Anna University, Chennai
SRINIVASAN ENGINEERING COLLEGE DEPARTMENT OF ECE
QUESTION BANK DIGITAL SIGNAL PROCESSING
BRANCH/SEM/SEC:CSE/IV/A& B UNIT I
SIGNALS AND SYSTEMS Part – A
1. What do you understand by the terms : signal and signal processing
2. Determine which of the following signals are periodic and compute their fundamental period (AU DEC 07)
a) sin√2 Лt b)sin20 Лt+sin5Лt
3. What are energy and power signals? (MU Oct. 96)
4. State the convolution property of Z transform (AU DEC 06)
5. Test the following systems for time invariance: (DEC 03)
a) y(n)=n x2 (n) b)a x(n)
6. Define symmetric and antisymmetric signals. How do you prevent alaising while
sampling a CT signal? (AU MAY 07)(EC 333, May „07)
7. What are the properties of region of convergence(ROC) ?(AU MAY 07)
8. Differentiate between recursive and non recursive difference equations
(AU APR 05)
9. What are the different types of signal representation?
10. Define correlation (AU DEC 04)
11. what is the causality condition for LTI systems? (AU DEC 04)
12. define linear convolution of two DT signals (AU APR 04)
13. Define system function and stability of DT system (AU APR 04)
14. Define the following (a) System (b) Discrete-time system
15. What are the classifications of discrete-time system?
16. What is the property of shift-invariant system?
17. Define (a) Static system (b) Dynamic system? (AU DEC 03)
18. define cumulative and associative law of convolution (AU DEC 03)
19. Define a stable and causal system
20. What is the necessary and sufficient condition on the impulse response for stability? (MU APR.96)
21. What do you understand by linear convolution? (MU APR. 2000)
22. What are the properties of convolution? (AU IT Dec. 03) State Parseval‟s energy theorem for discrete-time aperiodic signals(AU DEC
23. 04)
24. Define DTFT pair (MU Apr. 99)
25. What is aliasing effect? (AU MAY 07) (EC 333 DEC 03)
26. State sampling theorem
27. What is an anti-aliasing filter?
28. What is the necessary and sufficient condition on the impulse response for stability? (EC 333, May „07)
22. State the condition for a digital filter to be causal and stable
Part-B
1. a) Compute the convolution y(n) of the signals (AU DEC 07)
n
x(n)= a
-3≤n≤5
0 elsewhere and h(n)= 1 0≤n≤4
0 elsewhere
b) A discrete time system can be static or dynamic, linear or non-linear, Time variant or time invariant, causal or non causal, stable or unstable. Examine the following system with respect to the properties also (AU DEC 07)
1) y(n)=cos(x(n))
2) y(n)=x(-n+2)
3) y(n)=x(2n)
4)y(n)=x(n) cos ωn
2. a) Determine the response of the causal system
y(n)-y(n-1)=x(n)+x(n-1) to inputs x(n)=u(n) and x(n)=2 –n u(n).Test its stability
2
b) Determine the IZT of X(Z)=1/(1-Z-1)(1-Z-1)
(AU DEC 07)
Determine whether each of the following systems defined below is (i) casual (ii)
linear (iii) dynamic (iv) time invariant (v) stable
(a) y(n) = log10[{x(n)}] (b) y(n) = x(-n-2)
(c) y(n) = cosh[nx(n) + x(n-1)]
3. Compute the convolution of the following signals x(n) = {1,0,2,5,4} h(n) = {1,-1,1,-1}
↑ ↑
h(n) = {1,0,1} x(n) = {1,-2,-2,3,4}
↑ ↑
