16. What is the output of the system with system function H1 and H2 when connected in
cascade and parallel?
Ans:
When the system with input x(t) is connected in cascade with the system H1 and H2 the
output of the system is
y(t)=H2{H1{x(t)}}
When the system is connected in parallel the output of the system is given by
y(t)=H1x1(t)+H2x2(t).
17. What do you mean by periodic and non-periodic signals?
A signal is said to be periodic if
x(n+N)=x(n)
Where N is the time period.
A signal is said to be non-periodic if
x(n+N) x(n) .
18.Determine the convolution sum of two sequences x(n) = {3, 2, 1, 2} and
h(n) = {1, 2, 1, 2}
Ans: y(n) = {3,8,8,12,9,4,4}
19.Find the convolution of the signals
x(n) = 1 n=-2,0,1
= 2 n=-1
= 0 elsewhere.
Ans: y(n) = {1,1,0,1,-2,0,-1}
20.Detemine the solution of the difference equation
y(n) = 5/6 y(n-1) – 1/6 y(n-2) + x(n) for x(n) = 2n u(n)
Ans: y(n) = -(1/2)n u(n) + 2/3(1/3)n u(n)+8/5 2nu(n)
21.Determine the response y(n), n>=0 of the system described by the second order
difference equation
y(n) – 4y(n-1) + 4y(n-2) = x(n) – x(n-1) when the input is x(n) = (-1)n u(n) and the
initial condition are y(-1) = y(-2)=1.
Ans:y(n) = (7/9-5/3n)2n u(n) +2/9(-1)n u(n)
22. Differentiate DTFT and DFT
DTFT output is continuous in time where as DFT output is Discrete in time.
23.Differentiate between DIT and DIF algorithm
DIT – Time is decimated and input is bi reversed format output in natural order
DIF – Frequency is decimated and input is natural order output is bit reversed
format.
24. How many stages are there for 8 point DFT
8
25 How many multiplication terms are required for doing DFT by expressional
method and FFT method
expression –n2 FFT N /2 log N
26. Distinguish IIR and FIR filters
27. Distinguish analog and digital filters
Analog digital
Constructed using active or
passive components and it is
described by a differential
equation
Consists of elements like adder,
subtractor and delay units and it is
described by a difference equation
Frequency response can be
changed by changing the
components
Frequency response can be
changed by changing the filter
coefficients
It processes and generates
analog output
Processes and generates digital
output
Output varies due to external
conditions
Not influenced by external
conditions
28. Write the expression for order of Butterworth filter?
The expression is N=log ( /€) 1/2/log (1/k) ½
29. Write the expression for the order of chebyshev filter?
N=cosh-1( /e)/cosh-1(1/k)
30. Write the various frequency transformations in analog domain?
LPF to LPF:s=s/ c
LPF to HPF:s= c/s
LPF to BPF:s=s2xlxu/s(xu-xl)
LPF to BSF:s=s(xu-xl)?s2=xlxu. X=
31. Write the steps in designing chebyshev filter?
1. Find the order of the filter.
2. Find the value of major and minor axis.
3. Calculate the poles.
FIR IIR
Impulse response is finite
They have perfect linear phase
Impulse Response is infinite
They do not have perfect linear
phase
Non recursive Recursive
Greater flexibility to control the
shape of magnitude response
Less flexibility
4. Find the denominator function using the above poles.
5. The numerator polynomial value depends on the value of n.
If n is odd: put s=0 in the denominator polynomial.
If n is even put s=0 and divide it by (1+e2)1/2
32. Write down the steps for designing a Butterworth filter?
1. From the given specifications find the order of the filter
2 find the transfer function from the value of N
3. Find c
4 find the transfer function ha(s) for the above value of c by su s by that value.
33. State the equation for finding the poles in chebyshev filter
sk=acos¢k+jbsin¢k,where ¢k=
/2+(2k-1)/2n)
34. State the steps to design digital IIR filter using bilinear method
Substitute s by 2/T (z-1/z+1), where T=2/ (tan (w/2) in h(s) to get h (z)
35. What is warping effect?
For smaller values of w there exist linear relationship between w and .but for
larger values of w the relationship is nonlinear. This introduces distortion in the
frequency axis. This effect compresses the magnitude and phase response. This
effect is called warping effect
36. Write a note on pre warping.
The effect of the non linear compression at high frequencies can be compensated.
