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JNTU B.Tech III DIGITAL SIGNAL PROCESSING Previous Question Paper (March - 2024 - R16)

B.Tech | III | III-II | R16 | March - 2024

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

Question paper consists of Part A and Part B. Part A is compulsory (25 marks). In Part B, answer any one question from each unit (10 marks each).

Part A

125 marks

Determine the fundamental period of the signal

x(n) = cos(60πn / 110)

2 marks

Answer

The signal is of the form cos(ωn), where ω = 60π/110 = 6π/11. For a discrete-time signal to be periodic, ω/2π must be a rational number: ω/2π = (6π/11) / 2π = 3/11. Since this is a rational number k/N = 3/11, the fundamental period N is 11.

Outline Parseval’s relation in Z-transform.

3 marks

Answer

Parseval's relation for the Z-transform states that for two sequences x(n) and y(n) with Z-transforms X(z) and Y(z), the sum of the product of the sequences is related to a contour integral in the Z-domain:

Σ x(n) y*(n) = (1 / 2πj) ∮ X(z) Y*(1/z*) z^-1 dz

where the integral is taken over a closed contour in the region of convergence.

State the property of Circular Shift of a Sequence in DFT.

2 marks

Answer

State the difference between DIT and DIF algorithms.

3 marks

Answer

How is the order of a Butterworth filter required to achieve a certain stopband attenuation determined?

2 marks

Answer

What is meant by Warping effect and how can it be eliminated?

3 marks

Answer

What are the desirable characteristics of a Window?

2 marks

Answer

Discuss situations where FIR filters are preferred over IIR filters, and vice versa.

3 marks

Answer

Define upsampling and interpolation and explain their relationship.

2 marks

Answer

What are the strategies for optimizing filter design to achieve the desired balance between round-off and overflow noise?

3 marks

Answer

Part B

Find the output response of the discrete time system described by the difference equation

y(n) - 0.86y(n-1) + 0.186y(n-2) = x(n)

where

x(n) = (8/9)^n u(n)

subjected to the initial conditions

y(-1) = 1

and

y(-2) = 2

. Also find out the step response.

10 marks

Solve the difference equation as specified.

5 marks

Answer

For the signals, determine linearity, shift invariance, causality, and stability: i)

y(n) = sinh[nx(n) + x(n + 5)]

ii)

y(n) = x(-n - 7)

5 marks

Answer

310 marks

Solve for

x(∞)

, if

X(Z) = (z + 4) / (8(z^2 - 1)(z + 0.7))

3 marks

Answer

Determine the system function

H(z)

, impulse response

h(n)

, magnitude response and phase response of the system

y(n) = x(n) + 3x(n-1) + 2y(n-1) - y(n-2)

7 marks

Answer

410 marks

Given

x[n] = {1, 2, 3, 4, 5}

and

N = 3

, compute DFT using the Over-Lap Save method.

5 marks

Answer

Express the relationship between DTFT, DFS, DFT, and Z-Transform.

5 marks

Answer

510 marks

The 8-point DFT of the sequence

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

. Solve using DIT-FFT algorithm.

5 marks

Answer

Evaluate IDFT of

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

5 marks

Answer

610 marks

Design a digital Chebyshev low pass filter using Bilinear transformation for

0.707 ≤ |H(ejω)| ≤ 1.0

0 ≤ ω ≤ 0.4π

and

|H(ejω)| ≤ 0.2

0.6 ≤ ω ≤ π

with

T=1 sec

5 marks

Answer

Discuss transformations relating low pass filter to HPF, BPF and BRF in Digital domain.

5 marks

Answer

710 marks

Design a Band pass Butterworth filter with sampling frequency

F=7KHz

αp = 3dB

in passband

800Hz ≤ f ≤ 1000 Hz

αs = 40dB

in stopband

4000Hz ≤ f ≤ ∞

5 marks

Answer

Describe the design of Analog Low pass filter using Chebyshev Type-I filter.

5 marks

Answer

810 marks

Explain the steps in designing FIR filter using frequency sampling technique.

5 marks

Answer

Design an ideal differentiator

H(ejω) = jω

using hamming window with

N=11

5 marks

Answer

910 marks

Discuss the Fourier series method for designing FIR filters.

5 marks

Answer

Design an FIR low-pass filter with cutoff

1000 Hz

using Hanning window,

Fs=8000 Hz

5 marks

Answer

1010 marks

Explain sampling rate conversion by factor

I/D

5 marks

Answer

Explain polyphase decomposition and its role in bandpass signal conversion.

5 marks

Answer

1110 marks

Explain how computational output round-off noise affects digital filter performance.

5 marks

Answer

Investigate dead band effects for

H(z) = 1 / (1 - 0.8z^-1)

5 marks

JNTU B.Tech III DIGITAL SIGNAL PROCESSING Previous Question Paper (March - 2024 - R16)

Part A

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Part B

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