4. Find the convolution of the two signals x(n) = 3nu(-n); h(n) = (1/3)n u(n-2) x(n) = (1/3) –n u(-n-1); h(n) = u(n-1)
x(n) = u(n) –u(n-5); h(n) = 2[u(n) – u(n-3)]
5. Find the discrete-time Fourier transform of the following x(n) = 2-2n for all n
|
x(n) = n [1/2] (n)
6. Determine and sketch the magnitude and phase response of the following systems
(a) y(n) = 1/3 [x(n) + x(n-1) + x(n-2)] (b) y(n) = ½[x(n) – x(n-1)]
(c) y(n) - 1/2y(n-1)=x(n)
7. a) Determine the impulse response of the filter defined by y(n)=x(n)+by(n-1)
b) A system has unit sample response h(n) given by h(n)=-1/δ(n+1)+1/2δ(n)-1-
1/4 δ(n-1). Is the system BIBO stable? Is the filter
causal? Justify your answer (DEC 2003)
8. Determine the Fourier transform of the following two signals(CS 331 DEC 2003)
a) a n u(n) for a<1
b) cos ωn u(n)
9. Check whether the following systems are linear or not (AU APR 05)
a) y(n)=x 2 (n) b) y(n)=n x(n)
10. For each impulse response listed below, dtermine if the corresponding system is i) causal ii) stable (AU MAY 07)
1) 2 n u(-n)
2) sin nЛ/2 (AU DEC 04)
3) δ(n)+sin nЛ
4) e 2n u(n-1)
11. Explain with suitable block diagram in detail about the analog to digital
conversion and to reconstruct the analog signal (AU DEC 07)
12. Find the cross correlation of two sequences
x(n)={1,2,1,1} y(n)={1,1,2,1} (AU DEC 04)
13. Determine whether the following systems are linear , time invariant
1) y(n)=A x(n)+B
2) y(n)=x(2n)
Find the convolution of the following sequences: (AU DEC 04)
1) x(n)=u(n) h(n)=u(n-3)
2) x(n)={1,2,-1,1} h(n)={1,0,1,1}
UNIT II
FAST FOURIER TRANSFORMS
1) THE DISCRETE FOURIER TRANSFORM
PART A
1. Find the N-point DFT of a sequence x(n) ={1 ,1, 2, 2}
2. Determine the circular convolution of the sequence x1(n)={1,2,3,1} and x2(n)={4,3,2,1} (AU DEC 07)
3. Draw the basic butterfly diagram for radix 2 DIT-FFT and DIF-FFT(AU DEC 07)
4. Determine the DTFT of the sequence x(n)=a n u(n) for a<1 (AU DEC 06)
5. Is the DFT of the finite length sequence periodic? If so state the reason
(AU DEC 05)
6. Find the N-point IDFT of a sequence X(k) ={1 ,0 ,0 ,0} (Oct 98)
7. what do you mean by „in place‟ computation of FFT? (AU DEC 05)
8. What is zero padding? What are its uses? (AU DEC 04)
9. List out the properties of DFT (MU Oct 95,98,Apr 2000)
10. Compute the DFT of x(n)=∂(n-n0)
11. Find the DFT of the sequence of x(n)= cos (n∏/4) for 0≤n≥ 3 (MU Oct 98)
12. Compute the DFT of the sequence whose values for one period is given by
x(n)={1,1,-2,-2}. (AU Nov 06,MU Apr 99)
13. Find the IDFT of Y(k)={1,0,1,0} (MU Oct 98)
14. What is zero padding? What are its uses?
15. Define discrete Fourier series.
16. Define circular convolution
17. Distinguish between linear convolution and Circular Convolution. (MU Oct 96,Oct 97,Oct 98)
18. Obtain the circular convolution of the following sequences x(n)={1, 2, 1} and h(n)={1, -2, 2}
19. Distinguish between DFT and DTFT (AU APR 04)
20. Write the analysis and synthesis equation of DFT (AU DEC 03)
21. Assume two finite duration sequences x1(n) and x2(n) are linearly combined.
What is the DFT of x3(n)?(x3(n)=Ax1(n)+Bx2(n)) (MU Oct 95)
