DHANALAKSHMI COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING EC2314- DIGITAL SIGNAL PROCESSING UNIT I INTRODUCTION PART A Classification of systems : Continuous and Discrete 1. What are the various classifications of discrete time system? Linear and Causal System 2. Define Causal System Dynamic and time variant systems 3. What is meant by linear time invariant system? (A-08) 4. Differentiate static system from dynamic system. Classification of signals : Continuous and Discrete 5. Define Even Signal and Odd Signal (A-11) 6. What is meant by deterministic signal? 7. Define Random Signal 8. What are the different types of operations performed on discrete time signals? Sampling Techniques 9. Define Sampling (M- 09) 10. State sampling theorem. (M-10) Quantization, Quantization error, Nyquist rate, aliasing effect 11. Define Nyquist Rate (M- 12) 12. What is meant by aliasing effect? (A-11) 13. What is meant by quantization error?
Digital Signal Representation 14. What are the advantages of digital signal processing? (N-07) 15. What are the different types of signal representation? PART B Classification of systems : Linear, causal, stable, dynamic, time variance, recursive 1. Determine the system stability and causality for the following impulse response: a) h(n)=sin (π n / 2) b) h(n) = δ (n ) + sin π n c) h(n) = 2 n u ( n) d) h(n)= e 2n u ( n 1) (16) (A-11) 2. Determine the linearity and time invariance of the following equations: a) y ( n ) = n x( n ) b) y(n) = a x(n) + b (16) (A-08) 3. Explain in detail, the recursive and non-recursive discrete time systems. (16) Classification of signals : Continuous and Discrete, energy and power, mathematical representation 4. Explain in detail, the following: a) Continuous time signal and deterministic signals b) Even and odd signals c) Periodic and non-periodic signals d) Energy and Power signals (16) (A-11) Sampling Techniques, Quantization 5. Explain in detail, the sampling theorem. (8) (N-12) 6. Explain in detail, the process of sampling and quantization. (16) Digital Signal Representation 7. Explain in detail, the application areas of digital signal processing with suitable example. (16) 8. Explain in detail, the analog and digital conversion with suitable block diagram. (16)
UNIT II DISCRETE TIME SYSTEM ANALYSIS PART A z-transform 1. What is meant by ROC? (A-11) 2. Find the z-transform of discrete impulse signal. (A-11) 3. List out the properties of ROC in z-transform. (N-07) 4. Define z - transform 5. Find the z- transform of the sequence, x ( n ) = { 1, 0, 2, 0, 3 } 6. Find the z-transform of unit step signal. (N-11) Properties of z-transform 7. List out the properties of z-transform. (N-12) 8. State initial value theorem of z-transform. (N-07) 9. State Parseval s relation using z-transform. (N-07) 10. Write the linearity property of z-transform. 11. Write the scaling property of z -transform. 12. Write the time reversal property of z - transform. 13. Write the convolution property of z - transform. 14. State final value theorem of z transform. Inverse z-transform 15. What are the different methods of evaluating inverse z - transform? (N-04) Stability analysis, Difference equation, Solution by z-transform 16. Define System Function
17. What is the condition for stability in z-transform? 18. Define Poles and Zeros of a system function Convolution 19. What is meant by discrete convolution? PART B z-transform and its properties 1. Determine the z-transform of the signal, x(n) = [3(3) n 4(2) n ] u(n). (8) (M-09) 2. Find the z-transform for the function, x(n) = cos nπ u(n) (8) (M-08, M-10) 3. Verify Parseval s theorem for the sequence, x(n) = [1/3] n u(n). (16) 4. Explain in detail, the properties of z-transform with suitable examples. (16) 5. Find the z-transform for the following: a) x ( n) = 2 n u( n 2 ) b) x (n) = n 2 u(n) (16) Inverse z-transform 6. Using differential property, find the inverse z - transform for the function given below: x(z ) = log ( 1 0.5 z 1 ) ; z > 0.5 (16) Difference equation, Solution by z-transform 7. Obtain the system function and impulse response of the following: y (n) 5y(n 1 ) = x(n) + x(n 1) (16) (M- 2011) 8. Explain in detail, the properties of LTI system with suitable equations. (16) (N-2008) Convolution 9. Determine the circular convolution for the function given below: x (n) = { 1, 3, 5, 7 } and h ( n ) = { 2, 4, 6, 8 } (16) (N-09) 10. Determine the linear convolution of the following sequences: a) x (n) = { 1, 1, -1, -1 } b) h(n) = { 1, -1, 2, 1 } (16) (M-12)
