JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B. Tech III Year II Semester DIGITAL SIGNAL PROCESSING Previous Question Paper (July - 2023 - R16)
Part A is compulsory. In Part B, Answer any one question from each unit.
Part A
Find the period of x(n) = cos [8πn/7 +2].
Answer
A discrete-time sinusoidal signal x(n) = cos(ω0n + θ) is periodic if the frequency f = ω0 / 2π is a rational number. Here, ω0 = 8π/7.
- f = (8π/7) / 2π = 4/7
- Since f is a rational number of the form k/N, where k=4 and N=7, the signal is periodic.
- The fundamental period N = 7.
Given x[n] = (0.5)^n u[n], find the signals z-transform X(z) and the corresponding ROC.
Answer
The Z-transform is defined as X(z) = Σ x(n)z-n from n=0 to ∞.
- X(z) = Σ (0.5)nz-n = Σ (0.5z-1)n
- Using the geometric series formula, X(z) = 1 / (1 - 0.5z-1)
- The ROC is the region where the series converges: |0.5z-1| < 1, which implies |z| > 0.5.
Compare Over-Lap add method and Over-Lap save method.
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Find the DTFT of the sequence x(n) = a^n u(n).
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Explain warping effect.
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Draw the direct form structure of IIR.
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Compare IIR and FIR filter.
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Show that the h(n) = [-1,0,1] is a linear phase filter.
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What are the quantization error due to finite word length register in digital filter?
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Draw a labelled block diagram of a unity-gain multirate signal processing system that converts an input signal with sampling frequency 8 kHz to an output signal with sampling frequency 12 kHz.
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Part B
A discrete time system can be static/dynamic, linear/nonlinear, time-invariant/time-varying, causal/non-causal, or stable/unstable. Examine the system y(n)= x(-n+2) with respect to these properties.
Answer
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Realize the system y(n) = 3/4 y(n-1) - 1/8 y(n-2) + x(n) + 1/3 x(n-1), using cascade form and parallel form.
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What do you mean by Radix-2 FFT? Draw the basic butterfly diagram of radix -2 FFT.
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Compute an 8-point DFT using DIF FFT radix -2 algorithm. x(n) = {1,2,3,4,5,6,7,8}.
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x(n)= {0.5,0.5,0.5,0.5,0,0,0,0}. Compute the DFT of the sequence using the inplace radix 2 DIF-FFT algorithm.
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Determine H(Z) using impulse invariant technique for the analog transfer function H(S) = 1/ [(S+1)(S+2)]. Assume T=1 sec.
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Design an analog Butterworth filter that satisfies the given constraints.
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Describe the design of FIR filter using frequency sampling technique.
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Design an ideal High Pass Filter where Hd(e^jω)= 1 for π/4 ≤|ω|≤π and Hd(e^jω)= 0 for |ω|≤π/4, using Hanning window with N=11.
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Discuss the steps involved in converting sampling rate by a factor of I/D.
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Determine the characteristics of a limit cycle oscillation for y(n) = 0.95y(n-1)+x(n). Determine the dead band with x(n) = +0.875 for n=0 and y(-1)=0 (4-bit sign magnitude).
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Develop an expression for y(n) as a function of x(n) for the given multirate system.
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