22. If X(k) is a DFT of a sequence x(n) then what is the DFT of real part of x(n)?
23. Calculate the DFT of a sequence x(n)=(1/4)^n for N=16 (MU Oct 97)
24. State and prove time shifting property of DFT (MU Oct 98)
25. Establish the relation between DFT and Z transform (MU Oct 98,Apr 99,Oct 00)
26. What do you understand by Periodic convolution? (MU Oct 00)
27. How the circular convolution is obtained using concentric circle method?
(MU Apr 98)
28. State the circular time shifting and circular frequency shifting properties of DFT
29. State and prove Parseval‟s theorem
30. Find the circular convolution of the two sequences using matrix method X1(n)={1, 2, 3, 4} and x2(n)={1, 1, 1, 1}
31. State the time reversal property of DFT
32. If the DFT of x(n) is X(k) then what is the DFT of x*(n)?
33. State circular convolution and circular correlation properties of DFT
34. Find the circular convolution of the following two sequences using concentric circle method
x1(n)={1, 2, 3, 4} and x2(n)={1, 1, 1, 1}
35. The first five coefficients of X(K)={1, 0.2+5j, 2+3j, 2 ,5 }Find the remaining coefficients
PART B
1. Find 4-point DFT of the following sequences
(a) x(n)={1,-1,0,0}
(b) x(n)={1,1,-2,-2} (AU DEC 06)
(c) x(n)=2n
(d) x(n)=sin(n∏/2)
2. Find 8-point DFT of the following sequences
(a) x(n)={1,1,1,1,0,0,0,0} (b) x(n)={1,2,1,2}
3. Determine IDFT of the following (a)X(k)={1,1-j2,-1,1+j2} (b)X(k)={1,0,1,0} (c)X(k)={1,-2-j,0,-
2+j}
4. Find the circular convolution of the following using matrix method and concentric circle method
(a) x1(n)={1,-1,2,3}; x2(n)={1,1,1};
(b) x1(n)={2,3,-1,2}; x2(n)={-1,2,-1,2}; (c) x1(n)=sin n∏/2; x2(n)=3n 0≤n≥7
5.Calculate the DFT of the sequence x(n)={1,1,-2,-2}
Determine the response of the LTI system by radix2 DIT-FFT? (AU Nov 06). If the impulse response of a LTI system is h(n)=(1,2,3,-1)
6. Determine the impulse response for the cascade of two LTI systems having impulse responses h1(n)=(1/2)^n* u(n),h2(n)=(1/4)^n*u(n) (AU May 07)
7. Determine the circular convolution of the two sequences x1(n)={1, 2, 3, 4}
x2(n)={1, 1, 1, 1} and prove that it is equal to the linear convolution of the same.
8. Find the output sequence y(n)if h(n)={1,1,1,1} and x(n)={1,2,3,1} using circular convolution (AU APR 04)
9. State and prove the following properties of DFT (AU DEC 03)
1) Cirular convolution 2) Parseval‟s relation
2) Find the circular convolution of x1(n)={1,2,3,4} x2(n)={4,3,2,1}
2) FAST FOURIER TRANSFORM
PART A
1. Why FFT is needed? (AU DEC 03) (MU Oct 95,Apr 98)
2. What is FFT? (AU DEC 06)
3. Obtain the block diagram representation of the FIR filter (AU DEC 06)
4. Calculate the number of multiplications needed in the calculation of DFT and FFT
with 64 point sequence. (MU Oct 97, 98).
5. What is the main advantage of FFT?
6. What is FFT? (AU Nov 06)
7. How many multiplications and additions are required to compute N-point DFT
using radix 2 FFT? (AU DEC 04)
8. Draw the direct form realization of FIR system (AU DEC 04)
9. What is decimation-in-time algorithm? (MU Oct 95).
10. What do you mean by „in place‟ computation in DIT-FFT algorithm? (AU APR 04)
11. What is decimation-in-frequency algorithm? (MU Oct 95,Apr 98).
12. Mention the advantage of direct and cascade structures (AU APR 04)
13. Draw the direct form realization of the system y(n)=0.5x(n)+0.9y(n-1)
(AU APR 05)
