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Digital Signal Processing and Application

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5th-sem_Digital Signal Processing and Application.pdf

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Most Frequently Asked Questions

Top recurring IOE board exam questions for Digital Signal Processing and Application with verified mark schemes, formula notation, and recurrence frequency.

Showing 30 of 30 top repeated questions

Discrete-Time Signals and Systems

4 Questions
#1Repeated 4 Times[8 Marks]Discrete-Time Signals and Systems
State and prove the Nyquist Sampling Theorem for bandlimited continuous-time signals. For an analog signal $x_a(t) = 3\cos(100\pi t) + 2\sin(250\pi t)$, determine the Nyquist sampling rate and the reconstructed continuous-time signal when sampled at $f_s = 200 \text{ Hz}$.
Appeared in:2081 Chaitra2080 Chaitra2079 Chaitra2076 Ashwin
#2Repeated 4 Times[8 Marks]Discrete-Time Signals and Systems
Explain Multirate Digital Signal Processing principles. Define Decimation (down-sampling by factor $M$) and Interpolation (up-sampling by factor $L$). Explain why an anti-aliasing lowpass filter is required before down-sampling and an anti-imaging filter is required after up-sampling.
Appeared in:2081 Chaitra2079 Chaitra2077 Magh2075 Chaitra
#3Repeated 3 Times[6 Marks]Discrete-Time Signals and Systems
Explain the conditions for a Discrete-Time LTI system to be causal and BIBO (Bounded-Input Bounded-Output) stable in terms of its impulse response $h[n]$ and pole locations in the z-plane.
Appeared in:2080 Chaitra2074 Magh2072 Ashwin
#4Repeated 3 Times[6 Marks]Discrete-Time Signals and Systems
Why do we need anti-aliasing pre-filters before sampling an analog signal? Explain the Nyquist sampling theorem, the effect of undersampling (aliasing), and sample-and-hold aperture distortion.
Appeared in:2077 Chaitra2074 Magh2071 Bhadra

Z-Transform and Analysis of LTI Systems

4 Questions
#1Repeated 5 Times[8 Marks]Z-Transform and Analysis of LTI Systems
List the properties of Region of Convergence (ROC) for the Z-transform. Determine the inverse Z-transform of $X(z) = \frac{1 - 0.5z^{-1}}{(1 - 0.8z^{-1})(1 + 0.4z^{-1})}$ for: (a) Causal stable system, (b) Non-causal system, and (c) Anti-causal system.
Appeared in:2080 Chaitra2077 Chaitra2075 Bhadra2074 Magh2071 Bhadra
#2Repeated 4 Times[8 Marks]Z-Transform and Analysis of LTI Systems
State and prove the Initial Value Theorem and Final Value Theorem for unilateral Z-transforms. Determine the inverse Z-transform of $X(z) = \frac{1}{(1 - 0.5z^{-1})(1 - 2z^{-1})}$ for: (a) stable system, (b) causal system, and (c) anti-causal system, clearly showing regions of convergence (ROC).
Appeared in:2081 Chaitra2079 Chaitra2077 Magh2074 Chaitra
#3Repeated 4 Times[8 Marks]Z-Transform and Analysis of LTI Systems
Explain causality and BIBO stability criteria in the Z-domain. For a discrete-time system described by difference equation $y(n) - 0.9 y(n-1) = x(n) + x(n-1)$, determine system function $H(z)$, pole-zero plot, impulse response $h(n)$, and frequency response magnitude $|H(e^{j\omega})|$.
Appeared in:2080 Chaitra2079 Chaitra2077 Magh2074 Chaitra
#4Repeated 3 Times[6 Marks]Z-Transform and Analysis of LTI Systems
Explain how the poles and zeros of a system function $H(z)$ affect the stability, causality, and magnitude frequency response $|H(e^{j\omega})|$ of a discrete-time filter with pole-zero geometric plots.
Appeared in:2079 Chaitra2074 Magh2071 Bhadra

