Code No: 16021/16021
NR
Set No. 2
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III B.Tech II Semester Supplimentary Examinations,February 2010 DIGITAL SIGNAL PROCESSING Common to Electronics And Telematics, Electronics And Control Engineering, Electronics And Instrumentation Engineering, Electronics And Communication Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????
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1. (a) Define DFT of a sequence x(n). Obtain the relationship between DFT and DTFS.
(b) Consider a sequence x(n) = {2, −1, 1, 1} and T = 0.5 compute its DFT and compare it with its DTDT. [8+8] 2. (a) What is the principle of designing FIR filters using windows.
or
(b) Using a rectangular window technique design a low pass filter with pass band gain of unity, cut-off frequency of 1kHz and working at a sampling frequency of 5 kHz. The length of the impulse response should be 7. [6+10]
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3. (a) Explain the factors that influence the choice of structure for realisation of a LTI system. (b) An LTI system is described by the difference equation y (n) = a1 y (n − 1) + x (n) + b1 x (n − 1) Realize it in direct form I structure and convert it to direct form II structure. [4+12] 4. (a) A discrete system is given by following difference equation y(n)-5y(n-1) = x(n) + 4x(n-1) where x(n) is the input and y(n) is the out put. Determine its magnitude and phase response as a function of frequency.
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(b) State and prove convolution theorem.
[8+8]
5. (a) Determine the frequency response , magnitude response and phase response for the system given by y(n) − 34 y(n − 1) + 81 y(n − 2) = x(n) − x(n − 1)
Aj
(b) A causal LTI system is described by the difference equation y(n)=y(n-1)+y(n2)+x(n-1), where x(n) is the input and y(n) is the output. Find i. The system function H(Z)=Y(Z)/X(Z) for the system, plot the poles and zeroes of H(Z) and indicate the region of convergence. ii. The unit sample response of the system. iii. Is this system stable or not? [6+10]
6. (a) Draw the flow graph of an 8-point DIF / FFT and explain briefly. (b) Find the DFT (8-Point) for a continuous time signal x(t) = Sin( 2Π f t) with f = 50Hz. Use DIF - FFT algorithm. [6+10] 1
Code No: 16021/16021
NR
Set No. 2
7. (a) Compare the Digital Butterworth and Chebyshev filters. (b) Explain method of constructing Butterworth circle in the Z-plane using Bilinear transformation method. [8+8] 8. (a) What is a causal system? Why are non-causal systems unrealizable?
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(b) Check whether the DSP systems described by the following equations are causal. i. y(n)=3x(n-2) +3x(n+2) ii. y(n) = x(n-1)+ax(n-2) iii. y(n) = x(-n)
Aj
nt
uW
or
?????
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(c) Define the terms ”impulse response” and ”unit step response” and give the relationship between them. [5+6+5]
2
Code No: 16021/16021
NR
Set No. 4
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III B.Tech II Semester Supplimentary Examinations,February 2010 DIGITAL SIGNAL PROCESSING Common to Electronics And Telematics, Electronics And Control Engineering, Electronics And Instrumentation Engineering, Electronics And Communication Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????
ld .
1. (a) Draw the flow graph of an 8-point DIF / FFT and explain briefly.
(b) Find the DFT (8-Point) for a continuous time signal x(t) = Sin( 2Π f t) with f = 50Hz. Use DIF - FFT algorithm. [6+10] 2. (a) Determine the frequency response , magnitude response and phase response for the system given by y(n) − 34 y(n − 1) + 81 y(n − 2) = x(n) − x(n − 1)
or
(b) A causal LTI system is described by the difference equation y(n)=y(n-1)+y(n2)+x(n-1), where x(n) is the input and y(n) is the output. Find
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i. The system function H(Z)=Y(Z)/X(Z) for the system, plot the poles and zeroes of H(Z) and indicate the region of convergence. ii. The unit sample response of the system. iii. Is this system stable or not? [6+10] 3. (a) A discrete system is given by following difference equation y(n)-5y(n-1) = x(n) + 4x(n-1) where x(n) is the input and y(n) is the out put. Determine its magnitude and phase response as a function of frequency. (b) State and prove convolution theorem.
[8+8]
nt
4. (a) Explain the factors that influence the choice of structure for realisation of a LTI system.
Aj
(b) An LTI system is described by the difference equation y (n) = a1 y (n − 1) + x (n) + b1 x (n − 1) Realize it in direct form I structure and convert it to direct form II structure. [4+12]
5. (a) What is the principle of designing FIR filters using windows. (b) Using a rectangular window technique design a low pass filter with pass band gain of unity, cut-off frequency of 1kHz and working at a sampling frequency of 5 kHz. The length of the impulse response should be 7. [6+10]
6. (a) Define DFT of a sequence x(n). Obtain the relationship between DFT and DTFS. (b) Consider a sequence x(n) = {2, −1, 1, 1} and T = 0.5 compute its DFT and compare it with its DTDT. [8+8] 3
Code No: 16021/16021
NR
Set No. 4
7. (a) Compare the Digital Butterworth and Chebyshev filters. (b) Explain method of constructing Butterworth circle in the Z-plane using Bilinear transformation method. [8+8] 8. (a) What is a causal system? Why are non-causal systems unrealizable?
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(b) Check whether the DSP systems described by the following equations are causal. i. y(n)=3x(n-2) +3x(n+2) ii. y(n) = x(n-1)+ax(n-2) iii. y(n) = x(-n)
Aj
nt
uW
or
?????
ld .