14. Draw the flow graph of a two point DFT for a DIT decomposition.
15. Draw the basic butterfly diagram for DIT and DIF algorithm. (AU 07).
16. How do we can calculate IDFT using FFT algorithm?
17. What are the applications of FFT algorithms?
18. Find the DFT of sequence x(n)={1,2,3,0} using DIT-FFT algorithms
19. Find the DFT of sequence x(n)={1,1, 1, 1} using DIF-FFT algorithms
(AU DEC 04)
PART B
1. Compute an 8-point DFT of the following sequences using DIT and DIF
algorithms
(a)x(n)={1,-1,1,-1,0,0,0,0}
(b)x(n)={1,1,1,1,1,1,1,1} (AU APR 05) (c)x(n)={0.5,0,0.5,0,0.5,0,0.5,0}
(d)x(n)={1,2,3,2,1,2,3,2}
(e)x(n)={0,0,1,1,1,1,0,0} (AU APR 04)
2. Compute the 8 point DFT of the sequence x(n)={0.5, 0.5 ,0.5,0.5,0,0,0,0} using radix 2 DIF and DIT algorithm (AU DEC 07)
3. a) Discuss the properties of DFT
b) Discuss the use of FFT algorithm in linear filtering (AU DEC 07)
4. How do you linear filtering by FFT using save-add method (AU DEC 06)
5. Compute the IDFT of the following sequences using (a)DIT algorithm (b)DIF
algorithms
(a)X(k)={1,1+j,1-j2,1,0,1+j2,1+j}
(b)X(k)={12,0,0,0,4,0,0,0} (c)X(k)={5,0,1-j,0,1,0,1+j,0} (d)X(k)={8,1+j2,1-j,0,1,0,1+j,1-j2}
(e)X(k)={16,1-j4.4142,0,1+j0.4142,0,1-j0.4142,0,1+j4.4142}
6. Derive the equation for DIT algorithm of FFT.
How do you do linear filtering by FFT using Save Add method? (AU Nov 06)
7. a) From first principles obtain the signal flow graph for computing 8 point
DFT using radix 2 DIT-FFT algorithm.
b) Using the above signal flow graph compute DFT of x(n)=cos(n*Л)/4 ,0<=n<=7 (AU May 07).
8. Draw the butterfly diagram using 8 pt DIT-FFT for the following sequences x(n)={1,0,0,0,0,0,0,0} (AU May 07).
9. a) From first principles obtain the signal flow graph for computing 8 point
DFT using radix 2 DIF-FFT algorithm.
b) Using the above signal flow graph compute DFT of x(n)=cos(n*Л)/4 ,0<=n<=7
10. State and prove circular time shift and circular frequency shift properties of DFT
11. State and prove circular convolution and circular conjugate properties of DFT
12. Explain the use of FFT algorithms in linear filtering and correlation
13. Determine the direct form realization of the following system
y(n)=-0.1y(n-1)+0.72y(n-2)+0.7x(n)-0.252x(n-2) (AU APR 05)
14. Determine the cascade and parallel form realization of the following system y(n)=-0.1y(n-1)+0.2y(n-2)+3x(n)+3.6x(n-1)+0.6x(n-2)
Expalin in detail about the round off errors in digital filters (AU DEC 04)
UNIT-III
IIR FILTER DESIGN
PART-A
1. Distinguish between Butterworth and Chebyshev filter
2. What is prewarping? (AU DEC 03)
3. Distinguish between FIR and IIR filters (AU DEC 07)
4. Give any two properties of Butterworth and chebyshev filters (AU DEC 06)
5. Give the bilinear transformation (AU DEC 03)
6. Determine the order of the analog butterworth filter that has a -2 dB pass band attenuation at a frequency of 20 rad/sec and atleast -10 dB stop band attenuation at 30 rad/sec (AU DEC 07)
7. By impulse invariant method obtain the digital filter transfer function and differential equation of the analog filter H(S)=1/S+1 (AU DEC 07)
8. Give the expression for location of poles of normalized butterworth filter
(EC 333, May „07)
