BSc IT Sem VI ATKT 2016-17 ATKT Digital Signal System Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 Attempt any of the following: 10 marks
   • a. With illustration, explain shifting, folding and time scaling discrete-time are continuous and discrete time systems classified?
   • c. Determine the inverse Fourier transform of the spectrum shown in fig
   • d. Find the Fourier transform of 2 t cos at and f(t) =
2. Q2 Attempt any two of the 10 marks
   • a. Find the Laplace transform ofthe following functions Derive from the principals, the laplace transform of a unit step function. Hence or
   • b. otherwise the Laplace transform of a unit ramp function and a unit impulse andL{ (0) = show that L( fi). =
   • d. Discuss and final value theorem in Laplace transform domain. @
3. Q3 two of the following: 10 marks
   • a. A system has an impulse response h(n) = {1,2,3} and output response yl ny = {1,1,2, —1,3}.Determine the input sequence x(n)
   • b. Define and explain cross-correlation and auto-correlation of sampled signals
   • c. residue method find the inverse z-transform of Using convolution find x(n) if X(z) is given by:
4. Q4 Attempt any of the following: Explain the Paley — Wiener criteria. 10 The discrete time systems are represented by the foll which x(n) is input and y(n) is difference in
   • i. y(n) = 1) — nx(n—1) 2x(n +1) and Are these systems linear? Shift-invariant? Causal? In each case justify your answer
   • c. Consider a causal and stable LTI system whose input x(n) and y(n) are related through the second order difference equation Determine the step response for the system Find the convolution of the two signals
5. Q5 Attempt any two of the following: 0 10 marks
   • a. Find the circular periodic convolution using and IDFT of the two sequences:
   • b. Derive the DFT for the sample data x(n) = {1,1,2,2,3,3 } and compute the amplitude and phase spectrum
   • c. Find the discrete time Fourier transtorm for the following finite duration sequence of find the inverse verify x(n) and A=1V
   • d. Find the 4-point DFT sequencex(n) = cos
6. Q6 Attempt any following: 10 marks
   • a. Designan to satisfy the following specifications:
   • (ii) stop band of 20 dB at 20 Hz and 8 kHz ; (iii) No rigple with both passband and stopband
   • b. Alow filter has the desired response as given below the filter coefficient h(n) for Type-I frequency sampling Design a bandpass filter to pass frequencies in the range 1-2 rad/see using
   • d. Design a digital Chebyshev filter to satisfy the Using bilinear transformation and assuming T=\s
7. Q7 Attempt three of the following: 15 marks
   • a. State and prove that convolution theorem for Fourier transform
   • b. In the parallel RLC circuit. A, C=2 F and R=0.5 0 at time Obtain the complete particular solution for the voltage v(t) the parallel network. Assume zero current through inductor L and zero capacitor C
   • c. Fora low pass RC network, R= 1 MQ and pF. output response for n in the range 0 <n when input has a step response of magniture 2 V and the
   • d. Distinguish between IR and FIR systems. Q
   • e. An FIR digital filter has the unit impulse response sequence, h(n) ={2,2,1}. Determine the output sequence in response to the input sequence) x(n) =.{3,0,-2,0,2,1,0,-2,-1,0} using the method
   • f. Design a Finite Impulse Response low pass filter a cut-off frequency of 1kHz and sampling rate of 4kHz with eleven samples Fourier series

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