(SEM VI) THEORY EXAMINATION 2017-18 DIGITAL SIGNAL PROCESSING

Digital Signal Processing (NEC-011)

Complete Section-Wise Explanation – B.Tech Semester VI

Introduction to the Subject

Digital Signal Processing (DSP) deals with the analysis and processing of signals using digital techniques. Signals such as audio, images, biomedical signals, and communication signals are converted into digital form and processed using algorithms like DFT, FFT, filtering, convolution, and system realization.
 

DSP is extremely important because it forms the backbone of:

Communication systems

Audio and image processing

Control systems

Biomedical signal analysis

Modern electronics and embedded systems
 

The paper tests both theoretical understanding and numerical problem-solving skills. It is divided into three sections: A, B, and C.
 

SECTION A – Fundamental Concepts (Short Answer)
 

Pattern:
Attempt all questions
10 questions × 2 marks = 20 marks

Nature of Section A

Section A checks whether your basic concepts and definitions are clear. Questions are short and direct, so answers must be precise and accurate. This section is usually scoring if fundamentals are well prepared.
 

Explanation of Section A Questions

This section includes questions on basic DSP operations and definitions.

You are asked to find time reversal and indexing operations on discrete sequences, which test your understanding of sequence manipulation.

Questions on DFT of delta sequence examine your understanding that the DFT of δ(n) is unity for all frequency indices.
 

The order of Butterworth filter formula tests analog filter fundamentals and its dependency on passband and stopband specifications.
 

The difference between IIR and FIR filters focuses on stability, phase linearity, feedback, and impulse response duration.
 

Gibbs phenomenon checks your understanding of oscillations near discontinuities in Fourier series and FIR filter design.
 

Questions on time reversal in DFT, twiddle factor, and Hamming window expression directly test FFT and windowing knowledge.
 

Differences between circular and linear convolution are very important, as they appear repeatedly in DSP exams.
 

Frequency transformation rules test knowledge of LP to HP digital filter conversion.
 

SECTION B – Numericals & DSP Algorithms

Pattern:
Attempt any three questions
3 × 10 marks = 30 marks

Nature of Section B

This section focuses on numerical problems, algorithms, and short theory notes. Proper step-by-step solution, formula usage, and clarity are essential for full marks.

Explanation of Section B Questions

Circular Convolution Using DFT and IDFT

This question checks understanding of the DFT-based convolution method. You first compute the DFT of both sequences, multiply them in frequency domain, and then apply IDFT to obtain circular convolution. This also reinforces the concept that circular convolution in time corresponds to multiplication in frequency.

DIF FFT Algorithm (8-Point DFT)

This problem tests your knowledge of Fast Fourier Transform algorithms, specifically Decimation in Frequency (DIF). You must show stages of computation, butterfly operations, and final output sequence. Correct signal flow and ordering are important.

Short Notes: Butterfly, In-Place Computation, Bit Reversal

These concepts explain how FFT achieves computational efficiency.
Butterfly computation shows pairwise combination of data points.
In-place computation highlights memory efficiency.
Bit reversal explains input or output reordering in FFT.

Bilinear Transformation – LP to HP Filter

This question applies bilinear transformation to convert an analog low-pass filter into a digital high-pass filter with given frequency specifications. Understanding of frequency warping and substitution is crucial here.

Digital Butterworth Filter Design

This is a classic design problem using Impulse Invariant Transformation. You must determine filter order, cutoff frequency, and final transfer function while meeting magnitude constraints.

SECTION C – Long Answer & Design Problems

Pattern:
Attempt any one part from each question
5 questions × 10 marks = 50 marks

This section carries the highest weightage and decides overall performance. Answers must be well structured, mathematically correct, and neatly presented.

Question 3

System Realization Using Ladder Structure

This problem tests your understanding of system realization techniques. You must decompose the given transfer function and realize it using ladder structure, which is preferred for numerical stability.

Circular Convolution Theorem

You are required to state and prove that circular convolution in time domain corresponds to multiplication in frequency domain. A clear mathematical derivation is expected.

Question 4

Circular vs Linear Convolution Comparison

This question reinforces the difference between circular and linear convolution using actual sequences. You compute both and compare results, showing how aliasing occurs in circular convolution.

Conjugate Symmetry Property of DFT

Given partial DFT values of a real-valued sequence, you must determine remaining values using complex conjugate symmetry property.

Question 5

Digital Filter Design Using Bilinear Transformation

This question involves converting an analog resonant filter into a digital filter using bilinear transformation and ensuring resonance at a given digital frequency.

FIR Filter Design Using Hanning Window

This is a practical FIR design question. You calculate normalized frequencies, determine filter length using stopband attenuation, and design coefficients using the Hanning window.

Question 6

System Realization (Direct, Cascade, Parallel Forms)

This question tests realization techniques. From the difference equation, you must derive:

Direct Form I               Direct Form II                 Cascade form                     Parallel form

Block diagrams and clarity in coefficients are important.

Inverse DFT Using DIT FFT

This numerical checks your understanding of inverse FFT computation using Decimation in Time (DIT) algorithm.

Question 7

Window Functions and Their Effects

This is a theory question explaining Rectangular, Hamming, Hanning, Blackman windows and their effect on main-lobe width, side-lobe attenuation, and ripple behavior in FIR filters.

DIF FFT Flow Graph for N = 8

This question tests algorithmic understanding. You must derive and draw the signal flow graph showing stages and butterfly computations.