9. What are the parameters(specifications) of a chebyshev filter (EC 333, May „07)
10. Why impulse invariance method is not preferred in the design of IIR filter other than low pass filter?
11. What are the advantages and disadvantages of bilinear transformation?(AU DEC 04)
12. Write down the transfer function of the first order butterworth filter having low pass behavior (AU APR 05)
13. What is warping effect? What is its effect on magnitude and phase response?
14. Find the digital filter transfer function H(Z) by using impulse invariance method for the analog transfer function H(S)= 1/S+2 (MAY AU ‟07)
15. Find the digital filter transfer function H(Z) by using bilinear transformation method for the analog transfer function H(S)= 1/S+3
16. Give the equation for converting a normalized LPF into a BPF with cutoff frequencies l
and u
17. Give the magnitude function of Butterworth filter. What is the effect of varying order of
N on magnitude and phase response?
18. Give any two properties of Butterworth low pass filters. (MU NOV 06).
19. What are the properties of Chebyshev filter? (AU NOV 06).
20. Give the equation for the order of N and cut off frequency c of Butterworth filter.
21. Give the Chebyshev filter transfer function and its magnitude response.
22. Distinguish between the frequency response of Chebyshev Type I filter for N odd and N
even.
23. Distinguish between the frequency response of Chebyshev Type I & Type II filter.
24. Give the Butterworth filter transfer function and its magnitude characteristics for different order of filters.
25. Give the equations for the order N, major, minor and axis of an ellipse in case of
Chebyshev filter.
26. What are the parameters that can be obtained from the Chebyshev filter specification?
(AU MAY 07).
27. Give the expression for the location of poles and zeros of a Chebyshev Type II filter.
28. Give the expression for location of poles for a Chebyshev Type I filter. (AU MAY 07)
29. Distinguish between Butterworth and Chebyshev Type I filter.
30. How one can design Digital filters from Analog filters.
31. Mention any two procedures for digitizing the transfer function of an analog filter. (AU APR 04)
32. What are properties that are maintained same in the transfer of analog filter into a digital filter.
33. What is the mapping procedure between s-plane and z-plane in the method of mapping of differentials? What is its characteristics?
34. What is mean by Impulse invariant method of designing IIR filter?
35. What are the different types of structures for the realization of IIR systems?
36. Write short notes on prewarping.
37. What are the advantages and disadvantages of Bilinear transformation?
38. What is warping effect? What is its effect on magnitude and phase response?
39. What is Bilinear Transformation?
40. How many numbers of additions, multiplications and memory locations are required to realize a system H(z) having M zeros and N poles in direct form-I and direct form –II realization?
41. Define signal flow graph.
42. What is the transposition theorem and transposed structure?
43. Draw the parallel form structure of IIR filter.
44. Give the transposed direct form –II structure of IIR second order system.
45. What are the different types of filters based on impulse response? (AU 07)
46. What is the most general form of IIR filter?
PART B
1. a) Derive bilinear transformation for an analog filter with system function H(S)=b/S+a (AU DEC 07) b) Design a single pole low pass digital IIR filter with-3 Db bandwidth of 0.2Л by using
bilinear transformation
2. a) Obtain the direct form I, Direct form II, cascade and parallel realization for the following
Systems y(n)=-0.1x(n-1)+0.2y(n-2)+3x(n)+3.6x(n-
1)+0.6x(n-2)
b) Discuss the limitation of designing an IIR filetr using impulse invariant method
(AU DEC 07)
3. Determine H(Z) for a Butterworth filter satisfying the following specifications:
0.8 ÷H(e j ô 1, for 0 /4
÷H(e j ô 0.2, for /2
Assume T= 0.1 sec. Apply bilinear transformation method (AU MAY 07)
4.Determine digital Butterworth filter satisfying the following specifications:
0.707 ÷H(e j ô 1, for 0 /2
÷ H(e j ô 0.2, for3 /4
Assume T= 1 sec. Apply bilinear transformation method. Realize the filter in mose
convenient form (AU DEC 06)
5. Design a Chebyshev lowpass filter with the specifications p=1 dB ripple in the pass band 0 0.2 , s=15 dB ripple in the stop band 0.3 using impulse invariance method(AU DEC 06)
6. Design a Butterworth high pass filter satisfying the following specifications. p =1 dB; s=15 dB
p =0.4 ; s =0.2
7. Design a Butterworth low pass filter satisfying the following specifications. (AU DEC 04)
p=0.10 Hz; p=0.5 dB
s=0.15 HZ; s=15 dB:F=1Hz.
