JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III Year DIGITAL SIGNAL PROCESSING Previous Question Paper (February - 2023 - R16)

B.Tech | III Year | II | R16 | February - 2023

Answer PaperPaper Code: 136BEMaximum Marks: 75Time: 3 Hours

Note: i) Question paper consists of Part A, Part B. ii) Part A is compulsory, which carries 25 marks. In Part A, Answer all questions. iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.

Part A

125 marks

Obtain the system function for the LTI system

y(n) + y(n-2) = x(n) + x(n-3)

2 marks

Answer

Taking the Z-transform of both sides of the difference equation y(n) + y(n-2) = x(n) + x(n-3), we get Y(z) + z^-2Y(z) = X(z) + z^-3X(z). The system function H(z) is defined as Y(z)/X(z) = (1 + z^-3) / (1 + z^-2).

Find the causality and stability of the systems

y(n) = x(-n) + x(n-4) + x(3n-2)

3 marks

Answer

The system y(n) = x(-n) + x(n-4) + x(3n-2) is non-causal because it depends on future values of the input (e.g., x(-n) for n < 0 and x(3n-2) for n > 1). It is unstable because the term x(3n-2) represents a time-scaled input, which can lead to an unbounded output for a bounded input.

Compute the N-point DFT of

x(n) = δ(n-n₀)

2 marks

Answer

Obtain the relation between DFT and Z-transform.

3 marks

Answer

How is the drawback in bilinear transformation method eliminated?

2 marks

Answer

Find the equivalent digital transfer function H(z) by using impulse invariant method for the analog transfer function

H(s) = 1/(s+2)

. Assume T=0.5sec.

3 marks

Answer

What is the necessary and sufficient condition for the linear phase characteristic of an FIR filter?

2 marks

Answer

What are the advantages and disadvantages of the window technique for designing FIR filter?

3 marks

Answer

What are the applications of Multirate DSP?

2 marks

Answer

Elaborate the meaning of fractional sampling rate conversion.

3 marks

Answer

Part B

210 marks

Determine the frequency response for the system given by

y(n) - (4/7)y(n-1) + (1/8)y(n-2) = x(n) + 5x(n-1)

4 marks

Answer

Check whether the following systems are Stable, Causal, Linear, Time Invariant and Memory less: i)

y(n) = sin(x(n))

ii)

y(n) = ∑x²(k)

6 marks

Answer

310 marks

For the system function

H(z) = (1+2z⁻¹+z⁻²) / (1-(5/7)z⁻¹+(3/7)z⁻²)

, draw a signal flow graph that implements this system as a cascade form & parallel form realization.

5 marks

Answer

A system is given by the difference equation

y(n) - (3/7)y(n-1) = x(n)

. Determine the solution when the input is

x(n) = (1/7)ⁿu(n)

and the initial condition is given by

y(-1) = 1

using Z-transform.

5 marks

Answer

410 marks

Compute the DFT for the sequence

x(n) = {0.5, 0.5, 0.5, 0.5, 0, 0, 0, 0}

. Also plot the magnitude and phase response.

5 marks

Answer

Find the circular convolution using DFT and IDFT of the sequence

x₁(n) = {4,3,1,2}

and

x₂(n) = {1,3,5,3}

5 marks

Answer

510 marks

Given the 8-point DFT of the sequence

x(n) = {1/√2, 1, 1/√2, 0, -1/√2, -1, -1/√2, 0}

. Compute the DFT of the sequence using DIT-FFT algorithm.

6 marks

Answer

Find the IDFT of the sequence

X(K) = {1, 1+j, 2, 1-2j, 0, 1+2j, 0, 1+j}

4 marks

Answer

610 marks

Design a digital Chebyshev filter using Bilinear transformation method satisfying the constraint

0.75 ≤ |H(eʲᵎ)| ≤ 1.0, 0 ≤ ω ≤ π/2

and

|H(eʲᵎ)| ≤ 0.2, 0.75π ≤ ω ≤ π

with T= 1 sec.

5 marks

Answer

What is a Filter? Mention the different types of filters based on frequency response. Also explain how an Analog filter is converted in to a Digital filter.

5 marks

Answer

710 marks

Design a Band pass Butterworth filter with sampling frequency f = 7 KHz, αₚ = 3 dB in the passband 800Hz ≤ f ≤ 1000 Hz, αₛ = 30dB in the stopband 2000Hz ≤ f ≤ ∞.

5 marks

Answer

Discuss the design procedure of Impulse Invariance method. Also explain why impulse invariant method is not preferred in the design of high pass IIR filter?

5 marks

Answer

810 marks

Determine the filter coefficients of an FIR filter for the desired frequency response

H(eʲᵎ) = {e⁻ʲ²ω |ω| ≤ π/4; 0 π/4 ≤ |ω| ≤ π}

. Find the frequency response H(ω) of the filter using rectangular window.

6 marks

Answer

Describe the frequency sampling realization of an FIR filter.

4 marks

Answer

910 marks

Determine the impulse response of an FIR filter with Pass band edge frequency of 1.5kHz, Stop Band Edge frequency of 2kHz, Sampling frequency of 8kHz using Hamming Window.

6 marks

Answer

Distinguish between the different windows used in the design of FIR filters.

4 marks

Answer

1010 marks

With necessary examples, explain the difference between single-rate and multi-rate systems.

5 marks

Answer

Explain the decimation and interpolation process with an example. Also find the spectrum.

5 marks

Answer

1110 marks

Describe in detail about the Roundoff Noise in IIR digital Filters.

5 marks

Answer

Discuss about the zero-input limit cycle oscillations due to finite word length of registers.

5 marks

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III Year DIGITAL SIGNAL PROCESSING Previous Question Paper (February - 2023 - R16)

Part A

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Part B

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