SRM University 2007 B.Tech Electronics and Communications Engineering BANK : Signals and Systems - Question Paper

y[n] = ½ x[n] +x[n-1] + ½ x[n-2]
17. Find the IDFT of the subsequent
X[k] = { 1,-1,-j2,-1,1+j2 }
X[k] = { 1,0,1,0}
18. Find the circular convolution of the subsequent sequence
X1 [n] = { 1,-1,2,3}
X2[n] = {0,1,2,3}
19. obtain the Z transform of the subsequent sequence
x[n] = u[n] – u[n-3]
x[n] = {1,2,-1,2,3}

UNIT-V

PART-A

1. Why FFT is needed?
2. What is the main advantage of FFT?
3. What is meant by radix-2 FFT?
4. How many multiplications and additions are needed to calculate N-point DFT using radix-2 FFT?
5. What is a twiddle factor?
6. What is DIT algorithm?
7. What is DIF algorithm?
8. How we compute IDFT using FFT algorithm?
9. What are the applications of FFT algorithm?
10. Find the system function and impulse response of the system defined by the difference formula y(n)=1/5y(n-1) + x(n).
11. Define System function.
12. Find the convolution of the subsequent using z-transform
a. x(n) = {1,2,1 } h(n)= {1,1,1}
13. What are the various kinds of structures for realization of IIR systems?
14. What is the main advantage of direct-form II realization when compared to direct-form I realization?
15. Distinguish ranging from recursive realization and non-recursive realization.
16. Draw the parallel form structure of IIR filter.
17. Define the terms i) natural response ii) forced response.
18. Define the impulse response and step response of a system.
19. What are the properties of convolution?
20. Find the convolution of x(n)= { 1,-2,3,1} and h(n) = {2, -3 ,2}.
21. How do you represent a discrete –time signal in terms of impulses.
22. Represent the sequence x(n) = {3,2,-1,2,4,1} as sum of shifted unit impulses.
23. what is meant by zero input response and zero state response?
24. Define convolution sum.
25. Test if the subsequent system are stable or not.
Y(n) = cos x(n)
26. How can you obtain the step response of a system if the impulse response h(n) is known?
27. Find the step response if the impulse response is provided by (-a)nu(n).
28. Define frequency response of a discrete –time system.
29. What are the properties of frequency response H (ej?) of an LTI system?
30. Define FIR and IIR system.

PART-B

1. Find the natural response of the system defined by difference formula
Y(n) – 1.5y(n-1) + 0.5 y(n-2) = x(n) , y(-1) = one ; y(-2) = 0
2. Find the forced response of the system defined by the difference formula
Y(n) – 1.5y(n-1) + 0.5 y(n-2) = x(n), for input x(n) = 2n u(n).
3. Determine the impulse response h(n) for the system defined by the second-order difference formula y(n) = 0.6 y(n-1) -0.08 y(n-2) + x(n)

4. Determine the impulse response h(n) for the system defined by difference formula
y(n) + y(n-1) -2 y(n-2) = x(n-1) + 2x(n-2)

5. Determine the step response of the system defined by difference formula
Y(n) +4y(n-1) + 4y(n-2) = x(n)

6. Determine the response y(n),n = 0 , of the system defined by the 2nd order difference formula y(n) -3y(n-1) -4y(n-2) = x(n) +2x(n-1) to the input x(n)= 4nu(n).

7. Find the solution of a linear constant coefficient difference formula
Y(n) – 3/2 y(n-1) +1/2 y(n-2) = (1/4)n for n=0
With initial conditions y(-1) =4 and y(-2) =10.

8. Determine the convolution sum of 2 sequences
X(n)= ( 1,4,3,2 ) h(n) = (1, 3, 2,1)

9. Determine the output response of the subsequent sequence
X(n) = 2d(n+1) – d(n) + d(n-1) + three d(n-2)
H(n) = 3d(n-1)+4 d(n-2) +2 d(n-3)

10. Find the convolution of 2 infinite duration sequences
H(n) = anu(n) for all n, x(n) = bnu(n) for all n
i). when a?b ii). When a=b

11. Find the DFT of a sequence x(n)={1,2,3,4,4,3,2,1} using DIT & DIF algorithm.
12. Compute 4-point DFT of a sequence x(n)={0,1,2,3} using DIT,DIF algorithm.
13. Compute IDFT of a sequence
X(k)={7,-0.707-j0.707,-j,0.707-j0.707,1,0.707+j0.707,j,-0.707+j0.707} using DIT& DIF algorithm.
14. Find the system function and the impulse response of the system defined by the difference formula y(n) = x(n) +2x(n-1) – 4x(n-2) + x(n-3).
15. Determine the pole-zero plot for the system defined by difference formula
y(n) – ¾ y(n-1) +1/8y(n-2) = x(n) –x(n-1).
16. Determine the direct form I & direct form II for the provided system
y(n) = 1/2y(n-1) -1/4y(n-2) + x(n) +x(n-1).
17. Realize the system with difference formula y(n) = 3/4y(n-1) -1/8y(n-2) +x(n) +1/3x(n-1) in cascade form.
18. Realize the system provided by difference formula
y(n) = -0.1y(n-1) +0.72y(n-2) + 0.7x(n) -0.252x(n-2) in parallel form.

19. Find the impulse response and step response for the subsequent system.
y(n) -3/4 y(n-1) + 1/8 y(n-2) = x(n)
y(n) = x(n) + 2x (n-1) -4 x(n-2) +x(n-3) in z-transform.
20. Find the frequency response of a I order system defined by difference formula
Y(n) = ay(n-1) +x(n) plot the magnitude and phase response of a system whose impulse response h(n) = an u(n) for a=0.5.
21. A causal system is represented by the subsequent difference formula y(n) +1/4 y(n-1) = x(n) + ½ x(n-1) a).Find the system function H(z) and provide the corresponding region of convergence. b). obtain the unit sample response of the system. C). obtain the frequency response H(ej?) and determine its magnitude and phase.
22.Find the output of the system whose input and output are related by y(n) = 7y(n-1) – 12
y(n-2) + 2x(n) – x(n-2) for the input x(n) = u(n).






























ques. BANK
EC209
SIGNALS AND SYSTEMS

Earning:   Approval pending.