8. Design (a) a Butterworth and (b) a Chebyshev analog high pass filter that will pass all radian frequencies greater than 200 rad/sec with no more that 2 dB attuenuation and have a stopband attenuation of greater than 20 dB for all less than 100 rad/sec.
9. Design a digital filter equivalent to this using impulse invariant metho
H(S)=10/ 2+7S+10 (AU DEC 03)(AU DEC 04)
10. Use impulse invariance to obtain H(Z) if T= 1 sec and H(s)
2
is 1/(s3 +3s
+4s+1)
1/(s2+ 2 s +1)
11. Use bilinear transformation method to obtain H(Z) if T= 1 sec and H(s) is
1/(s+1)(S+2) (AU DEC 03)
1/(s2+ 2 s +1)
12. Briefly explain about bilinear transformation of digital filter design(AU APR 05)
13. Use bilinear transform to design a butterworth LPF with 3 dB cutoff frequeny of
0.2 (AU APR 04)
14. Compare bilinear transformation and impulse invariant mapping
15. a) Design a chebyshev filter with a maxmimum pass band attenuation of 2.5 Db; at Ωp=20 rad/sec and the stop band attenuation of 30 Db at Ωs=50 rad/sec. b)Realize the system given by difference equation
y(n)=-0.1 y(n-1)+0.72y(n-2)+0.7x(n)-0.25x(n-2) in parallel form
(EC 333 DEC „07 )
UNIT IV
FIR FILTER DESIGN
PART A
1. What are the desirable and undesirable features of FIR filter?
2. Discuss the stability of the FIR filters (AU APR 04) (AU DEC 03)
3. What are the main advantages of FIR over IIR (AU APR 04)
4. What is the condition satisfied by Linear phase FIR filter? (DEC 04) (EC 333
MAY 07)
5. What are the design techniques of designing FIR filters?
6. What condition on the FIR sequence h(n) are to be imposed in order that this filter can be called a Linear phase filter? (AU 07)
7. State the condition for a digital filter to be a causal and stable. (AU 06)
8. What is Gibbs phenomenon? (AU DEC 04) (AU DEC 07)
9. Show that the filter with h(n)={-1, 0, 1} is a linear phase filter
10. Explain the procedure for designing FIR filters using windows. (MU 02)
11. What are desirable characteristics of windows?
12. What is the principle of designing FIR filters using windows?
13. What is a window and why it is necessary?
14. Draw the frequency response of N point rectangular window. (MU 03)
15. Give the equation specifying Hanning and Blackman windows.
16. Give the expression for the frequency response of
17. Draw the frequency response of N point Bartlett window
18. Draw the frequency response of N point Blackman window
19. Draw the frequency response of N point Hanning window. (AU DEC 03)
20. What is the necessary and sufficient condition for linear phase characteristics in FIR
filter. (MU Nov 03)
21. Give the equation specifying Kaiser window.
22. Compare rectangular and hanning window functions
23. Briefly explain the frequency sampling method of filter design
24. Compare frequency sampling and windowing method of filter design
PART-B
1. Use window method with a Hamming window to design a 13-tap differentiator
(N=13). (AU „07)
2. i) Prove that FIR filter has linear phase if the unit impulse responsesatisfies the condition h(n)=h(N-1-n), n=0,1,……M-1. Also discuss symmetric and antisymmetric cases of FIR filter (AU DEC 07)
3. What are the issues in designing FIR filter using window method?(AU APR 04, DEC 03)
4. ii) Explain the need for the use of window sequences in the design of FIR filter.
