Download GTU BE/B.Tech 2019 Summer 7th Sem Old 171003 Digital Signal Processing Question Paper

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Subject Code: 171003

GUJARAT TECHNOLOGICAL UNIVERSITY

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BE - SEMESTER-VII (OLD) EXAMINATION — SUMMER 2019
Subject Name: Digital Signal Processing
Time: 02:30 PM TO 05:00 PM

Instructions:

1. Attempt all questions.

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2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

Q1 (a) Draw the block diagram architecture of TMSC6000 series Digital Signal Processor. Briefly describe each block functions. (07)
(b) Define ROC for z-transform? List the properties of the ROC. (07)

Q2 (a) State and prove Time Shifting and Scaling in z domain properties for z-transform. (07)

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(b) State and prove convolution theorem and the correlation theorem for Fourier transform (07)

OR

Q2 (a) Determine the z-transform of the following signals. (07)
1) x(n) = u(n) (3-Marks)
2) x(n) = (cos ?n)u(n) (4-Marks)

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(b) Determine the inverse z-transform of X (z) = z² / (1-1.5z^-1 +0.5z^-2) if (07)
(i) ROC: |z| >1
(ii) ROC: |z|<0.5
(iii) ROC: 0.5<|z|<1

Q3 (a) Determine the range of value of a and b-for which the liner time-invariant system with impulse response (07)

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h(n) = { aⁿ, n>=0; bⁿ, n<0 } is stable.

OR

Q3 (a) Determine the spectra of the signals (07)
1) x(n) = cos 2pn (3-marks)
2) x(n) = cos pn/3 (4-marks)

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(b) The impulse response of a linear time invariant system is h(n) = {1,2,3,1}. Determine the response of the system to the input signal x(n)= {1,2,1,—1} (07)

Q4 (a) Compute the DFT of the four-point sequence x(n)={0 1 2 3} (07)
(b) Obtain direct form-I and direct form-II structures for the system y(n) = ⁵/₆y(n—1)—¹/₆y(n—2)+x(n)+¹/₈x(n—1). (07)

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Date: 16/05/2019

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Total Marks: 70

OR

Q4 (a) State the Sampling theorem. Consider the analog signal (07)
x_a(t) =3cos2000pt+ 5sin6000pt+10cos12000pt .
1) What is the Nyquist rate for this signal?

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2) Assume now that we sample this signal using a sampling rate Fs=5000samples/s. What is the discrete-time signal obtained after sampling?

(b) How many numbers of additions, multiplications and memory locations will be required to realize a system H(z) having M zeros and N poles in (i) Direct-form I and Direct-form-II realization?. (ii) Give direct form-I and Direct form-II structures of second order system realization. (07)

Q.5 (a) Perform the circular convolution of the following two sequences: (07)
x₁(n) ={2,1,2,1}
x₂(n)={1,2,3,4}

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(b) Classify the discrete time signals. Give one example of each class. (07)

OR

Q.5 (a) Differentiate IIR and FIR systems. (07)
(b) Explain the Decimation in Time FFT algorithm. (07)

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