Discrete Fourier Transform (DFT) and FFT Algorithms

6 Questions
#1Repeated 5 Times[8 Marks]Discrete Fourier Transform (DFT) and FFT Algorithms
Discuss the computational efficiency of FFT algorithms over direct DFT computation ($O(N^2)$ vs $O(N \log_2 N)$). Draw the complete 8-point Decimation-in-Time (DIT) Radix-2 FFT butterfly flow graph and compute the DFT of sequence $x[n] = \{1, 1, 0, -1, 2, 0, 0, 0\}$.
Appeared in:2081 Chaitra2077 Chaitra2075 Bhadra2074 Magh2072 Ashwin
#2Repeated 4 Times[6 Marks]Discrete Fourier Transform (DFT) and FFT Algorithms
Differentiate between linear convolution and circular convolution. Compute the linear convolution of two sequences $x_1[n] = \{1, 1, 1\}$ and $x_2[n] = \{2, 2, 2\}$ using circular convolution and explain the role of zero padding.
Appeared in:2077 Chaitra2075 Bhadra2074 Magh2072 Ashwin
#3Repeated 4 Times[8 Marks]Discrete Fourier Transform (DFT) and FFT Algorithms
Define Circular Convolution of two finite-duration sequences $x_1(n)$ and $x_2(n)$ of length $N$. Explain how linear convolution can be computed using circular convolution and describe the Overlap-Add and Overlap-Save block convolution methods for filtering long audio sequences.
Appeared in:2081 Chaitra2080 Chaitra2078 Kartik2075 Chaitra
#4Repeated 4 Times[8 Marks]Discrete Fourier Transform (DFT) and FFT Algorithms
Derive the Radix-2 Decimation-in-Frequency (DIF) Fast Fourier Transform algorithm. Draw the complete 8-point butterfly signal flow graph, explain bit-reversal indexing, and compare computational complexity with direct DFT ($O(N^2)$ vs $O(N \log_2 N)$).
Appeared in:2081 Chaitra2080 Chaitra2078 Bhadra2076 Chaitra
#5Repeated 4 Times[6 Marks]Discrete Fourier Transform (DFT) and FFT Algorithms
Differentiate between Discrete-Time Fourier Transform (DTFT) and Discrete Fourier Transform (DFT). Explain how DFT samples DTFT and describe Spectral Leakage, Picket-Fence effect, and the role of Zero Padding in spectral analysis.
Appeared in:2081 Chaitra2080 Chaitra2078 Kartik2075 Chaitra
#6Repeated 2 Times[6 Marks]Discrete Fourier Transform (DFT) and FFT Algorithms
Explain Decimation-in-Frequency (DIF) Radix-2 FFT algorithm. How does the DIF butterfly structure differ from the DIT butterfly structure in terms of input ordering, twiddle factors, and output bit reversal?
Appeared in:2075 Bhadra2073 Bhadra

Implementation of Discrete-Time Systems

6 Questions
#1Repeated 4 Times[8 Marks]Implementation of Discrete-Time Systems
Draw Direct Form I, Direct Form II, Cascade, and Parallel realizations for the LTI system characterized by the system function: $$H(z) = \frac{1 + 2z^{-1} + z^{-2}}{1 - 0.75z^{-1} + 0.125z^{-2}}$$
Appeared in:2080 Chaitra2077 Chaitra2074 Magh2072 Ashwin
#2Repeated 4 Times[6 Marks]Implementation of Discrete-Time Systems
Compute the lattice reflection coefficients $K_1, K_2, K_3$ and draw the Lattice filter structure for the all-pole (or FIR) system given by the transfer function $H(z)$.
Appeared in:2079 Chaitra2077 Chaitra2075 Bhadra2074 Magh
#3Repeated 4 Times[6 Marks]Implementation of Discrete-Time Systems
What are round-off noise and finite word-length effects in digital filters? Explain Limit Cycle Oscillations (zero-input limit cycles and overflow oscillations) with an illustrative second-order recursive system.
Appeared in:2079 Chaitra2075 Bhadra2073 Bhadra2069 Bhadra
#4Repeated 4 Times[6 Marks]Implementation of Discrete-Time Systems
Explain the architectural features of Digital Signal Processors (DSP). Explain bit-serial arithmetic, pipelining, and distributed arithmetic used in real-time DSP hardware implementations.
Appeared in:2081 Chaitra2079 Chaitra2077 Chaitra2074 Magh
#5Repeated 4 Times[8 Marks]Implementation of Discrete-Time Systems
Explain Finite Word Length Effects in digital filter implementations: Input Quantization Error, Coefficient Quantization Error, and Limit Cycle Oscillations (Zero-Input Dead-Band and Overflow Oscillations). How does saturation arithmetic mitigate overflow oscillations?
Appeared in:2081 Chaitra2080 Chaitra2078 Bhadra2076 Chaitra
#6Repeated 4 Times[8 Marks]Implementation of Discrete-Time Systems
Describe the architectural features of Digital Signal Processors (DSPs) optimized for high-throughput arithmetic. Compare Harvard Architecture with Von Neumann Architecture, and explain Multiply-Accumulate (MAC) units, circular addressing, and bit-reversed addressing.
Appeared in:2080 Chaitra2079 Chaitra2077 Magh2074 Chaitra