Describe the window sequences generally used and compare their properties
5. Derive the frequency response of a linear phase FIR filter when impulse responses symmetric & order N is EVEN and mention its applications
6. i) Explain the type I design of FIR filter using frequency sampling method ii) A low pass filter has the desired response as given below
j
Hd(e
)= e –j3 , 0≤ ≤Л/2
0 Л/2≤ ≤Л
Determine the filter coefficients h(n) for M=7 using frequency sampling technique (AU DEC 07)
7. i) Derive the frequency response of a linear phase FIR filter when impulse responses antisymmetric & order N is odd
ii) Explain design of FIR filter by frequency sampling technique (AU MAY 07)
7. Design an approximation to an ideal bandpass filter with magnitude response
j
H(e
) = 1 ; 4 3 4
0 ; otherwise
Take N=11. (AU DEC 04)
8. Design a 15-tap linear phase filter to the following discrete frequency response
(N=15) using frequency sampling method (MU 03) H(k) = 1 0 k 4
= 0.5 k=5
= 0.25 k=6
= 0.1 k=7
= 0 elsewhere
9. Design an ideal band pass digital FIR filter with desired frequency response
H(e j )= 1 for 0.25 ÷ ô 0.75
0 forô ô 0.25 and 0.75 ÷ ô
by using rectangular window function of length N=11. (AU DEC 07)
10. Design an Ideal Hilbert transformer using hanning window and Blackman window for N=11. Plot the frequency response in both Cases
11. a) How is the design of linear phase FIR filter done by frequency sampling method?
Explain.
b) Determine the coefficients of a linear phase FIR filter of length N=15 which has Symmetric unit sample response and a frequency response that satisfies the following conditions
H r (2 k/15) = 1 for k=0,1,2,3
0 for k=4
0 for k=5,6,7
12. An FIR filter is given by the difference equation
y(n)=2x(n)+4/5 x(n-1)+3/2 x(n-2)+2/3 x(n-3) Determine its lattice form(EC 333 DEC 07)
13. Using a rectangular window technique design a low pass filter with pass band gain of unity cut off frequency of 1000 Hz and working at a sampling frequency of 5 KHz. The length of the impulse response should be 7.( EC 333 DEC 07)
16. Design an Ideal Hilbert transformer using rectangular window and Black man window for N=11. Plot the frequency response in both Cases (EC 333 DEC ‟07)
9. 17. Design an approximation to an ideal lowpass filter with magnitude response
j
H(e
) = 1 ; 0 4
0 ; otherwise
Take N=11.Use hanning and hamming window (AU DEC 04)
UNIT V
FINITE WORD LENGTH EFFECTS
PART –A
1. What do you understand by a fixed point number? (MU Oct‟95)
2. Express the fraction 7/8 and -7/8 in sign magnitude, 2‟s complement and 1‟s complement (AU DEC 06)
3. What are the quantization errors due to finite word length registers in digital filters?
(AU DEC 06)
4. What are the different quantization methods? (AU DEC 07)
5. What are the different types of fixed point number representation?
6. What do you understand by sign-magnitude representation?
7. What do you understand by 2‟s complement representation?
8. Write an account on floating point arithmetic? (MU Apr 2000)
9. What is meant by block floating point representation? What are its advantages?
10. what are advantages of floating point arithmetic?
11. Compare the fixed point and floating point arithmetic.
(MU Oct‟96)
12. What are the three quantization errors due to finite word length registers in
(MU
digital filters?
13. How the multiplication and addition are carried out in floating point arithmetic?
14. Brief on co-efficient inaccuracy.
15. What do you understand by input quantization error?
16. What is product quantization error?
Oct‟98)
17. What is meant by A/D conversion mode?
18. What is the effect of quantization on pole locations?
19. What are the assumptions made concerning the statistical independence of various noise sources that occur in realizing the filter? (M.U. Apr 96)
20. What is zero input limit cycle overflow oscillation (AU 07)
21. What is meant by limit cycle oscillations?(M.U Oct 97, 98, Apr 2000) (AU DEC 07)
29. Explain briefly the need for scaling digital filter implementation?
(M.U Oct 98)(AU-DEC 07)
30. Why rounding is preferred than truncation in realizing digital filter? (M.U. Apr 00)
31. Define the deadband of the filter? (AU 06)
25. Determine the dead band of the filter with pole at 0.5 and the number of bits used for quantization is 4(including sign bit)
26. Draw the quantization noise model for a first order IIR system
27. What is meant by rounding? Draw the pdf of round off error
28. What is meant by truncation? Draw the pdf of round off error
29. What do you mean by quantization step size?
30. Find the quantization step size of the quantizer with 3 bits
31. Give the expression for signal to quantization noise ratio and calculate the improvement with an increase of 2 bits to the existing bit.