When the desired magnitude response is piecewise constant over frequency, this
compression can be compensated by introducing a suitable rescaling or prewar
ping the critical frequencies.
37. Give the bilinear transform equation between s plane and z plane
s=2/T (z-1/z+1)
38. Why impulse invariant method is not preferred in the design of IIR filters other
than low pass filter?
In this method the mapping from s plane to z plane is many to one. Thus there ire
an infinite number of poles that map to the same location in the z plane, producing
an aliasing effect. It is inappropriate in designing high pass filters. Therefore this
method is not much preferred.
39. By impulse invariant method obtain the digital filter transfer function and the
differential equation of the analog filter h(s) =1/s+1
H (z) =1/1-e-Tz-1
Y/x(s) =1/s+1
Cross multiplying and taking inverse lap lace we get,
D/dt(y(t)+y(t)=x(t)
40. What is meant by impulse invariant method?
In this method of digitizing an analog filter, the impulse response of the resulting
digital filter is a sampled version of the impulse response of the analog filter. For
e.g. if the transfer function is of the form, 1/s-p, then
H (z) =1/1-e-pTz-1
41. What do you understand by backward difference?
One of the simplest methods of converting analog to digital filter is to
approximate the differential equation by an equivalent difference equation.
d/dt(y(t)/t=nT=(y(nT)-y(nT-T))/T
42. What are the properties of chebyshev filter?
1. The magnitude response of the chebyshev filter exhibits ripple either in the stop
band or the pass band.
2. The poles of this filter lies on the ellipse
43. Give the Butterworth filter transfer function and its magnitude characteristics for
different orders of filter.
The transfer function of the Butterworth filter is given by
H (j ) =1/1+j ( / c) N
44. Give the magnitude function of Butterworth filter.
The magnitude function of Butterworth filter is
|h(j )=1/[1+( / c)2N]1/2 ,N=1,2,3,4,….
45. Give the equation for the order N, major, minor axis of an ellipse in case of
chebyshev filter?
The order is given by N=cosh-1(((10.1 p)-1/10.1 s-1)1/2))/cosh-1 s/ p
A= (μ1/N-μ-1/N)/2Ωp
B=Ωp (μ1/N+ μ-1/N)/2
46. Give the expression for poles and zeroes of a chebyshev type 2 filters
The zeroes of chebyshev type 2 filter SK=j s/sink k, k=1….N
The poles of this filter xk+jyk
xk= s k/ s2+ k2
yk= s k/ s2+ k2 k=acos k
47. How can you design a digital filter from analog filter?
Digital filter can de designed from analog filter using the following methods
1. Approximation of derivatives
2. Impulse invariant method
3. Bilinear transformation
48. write down bilinear transformation.
s=2/T (z-1/z+1)
49. List the Butterworth polynomial for various orders.
N Denominator polynomial
1 S+1
2 S2+.707s+1
3 (s+1)(s2+s+1)
4 (s2+.7653s+1)(s2+1.84s+1)
5 (s+1)(s2+.6183s+1)(s2+1.618s+1)
6 (s2+1.93s+1)(s2+.707s+1)(s2+.5s+1)
7 (s+1)(s2+1.809s+1)(s2+1.24s+1)(s2+.48s+1)
50. Differentiate Butterworth and Chebyshev filter.
Butterworth dampimg factor 1.44 chebysain Hd(n)
Convert the infinite duration sequence Hd(n) to h(n)
Take Z transform of h(n) to get H(Z)
56. What are advantages of FIR filter?
Linear phase FIR filter can be easily designed .
Efficient realization of FIR filter exists as both recursive and non-recursive
structures.
FIR filter realized non-recursively stable.
The round off noise can be made small in non recursive realization of FIR filter.
57. What are the disadvantages of FIR FILTER
The duration of impulse response should be large to realize sharp cutoff filters.
The non integral delay can lead to problems in some signal processing
applications.
58. What is the necessary and sufficient condition for the linear phase characteristic of
a FIR filter?
The phase function should be a linear function of w, which inturn requires
constant group delay and phase delay.
59. List the well known design technique for linear phase FIR filter design?
Fourier series method and window method
Frequency sampling method.
