JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III DIGITAL SIGNAL PROCESSING Previous Question Paper (August/September - 2024 - R16)
Question paper consists of Part A, Part B.
Part A is compulsory, which carries 25 marks. In Part A, Answer all questions.
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
Explain causality and stability of a linear time invariant system.
Answer
A linear time-invariant (LTI) system is causal if its output at any time depends only on present and past input values, not on future values. For a discrete-time LTI system, this requires the impulse response h(n) to be zero for all n < 0.
An LTI system is stable in the bounded-input bounded-output (BIBO) sense if every bounded input produces a bounded output. For a discrete-time LTI system, this condition is satisfied if and only if the impulse response is absolutely summable, expressed as:
State and prove time convolution property of Z-Transforms.
Answer
The time convolution property states that if the Z-transform of two sequences x1(n) and x2(n) are X1(z) and X2(z) respectively, then the Z-transform of their convolution x1(n) * x2(n) is the product of their individual Z-transforms, X1(z)X2(z).
To prove this, consider the definition of the convolution sum:
Taking the Z-transform of y(n):
Interchanging the order of summation:
Let m = n - k, which implies n = m + k. As n goes from -∞ to ∞, m also goes from -∞ to ∞:
Since the inner sum is the definition of X2(z) and the outer sum is X1(z), we obtain:
Define and differentiate over-lap add method and over-lap save method.
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Write the properties of DFS.
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What are the parameters that can be obtained from the Chebyshev filter specification?
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What is warping effect? What is its effect on magnitude and phase response?
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Under what condition an FIR filter will exhibit linear phase response.
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Why the limit cycle problem does not exist when FIR digital filter is realized in direct form?
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What is overflow and truncation error?
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What is the need for anti-aliasing filter prior to down sampling?
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Part B
Determine the frequency response, magnitude and phase responses and time delay of the systems given by
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Determine the z-transform for the following sequence.
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Determine the impulse response h(n) for the system described by the second order difference equation
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Obtain the parallel form realization for the IIR system described by the transfer function
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Find the output y(n) of a filter whose impulse response h(n) is {1,1,1} and input signal x(n)= {3, -1,0,1,3,2,0,1,2,1} using Over-Lap Add Method.
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Find the DFT of the following sequence using FFT DIF? X(n) = {1,2,3,5,5,3,2,1}.
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Find the linear convolution of the sequences x[n] = {1,4,0,9, -1} and h[n]= {-3, -4,0,7}
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Compute the DFT of the sequence x(n) = sin[nπ/4], where N=8 using DIT FFT algorithm.
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Design a Chebyshev filter with a maximum passband attenuation of 2 dB; at Ωp=20rad/sec and the stopband attenuation of 35 dB at Ωs=50 rad/sec.
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Convert the analog filter to a digital filter whose system function is 𝐻(𝑆) = 1/(S+2)^2(S+1), Use bilinear transformation.
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For the given specifications design an analog Butterworth filter 0.9 ≤ |𝐻(𝑗Ω)| ≤ 1 𝑓𝑜𝑟 0 ≤ Ω ≤ 0.2𝜋 and |𝐻(𝑗Ω)| ≤ 0.2 𝑓𝑜𝑟 0.4𝜋 ≤ Ω ≤ 𝜋
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Consider an analog filter with transfer function 𝐻(𝑠) = 1/((S+1)(S^2+S+1)). Is this a Butterworth or Chebyshev filter? Obtain the transfer function of an IIR digital filter using impulse invariant transformation. Assume T = 1 Sec.
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What is a Kaiser window? In what way is it superior to other window functions?
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Explain the frequency-sampling method of FIR filter design with an example.
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Define the Characteristics of FIR filters and differentiate with IIR filter.
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Using a rectangular window technique, design a low pass filter with pass band gain of unity, cut-off frequency of 1000Hz and working at a sampling frequency of 5 KHz. The length of the impulse response should be 7.
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Explain the decimation and interpolation process with an example. Also find the spectrum.
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Explain how reduction of product round-off error is achieved in digital filters.
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With necessary derivation, explain the operation of sampling rate conversion by a non-integer.
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Write a short note on round-off noise in IIR digital filter.
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