32. Express the following binary numbers in decimal
A) (100111.1110)2 (B) (101110.1111)2 C (10011.011)2
33.Why rounding is preferred to truncation in realizing digital filter? (EC 333, May „07)
34. List the different types of frequency domain coding (EC 333 MAY 07)
35. What is subband coding? (EC 333 MAY 07)
PART-B
1. Draw the quantization noise model for a second order system and explain H(z)=1/(1-
2rcos z-1+r2z-2) and find its steady state output noise variance (ECE AU‟ 05)
2. Consider the transfer function H(z)=H1(z)H2(z) where
-1 -2
H1(z)=1/(1-a1z
) , H2(z)=1/(1-a2z
).Find the output round off noise power.
Assume a1=0.5 and a2=0.6 and find out the output round off noise power.
(ECE AU‟ 04)(EC 333 DEC 07)
3. Find the effect of coefficient quantiztion on pole locations of the given second order IIR system when it is realized in direct form –I and in cascade form. Assume a word length of 4-bits through truncation.
H(z)= 1/(1-0.9z-1+0.2z –2) (AU‟ Nov 05)
4. Explain the characteristics of Limit cycle oscillations with respect to the system described by the differential equations.
y(n)=0.95y(n-1)+x(n) and
determine the dead band of the filter (AU‟ Nov 04)
5. i) Describe the quantization errors that occur in rounding and truncation in two‟s complement
ii) Draw a sample/hold circuit and explain its operation
iii) What is a vocoder? Expalin with a block diagram (AU DEC 07)
6. Two first order low pass filter whose system functions are given below are connected in cascade. Determine the overall output noise power
H1(Z)=1/(1-0.9Z-1) H2(Z)=1/(1-0.8Z-1) (AU DEC 07)
7. Consider a Butterworth lowpass filter whose transfer function is
H(z)=0.05( 1+z-1)2 /(1-1.2z-1 +0.8 z-2 ).
Compute the pole positions in z-plane and calculate the scale factor So to prevent overflow in adder 1.
8. Express the following decimal numbers in binary form
A) 525 B) 152.1875 C) 225.3275
10. Express the decimal values 0.78125 and -0.1875 in
One‟s complement form sign magnitude form Two‟s complement form.
11. Express the decimal values -6/8 and 9/8 in (i) Sign magnitude form (ii) One‟s complement form (iii) Two‟s complement form
12. Study the limit cycle behavior of the following systems i. y(n) = 0.7y(n-1) + x (n)
ii. y(n) = 0.65y(n-2) + 0.52y (n-1) + x (n)
13. For the system with system function H (z) =1+0.75z-1 / 1-0.4z-1 draw the signal flow graph
14. and find scale factor s0 to prevent overflow limit cycle oscillations
15. Derive the quantization input nose power and determine the signal to noise ratio of the system
16. Derive the truncation error and round off error noise power and compare both errors
17. Explain product quantization error and coefficient quantization error with examples
18. Derive the scaling factor So that prevents the overflow limit cycle oscillations in a second order IIR system.
19. The input to the system y(n)=0.999y(n-1)+x(n) is applied to an ADC. What is the power produced by the quantization noise at the output of the filter if the input is quantized to
1) 8 bits 2) 16 bits (EC 333 DEC 07)
19. Convert the following decimal numbers into binary: (EC 333 DEC 07)
1) (20.675) 2) (120.75)
10 10
20. Find the steady state variance of the noise in the output due to quantization of input for the
(EC 333 DEC 07)
first order filter y(n)=ay(n-1)+x(n)
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