Optimal filter design method.
60. Define IIR filter?
The filter designed by considering all the infinite samples of impulse response are
called IIR filter.
61. For what kind of application , the antisymmetrical impulse response can be used?
The ant symmetrical impulse response can be used to design Hilbert transforms
and differentiators.
62. For what kind of application , the symmetrical impulse response can be used?
The impulse response ,which is symmetric having odd number of samples can be
used to design all types of filters ,i.e , lowpass,highpass,bandpass and band reject.
The symmetric impulse response having even number of samples can be used
to design lowpass and bandpass filter.
63.What is the reason that FIR filter is always stable?
FIR filter is always stable because all its poles are at the origin.
64.What condition on the FIR sequence h(n) are to be imposed n order that this filter
can be called a liner phase filter?
The conditions are
(i) Symmetric condition h(n)=h(N-1-n)
(ii) Antisymmetric condition h(n)=-h(N-1-n)
65. Under what conditions a finite duration sequence h(n) will yield constant group
delay in its frequency response characteristics and not the phase delay?
If the impulse response is anti symmetrical ,satisfying the condition
H(n)=-h(N-1-n)
The frequency response of FIR filter will have constant group delay and not the
phase delay .
66. State the condition for a digital filter to be causal and stable?
A digital filter is causal if its impluse response h(n)=0 for n<0.
A digital filter is stable if its impulse response is absolutely summable ,i.e,
¥
½h(n)½< ¥
n=-¥
67. What are the properties of FIR filter?
1.FIR filter is always stable.
2.A realizable filter can always be obtained.
3.FIR filter has a linear phase response.
68. When cascade from realization is preferred in FIR filters?
The cascade from realization is preferred when complex zeros with absolute
magnitude less than one.
69. What are the disadvantage of Fourier series method ?
In designing FIR filter using Fourier series method the infinite duration impulse
response is truncated at n= ± (N-1/2).Direct truncation of the series will lead to fixed
percentage overshoots and undershoots before and after an approximated discontinuity in
the frequency response .
70. What is Gibbs phenomenon?
OR
What are Gibbs oscillations?
One possible way of finding an FIR filter that approximates H(ejw)would be to
truncate the infinite Fourier series at n= ± (N-1/2).Abrupt truncation of the series
will lead to oscillation both in pass band and is stop band .This phenomenon is
known as Gibbs phenomenon.
71. What are the desirable characteristics of the windows?
The desirable charaterstics of the window are
1.The central lobe of the frequency response of the window should contain
most of the energy and should be narrow.
2.The highest side lobe level of the frequency response should be small.
3.The sides lobes of the frequency response should decrease in energy
rapidly as w tends to p .
72. Compare Hamming window with Kaiser window.
Hamming window Kaiser window
1.The main lobe width is equal to8p/N
and the peak side lobe level is –41dB.
2.The low pass FIR filter designed will
have first side lobe peak of –53 dB
The main lobe width ,the peak side lobe
level can be varied by varying the
parameter a and N.
The side lobe peak can be varied by
varying the parameter a.
73.What is the necessary and sufficient condition for linear phase characteristics in
FIR filter?
The necessary and sufficient condition for linear phase characteristics in FIR filter
is the impulse response h(n) of the system should have the symmetry property,i.e,
H(n) = h(N-1-n)
Where N is the duration of the sequence .
74.What are the advantage of Kaiser widow?
1.It provides flexibility for the designer to select the side lobe level and N .
2. It has the attractive property that the side lobe level can be varied
continuously from the low value in the Blackman window to the high value in the
rectangle window .
75.What is the principle of designing FIR filter using frequency sampling method?
In frequency sampling method the desired magnitude response is sampled and a linear
phase response is specified .The samples of desired frequency response are defined as
DFT coefficients. The filter coefficients are then determined as the IDFT of this set of
samples.
76.For what type of filters frequency sampling method is suitable?
Frequency sampling method is attractive for narrow band frequency selective
filters where only a few of the samples of the frequency response are non-zero.
77.What is meant by autocorrelation?
The autocorrelation of a sequence is the correlation of a sequence with its shifted
version, and this indicates how fast the signal changes.
78.Define white noise?