UNIT III DISCRETE FOURIER TRANSFORM AND COMPUTATION PART A DFT and its properties 1. What is meant by DFT? (M-09) 2. List out the properties of DFT. (M-09) 3. Find the DFT of the sequence, x(n) = { 1, 0, 0, 1 }. (N-09) 4. State and prove the time shifting property of DFT. (N-09) 5. What is meant by zero padding? (N-07) 6. Define Circular Convolution 7. State periodicity property with respect to DFT. 8. State time reversal property with respect to DFT. 9. What is the DFT of a unit impulse signal? 10. Define IDFT Computation of DFT using FFT algotithm DIT and DIF 11. What is FFT? (N-09) 12. Differentiate DTFT from DFT. (M-10) 13. Compute DFT for the function, x(n) = δ (n n 0 ). 14. How is linear filtering done using FFT? 15. What are the differences between DIT and DIF algorithm? 16. What is meant by in-place computation in FFT? Butterfly structure 17. What are the properties of twiddle factor? (M-09) 18. What are the applications of FFT algorithm?
PART B DFT and its properties 1. Explain the following properties of DFT: a) Linearity b) Symmetry property c) Circular convolution (16) (M-11) 2. Find the DFT of the sequence, x(n) = {1,1,0,0}. (6) (N-07, A-11) 3. Calculate the IDFT of the sequence, x(k) = { 4,0, 0, 0 }. (6) 4. Derive the relation between z-transform and DTFT. (10) 5. Perform the circular convolution for the following sequences by means of DFT and IDFT: a) x 1 (n) = { 1, 2, 3, 1} b) x 2 (n) = { 4, 3, 2, 2 } (16) (N-07) Computation of DFT using FFT algorithm DIT and DIF, Butterfly structure 6. Find the DFT of the sequence, x ( n ) = { 1, 2, 3, 4, 4, 3, 2, 1 } using DIT algorithm. (12) 7. Compute 4 point DFT of the sequence x ( n ) = { 0, 1, 2, 3 } using DIT and DIF algorithms. (10) 8. Given x ( n ) = { 0, 1, 2, 3, 4, 5, 6, 7 }, find x(k) using DIT FFT algorithm. (12) 9. Using DIF, radix-2 FFT algorithm, find the 8 point DFT for the sequence given below: x(n) = { 0, 1, 2, 3, 4, 5, 6, 7 }. (12) 10. Using 8 point DIT-FFT, draw the butterfly diagram for the sequence given below: x(n) = { 1, 0, 0, 0, 0, 0, 0, 0 }. (16) FFT using radix-2 11. Derive and draw the radix-2 DIT algorithm for FFT of 8 points. (10) (M-11)
UNIT IV DESIGN OF DIGITAL FILTERS PART A FIR and IIR filter realization Parallel and cascade forms 1. What is the difference between analog and digital filters? (M-10) 2. Write the steps to design a digital IIR filter using bilinear method. (N-11) 3. Draw the direct form realization of FIR system. (N-06) 4. What is meant by Gibbs phenomenon? (M-12) 5. What is meant by digital filter? 6. What are the main disadvantages of direct form realization? 7. What is the advantage of cascade realization? 8. What are the design techniques of linear phase FIR filters? 9. Distinguish between recursive realization and non-recursive realization. IIR design : Analog filter design- Butterworth approximations 10. Write the expression for the order of Butterworth filter. (N-09) 11. List out the properties of Butterworth lowpass filter. (A-11) 12. What are the basic types of analog filter? 13. Write the steps in designing a Butterworth filter. 14. Define IIR Filter Chebyshev approximations 15. Write the expression for the order of Chebyshev filter. (N-10) 16. Write the steps in designing Chebyshev filter. 17. What are the properties of Chebyshev filter? Digital design using impulse invariant and bilinear transformation 18. What is meant by impulse invariant method? (M-09) 19. What are the types of digital filter with respect to their impulse response?