(c) Define the terms ”impulse response” and ”unit step response” and give the relationship between them. [5+6+5]
4
Code No: 16021/16021
NR
Set No. 1
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1. (a) What is the principle of designing FIR filters using windows.
in
III B.Tech II Semester Supplimentary Examinations,February 2010 DIGITAL SIGNAL PROCESSING Common to Electronics And Telematics, Electronics And Control Engineering, Electronics And Instrumentation Engineering, Electronics And Communication Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????
(b) Using a rectangular window technique design a low pass filter with pass band gain of unity, cut-off frequency of 1kHz and working at a sampling frequency of 5 kHz. The length of the impulse response should be 7. [6+10] 2. (a) Draw the flow graph of an 8-point DIF / FFT and explain briefly.
or
(b) Find the DFT (8-Point) for a continuous time signal x(t) = Sin( 2Π f t) with f = 50Hz. Use DIF - FFT algorithm. [6+10] 3. (a) Determine the frequency response , magnitude response and phase response for the system given by y(n) − 34 y(n − 1) + 81 y(n − 2) = x(n) − x(n − 1)
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(b) A causal LTI system is described by the difference equation y(n)=y(n-1)+y(n2)+x(n-1), where x(n) is the input and y(n) is the output. Find i. The system function H(Z)=Y(Z)/X(Z) for the system, plot the poles and zeroes of H(Z) and indicate the region of convergence. ii. The unit sample response of the system. iii. Is this system stable or not? [6+10]
nt
4. (a) Explain the factors that influence the choice of structure for realisation of a LTI system.
Aj
(b) An LTI system is described by the difference equation y (n) = a1 y (n − 1) + x (n) + b1 x (n − 1) Realize it in direct form I structure and convert it to direct form II structure. [4+12]
5. (a) Define DFT of a sequence x(n). Obtain the relationship between DFT and DTFS. (b) Consider a sequence x(n) = {2, −1, 1, 1} and T = 0.5 compute its DFT and compare it with its DTDT. [8+8]
6. (a) A discrete system is given by following difference equation y(n)-5y(n-1) = x(n) + 4x(n-1) where x(n) is the input and y(n) is the out put. Determine its magnitude and phase response as a function of frequency. (b) State and prove convolution theorem. 5
[8+8]
Code No: 16021/16021
NR
Set No. 1
7. (a) What is a causal system? Why are non-causal systems unrealizable? (b) Check whether the DSP systems described by the following equations are causal.
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i. y(n)=3x(n-2) +3x(n+2) ii. y(n) = x(n-1)+ax(n-2) iii. y(n) = x(-n) (c) Define the terms ”impulse response” and ”unit step response” and give the relationship between them. [5+6+5] 8. (a) Compare the Digital Butterworth and Chebyshev filters.
Aj
nt
uW
or
?????
ld .
(b) Explain method of constructing Butterworth circle in the Z-plane using Bilinear transformation method. [8+8]
6
Code No: 16021/16021
NR
Set No. 3
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1. (a) Compare the Digital Butterworth and Chebyshev filters.
in
III B.Tech II Semester Supplimentary Examinations,February 2010 DIGITAL SIGNAL PROCESSING Common to Electronics And Telematics, Electronics And Control Engineering, Electronics And Instrumentation Engineering, Electronics And Communication Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????
(b) Explain method of constructing Butterworth circle in the Z-plane using Bilinear transformation method. [8+8] 2. (a) What is the principle of designing FIR filters using windows.
or
(b) Using a rectangular window technique design a low pass filter with pass band gain of unity, cut-off frequency of 1kHz and working at a sampling frequency of 5 kHz. The length of the impulse response should be 7. [6+10] 3. (a) What is a causal system? Why are non-causal systems unrealizable?
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(b) Check whether the DSP systems described by the following equations are causal. i. y(n)=3x(n-2) +3x(n+2) ii. y(n) = x(n-1)+ax(n-2) iii. y(n) = x(-n)
(c) Define the terms ”impulse response” and ”unit step response” and give the relationship between them. [5+6+5] 4. (a) Draw the flow graph of an 8-point DIF / FFT and explain briefly.
nt
(b) Find the DFT (8-Point) for a continuous time signal x(t) = Sin( 2Π f t) with f = 50Hz. Use DIF - FFT algorithm. [6+10]
5. (a) Explain the factors that influence the choice of structure for realisation of a LTI system.
Aj
(b) An LTI system is described by the difference equation y (n) = a1 y (n − 1) + x (n) + b1 x (n − 1) Realize it in direct form I structure and convert it to direct form II structure. [4+12]
6. (a) Define DFT of a sequence x(n). Obtain the relationship between DFT and DTFS. (b) Consider a sequence x(n) = {2, −1, 1, 1} and T = 0.5 compute its DFT and compare it with its DTDT. [8+8]
7
Code No: 16021/16021
NR
Set No. 3
7. (a) Determine the frequency response , magnitude response and phase response for the system given by y(n) − 34 y(n − 1) + 81 y(n − 2) = x(n) − x(n − 1) (b) A causal LTI system is described by the difference equation y(n)=y(n-1)+y(n2)+x(n-1), where x(n) is the input and y(n) is the output. Find
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i. The system function H(Z)=Y(Z)/X(Z) for the system, plot the poles and zeroes of H(Z) and indicate the region of convergence. ii. The unit sample response of the system. iii. Is this system stable or not? [6+10]
(b) State and prove convolution theorem.
Aj
nt
uW
or
?????
ld .
8. (a) A discrete system is given by following difference equation y(n)-5y(n-1) = x(n) + 4x(n-1) where x(n) is the input and y(n) is the out put. Determine its magnitude and phase response as a function of frequency.
8
[8+8]