A stationary random process is said to be white noise if its power density
spectrum is constant. Hence the white noise has flat frequency response spectrum.
SX(w) = x
2, - w
79.what do you understand by a fixed-point number?
In fixed point arithmetic the position of the binary point is fixed. The bit to the right
represent the fractional part of the number & those to the left represent the integer part.
For example, the binary number 01.1100 has the value 1.75 in decimal.
80.What is the objective of spectrum estimation?
The main objective of spectrum estimation is the determination of the power
spectral density of a random process. The estimated PSD provides information about the
structure of the random process which can be used for modeling, prediction or filtering of
the deserved process.
81.List out the addressing modes supported by C5X processors?
1. Direct addressing
2. Indirect addressing
3. Immediate addressing
4. Dedicated-register addressing
5. Memory-mapped register addressing
6. Circular addressing
82.what is meant by block floating point representation? What are its advantages?
In block point arithmetic the set of signals to be handled is divided into blocks. Each
block have the same value for the exponent. The arithmetic operations with in the block
uses fixed point arithmetic & only one exponent per block is stored thus saving memory.
This representation of numbers is more suitable in certain FFT flow graph & in digital
audio applications.
83.what are the advantages of floating point arithmetic?
1. Large dynamic range
2. Over flow in floating point representation is unlike.
84.what are the three-quantization errors to finite word length registers in digital filters?
1. Input quantization error 2. Coefficient quantization error 3. Product quantization
error
85.How the multiplication & addition are carried out in floating point arithmetic?
In floating point arithmetic, multiplication are carried out as follows,
Let f1 = M1*2c1 and f2 = M2*2c2. Then f3 = f1*f2 = (M1*M2) 2(c1+c2)
That is, mantissa is multiplied using fixed-point arithmetic and the exponents are
added.
The sum of two floating-point number is carried out by shifting the bits of the mantissa
of the smaller number to the right until the exponents of the two numbers are equal and
then adding the mantissas.
86.What do you understand by input quantization error?
In digital signal processing, the continuous time input signals are converted into digital
using a b-bit ACD. The representation of continuous signal amplitude by a fixed digit
produce an error, which is known as input quantization error.
87.List the on-chip peripherals in 5X.
The C5X DSP on-chip peripherals available are as follows:
1. Clock Generator
2. Hardware Timer
3. Software-Programmable Wait-State Generators
4. Parallel I/O Ports
5. Host Port Interface (HPI)
6. Serial Port
7. Buffered Serial Port (BSP)
8. Time-Division Multiplexed (TDM) Serial Port
9. User-Maskable Interrupts
88.what is the relationship between truncation error e and the bits b for representing a
decimal into binary?
For a 2's complement representation, the error due to truncation for both positive and
negative values of x is 0>=xt-x>-2-b
Where b is the number of bits and xt is the truncated value of x.
The equation holds good for both sign magnitude, 1's complement if x>0
If x<0, then for sign magnitude and for 1's complement the truncation error satisfies.
89.what is meant rounding? Discuss its effect on all types of number representation?
Rounding a number to b bits is accomplished by choosing the rounded result as the b
bit number closest to the original number unrounded.
For fixed point arithmetic, the error made by rounding a number to b bits satisfy the
inequality
-2-b 2-b
-----<=xt-x<= --------
2 2
for all three types of number systems, i.e., 2's complement, 1's complement & sign
magnitude.
For floating point number the error made by rounding a number to b bits satisfy the
inequality
-2-b<=E<=2-b where E=xt-x
--------
x
90.what is meant by A/D conversion noise?
A DSP contains a device, A/D converter that operates on the analog input x(t) to
produce xq(t) which is binary sequence of 0s and 1s.
At first the signal x(t) is sampled at regular intervals to produce a sequence x(n) is of
infinite precision. Each sample x(n) is expressed in terms of a finite number of bits given
the sequence xq(n). The difference signal e(n)=xq(n)-x(n) is called A/D conversion noise.
91.what is the effect of quantization on pole location?
Quantization of coefficients in digital filters lead to slight changes in their value. This
change in value of filter coefficients modify the pole-zero locations. Some times the pole
locations will be changed in such a way that the system may drive into instability.
92.which realization is less sensitive to the process of quantization?
Cascade form.
93.what is meant by quantization step size?