Design of Digital Filters (FIR and IIR)

10 Questions
#1Repeated 5 Times[8 Marks]Design of Digital Filters (FIR and IIR)
Design a digital low-pass Butterworth IIR filter using the Bilinear Transformation Method (BTM) to satisfy monotonic passband attenuation $\le 1\text{ dB}$ at $\omega_p = 0.2\pi$ and stopband attenuation $\ge 15\text{ dB}$ at $\omega_s = 0.3\pi$. Explain frequency warping and pre-warping.
Appeared in:2081 Chaitra2079 Chaitra2075 Bhadra2074 Magh2071 Bhadra
#2Repeated 5 Times[8 Marks]Design of Digital Filters (FIR and IIR)
What is the condition for an FIR filter to have linear phase? Design a linear-phase low-pass FIR filter with cut-off frequency $\omega_c = 0.5\pi\text{ rad/sample}$ and length $M = 7$ using a Hamming (or Hanning) window. Explain Gibbs phenomenon.
Appeared in:2080 Chaitra2077 Chaitra2075 Bhadra2074 Magh2073 Bhadra
#3Repeated 4 Times[6 Marks]Design of Digital Filters (FIR and IIR)
Explain FIR filter design using the Remez Exchange (Parks-McClellan) algorithm. Why is the Remez Exchange algorithm generally considered superior to the windowing method for equiripple filter design?
Appeared in:2079 Chaitra2075 Bhadra2074 Magh2071 Bhadra
#4Repeated 4 Times[8 Marks]Design of Digital Filters (FIR and IIR)
Explain the design of digital Chebyshev Type-I lowpass filters. Derive the Chebyshev polynomial $C_N(\Omega) = \cos(N \arccos \Omega)$ and formulate how filter order $N$ and cut-off frequency $\Omega_c$ are obtained from given passband ripple ($\alpha_p$) and stopband attenuation ($\alpha_s$) specifications.
Appeared in:2080 Chaitra2079 Chaitra2077 Magh2075 Chaitra
#5Repeated 4 Times[8 Marks]Design of Digital Filters (FIR and IIR)
Explain the Frequency Sampling Method for designing FIR digital filters. Derive the relationship expressing filter impulse response $h(n)$ in terms of frequency response samples $H(k)$. How is transition band optimization applied to minimize stopband ripple?
Appeared in:2081 Chaitra2080 Chaitra2078 Kartik2074 Chaitra
#6Repeated 4 Times[8 Marks]Design of Digital Filters (FIR and IIR)
Compare Window Functions used in FIR filter design: Rectangular, Hanning, Hamming, and Blackman windows. Contrast main lobe width, peak side lobe attenuation (dB), and transition bandwidth trade-offs.
Appeared in:2081 Chaitra2079 Chaitra2076 Ashwin2073 Chaitra
#7Repeated 4 Times[8 Marks]Design of Digital Filters (FIR and IIR)
Compare Impulse Invariance Method and Bilinear Transformation Method for IIR filter design. Explain the mapping from continuous $s$-plane to discrete $z$-plane, aliasing limitations, and the frequency warping effect in Bilinear Transformation with pre-warping formula $\Omega = \frac{2}{T} \tan\left(\frac{\omega}{2}\right)$.
Appeared in:2081 Chaitra2080 Chaitra2078 Bhadra2075 Chaitra
#8Repeated 4 Times[8 Marks]Design of Digital Filters (FIR and IIR)
Prove that an FIR filter with symmetric impulse response $h(n) = h(N - 1 - n)$ or anti-symmetric impulse response $h(n) = -h(N - 1 - n)$ possesses generalized linear phase. Classify Type-I, Type-II, Type-III, and Type-IV linear phase FIR filters and explain their frequency restrictions at $\omega = 0$ and $\omega = \pi$.
Appeared in:2081 Chaitra2080 Chaitra2078 Kartik2076 Ashwin
#9Repeated 3 Times[6 Marks]Design of Digital Filters (FIR and IIR)
Compare Butterworth filter approximation with Chebyshev Type I and Type II approximations in terms of pole locations, passband ripple, and roll-off rate.
Appeared in:2080 Chaitra2077 Chaitra2073 Bhadra
#10Repeated 3 Times[6 Marks]Design of Digital Filters (FIR and IIR)
Design a discrete-time low-pass filter using the Impulse Invariance Method (IIM). Discuss aliasing problems associated with the impulse invariance technique and why it is unsuitable for high-pass filters.
Appeared in:2075 Bhadra2073 Bhadra2069 Bhadra