20. What are the various properties of bilinear transformation? Warping, prewarping and frequency transformation 21. What is meant by warping effect or frequency warping? (N-12) 22. What is meant by pre-warping or pre-scaling? (M-10) PART B FIR and IIR filter realization Parallel and cascade forms 1. Obtain a direct form I realization for the system described by the difference equation given below: y (n) = 0.5 y(n 1) 0.25 y(n 2) + x(n) + 0.4 x(n 1). (10) (M-11) 2. Obtain the direct form II and parallel form realization for the system given below: y (n) = 0.1 y(n 1 ) + 0.2 y(n 2) + 3 x(n) + 3.6 x(n 1 ) + 0.6 x( n 2). (16) (N-12) FIR design : Windowing Techniques 3. Using a rectangular window technique, design a low pass filter with pass band gain of unity, cutoff frequency of 1000 Hz and working at a sampling frequency of 5 Hz. The length of the impulse response is 7. (16) 4. Determine the frequency response of FIR filter defined by y (n) = 0.25 x(n) + x(n 1) + 0.25 x(n 2 ). Calculate the phase delay and group delay. (16) 5. Explain in detail, the design techniques of FIR filters and explain any one technique. (16) IIR design : Analog filter design Butterworth and Chebyshev approximations 6. For the following specifications, design a Butterworth filter using the impulse variance method. (12) (N-07) 7. Design a Butterworth filter with 2 db pass band attenuation at a frequency of 20 rad / sec and 10 db stop band attenuation at 30 rad/sec. (16)
8. Design a Chebyshev filter using bilinear transformation for the following specifications (16) Digital design using impulse invariant method 9. Explain in detail, the impulse invariant method of designing IIR Filter. (16) (N-12)
UNIT V DIGITAL SIGNAL PROCESSORS PART A Introduction Architecture 1. What are the classifications of digital signal processor? (M-10) 2. What is meant by pipelining? (N-12) 3. What are the different buses of TMS320C5x? (N-09) 4. What is the function of parallel logic unit? (N-12) 5. What are the various types of interrupts supported by TMS320C54? (M-08) 6. List out the function of a program controller in DSP processor. (M-08) 7. What are the different stages of pipelining? (N-12) Features Addressing formats 8. List out the features of DSP processor.. (A-11) 9. What are the elements of CPU in TMS320C54x? (M-11) 10. List out the addressing modes available in TMS320C5x processor. Functional modes Introduction to commercial processors 11. Differentiate Von Neumann from Harvard architecture. (M-07) 12. What are the functions of program bus? 13. List out the functions of data read bus. 14. What are the arithmetic instructions of TMS320C5x? 15. What are the shift instructions of TMS320C5x? 16. What are the logical instructions of TMS320C5x? 17. What are load/store instructions of TMS320C5x? 18. List out the applications of DSP Processor. 19. List out the on-chip peripherals of TMS320C5x. 20. What is the function of NOP instruction?
PART B Introduction Architecture 1. Explain the addressing formats in the DSP processors. (8) (M-11) 2. Explain in detail, the pipelining in DSP. (8) (M-12) 3. Draw the block diagram of Harvard architecture. Also explain the various blocks. (8) 4. Explain in detail, the logical instructions of TMS320C5X processor. (16) 5. Explain in detail, the functions of multiply and accumulate unit. (16) 6. Write short notes on arithmetic instructions of TMS320C5X processor. (8) Addressing Formats 7. Write short notes on the following: (a) Memory mapped register addressing (b) Circular addressing mode (c) Auxillary registers (16) (N-07) Functional modes 8. Explain in detail, the functional modes present in the DSP processor. (8) (M-12) Introduction to commercial processors 9. Explain in detail, the different buses of TMS320C54X processor. (16) (M-08) 10. What are the different addressing modes of TMS320C5Xprocessor? (16) (M-11) 11. Explain in detail, the architecture of TMS320C54X with neat diagrams. (16) (N-07, M-11, N-12)