Let us assume a sinusoidal signal varying between +1 and -1 having a dynamic range
2. If the ADC used to convert the sinusoidal signal employs b+1 bits including sign bit,
the number of levels available for quantizing x(n) is 2b+1. Thus the interval between
successive levels
q= 2 =2-b
--------
2b+1
Where q is known as quantization step size.
94.How would you relate the steady-state noise power due to quantization and the b bits
representing the binary sequence?
Steady state noise power
Where b is the number of bits excluding sign bit.
95.what is overflow oscillation?
The addition of two fixed-point arithmetic numbers cause over flow the sum exceeds
the word size available to store the sum. This overflow caused by adder make the filter
output to oscillate between maximum amplitude limits. Such limit cycles have been
referred to as over flow oscillations.
96.what are the methods used to prevent overflow?
There are two methods used to prevent overflow
1. Saturation arithmetic 2. Scaling
97.what are the two kinds of limit cycle behavior in DSP?
1.zero input limit cycle oscillations
2.Overflow limit cycle oscillations
98.Determine "dead band" of the filter
The limit cycle occur as a result of quantization effect in multiplication. The
amplitudes of the output during a limit cycle are confined to a range of values called the
dead band of the filter.
99.Explain briefly the need for scaling in the digital filter implementation.
To prevent overflow, the signal level at certain points in the digital filter must be
scaled so that no overflow occurs in the adder.
100.What are the different buses of TMS320C5X and their functions?
The C5X architecture has four buses and their functions are as follows:
Program bus (PB):
It carries the instruction code and immediate operands from program memory
space to the CPU.
Program address bus (PAB):
It provides addresses to program memory space for both reads and writes.
Data read bus (DB):
It interconnects various elements of the CPU to data memory space.
Data read address bus (DAB):
It provides the address to access the data memory space.
Part B
1. Determine the DFT of the sequence
x(n) =1/4, for 0<=n <=2
0, otherwise
Ans: The N point DFT of the sequence x(n) is defined as
N-1
x(k)= x(n)e-j2 nk/N K=0,1,2,3,…N-1
n=0
x(n) = (1/4,1/4,1/4)
X(k) = ¼ e-j2 k/3[1+2cos(2 k/3)] where k= 0,1,……….,N-1
2. Derive the DFT of the sample data sequence x(n) = {1,1,2,2,3,3}and compute the
corresponding amplitude and phase spectrum.
Ans: The N point DFT of the sequence x(n) is defined as
N-1
X(k)= x(n)e-j2 nk/N K=0,1,2,3,…N-1
n=0
X(0) = 12
X(1) = -1.5 + j2.598
X(2) = -1.5 + j0.866
X(3) = 0
X(4) = -1.5 – j0.86{5/2, -1/2-j1/2, -1/2, -1/2+j1/2}
6. Design an ideal low pass filter with a frequency response Hd(e jw) =1 for –
/2<=w<=
/2
0 otherwise
find the value of h(n) for N=11 find H(Z) plot magnitude response
a. Find h(n) by IDTFT
b. Convert h(n) in to a fine length by truncation
c. H(0)=1/2,
h(1)=h(-1)=0.3183
h(2)=h(-2)=0
h(3)=h(-3)= -0.106
h(4)=h(-4)=0
h(5)=h(-5)=0.06366
d. Find the transfer function H(Z) which is not realizable conver in to realizable by
multiplying by z-(N-1/2)
e. H’(Z) obtained is 0.06366-0.106z-2+.3183Z-4+.5Z-5+.3183Z-6-.106Z-8+0.06366Z-
10
f. Find H (e jw) and plot amplitude response curve.
7. Design an ideal low pass filter with a frequency response Hd(e jw) =1 for –
/4<=|w|<=
0 otherwise
find the value of h(n) for N=11 find H(Z) plot magnitude response
g. Find h(n) by IDTFT
h. Convert h(n) in to a fine length by truncation
i. H(0)=0.75
h(1)=h(-1)=-.22
h(2)=h(-2)=-.159
h(3)=h(-3)= -0.075
h(4)=h(-4)=0
h(5)=h(-5)=0.045
j. Find the transfer function H(Z) which is not realizable conver in to realizable by
multiplying by z-(N-1/2)
k. H’(Z) obtained is 0.045-0.075z-2 -.159 Z-3-0.22Z-4+0.75Z-5-.22Z-6 -0.159Z-7 -.
075Z-8+0.045Z-10
l. Find H (e jw) and plot amplitude response curve.
8. Design band pass filter with a frequency response Hd(e jw) =1 for –
/3<=|w|<=2
/3
0 otherwise
find the value of h(n) for N=11 find H(Z) plot magnitude response
m. Find h(n) by IDTFT
n. Convert h(n) in to a fine length by truncation
o. Find the transfer function H(Z) which is not realizable conver in to realizable by
multiplying by z-(N-1/2)
p. H’(Z) obtained Find H (e jw) and plot amplitude response curve.
9. Design band reject filter with a frequency response Hd(e jw) =1 for
/4<=|w|<=3
/4
0 otherwise
find the value of h(n) for N=11 find H(Z) plot magnitude response
q. Find h(n) by IDTFT
r. Convert h(n) in to a fine length by truncation
s. Find the transfer function H(Z) which is not realizable conver in to realizable by
multiplying by z-(N-1/2)
t. H’(Z) obtained Find H (e jw) and plot amplitude response curve.
10. Derive the condition of FIR filter to be linear in phase.
Conditions are
Group delay and Phase delay should be constant
And
And show the condition is satisfied
11Derive the expression for steady state I/P Noise Power and Steady state O/P Noise
Power.
Write the derivation.
12 Draw the product quantatization model for first order and second order filter
Write the difference equation and draw the noise model.
13 For the second order filter Draw the direct form II realization and find the scaling
factor S0 to avoid over flow
Find the scaling factor from the formula
1+r2
I= ---------------------------------------
(1-r2)(1-2r2cos2ø =r4)
14 Explain Briefly about various number representation in digital computer.
1 Fixed point
2 Floating point
3 Block floating point
Signed magnitude represenation
1’s Complement
2’s Complement
etc
15 Consider the transfer function H(Z)=H1(Z)H2(Z) where H1(Z) =1/1-a1Z-1
H2(z) =1/ 1-a2Z-1
Find the o/p Round of noise power Assume a1=0.5 and a2= 0.6 and find o.p
round off noise power.
Draw the round of Noise Model.
By using residue method find 01
By using residue method find 02
= 01 2+ 02 2
2 –2b (5.43)
Ans:__________________
12
16.Explain the architecture of DSP processor .
Diagram. & explanation.
17.Describe briefly the different methods of power spectral estimation?
1. Bartlett method
2. Welch method
3. Blackman-Tukey method
and its derivation.
18.what is meant by A/D conversion noise. Explain in detail?
A DSP contains a device, A/D converter that operates on the analog input x(t) to
produce xq(t) which is binary sequence of 0s and 1s.
At first the signal x(t) is sampled at regular intervals to produce a sequence x(n) is of
infinite precision. Each sample x(n) is expressed in terms of a finite number of bits given
the sequence xq(n). The difference signal e(n)=xq(n)-x(n) is called A/D conversion noise.
+ derivation.
19 onsider the transfer function H(Z)=H1(Z)H2(Z) where H1(Z) =1/1-a1Z-1
H2(z) =1/ 1-a2Z-1
Find the o/p Round of noise power Assume a1=0.7 and a2= 0.8and find o.p round
off noise power.
Draw the round of Noise Model.
By using residue method find 01
By using residue method find 02
= 01 2+ 02 2
20.Given X(k) = {1,1,1,1,1,1,1,1,} ,find x(n) using inverse DIT FFT algorithm.
WN
k = ej(2 /N)k
Find x(n)
21.Find the inverse DFT of X(k) = {3,4,5,6}
Ans: The inverse DFT is defined as
N-1
x(n)=(1/N ) x(k)ej2 nk/N n=0,1,2,3,…N-1
k=0
22. Explain various addressing modes of TMS processor.
Immediate.
Register
Register indirect
Indexed
& its detail explanation.
23 Derive the expression for steady state I/P Noise Variance and Steady state O/P
Noise Variance
Write the derivation.
24. Explain briefly the periodogram method of power spectral estimation?
Write the derivation with explanation.
25. Explain various arithmetic instruction of TMS processor.
All arithmetic instruction with explanation.
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