Syllabus

Module-I: Signals and systems [2 hr.]
Continuous and discrete signals: Unit step and nascent delta functions, Relationship between complex exponentials and delta functions, Attributes of signals, Signal arithmetics and transformations, Linear and time-invariant systems, Signals through continuous LTI systems, Signals through discrete LTI systems, Continuous and discrete convolutions

Module-II: Signal Representation using Orthogonal Basis [12 hr]
Basis of Vectors, Matrix representation of vector space, Continuous Valued Signal, Sub-domain and Entire-domain Basis, Eigenfunctions

The Fourier series expansion of periodic signals: Formulation of the Fourier expansion, Physical interpretation, Properties of the Fourier series expansion, The Fourier expansion of typical functions

The Fourier transform of non-periodic signals, Formulation of the CTFT, Relation to the Fourier expansion, Properties of the Fourier transform, Fourier spectra of typical functions

Discrete-time Fourier transform: Fourier transform of discrete signals, Properties of the DTFT, DTFT of typical functions, The sampling theorem, Reconstruction by interpolation.

Discrete Fourier transform: Formulation of the DFT, Matrix representation, Properties of the DFT, DFT computation, and fast Fourier transform.

The z-transform: From Fourier transform to z-transform, Region of convergence, Properties of the z-transform, The z-transform of typical signals, Analysis of discrete LTI systems by z-transform, First- and second-order systems, The unilateral z-transform

Module-III: Structures for the Realisation of Discrete-Time Systems [6 hr]

Structures for FIR Systems: Direct-Form Structure, Cascade-Form Structures, Frequency-Sampling Structures, Lattice Structure


Structures for IIR Systems: Direct-Form Structures, Signal Flow Graphs and Transposed Structure, Cascade-Form Structures, Parallel-Form Structures, Lattice and Lattice-Ladder Structures for IIR Systems


State-Space System Analysis and Structures: State-Space Descriptions of Systems Characterised by Difference Equations, Solution of the State-Space Equations, Relationships Between Input-Output and State-Space Descriptions, State-Space Analysis in the z-Domain, Additional State-Space Structures

Module-IV: Design of Digital Filter [12 hr]
Design of FIR Filters: Symmetric and Antisymmetric FIR Filters, Design of Linear-Phase FIR Filters Using Windows, Design of Linear-Phase FIR Filters by the Frequency-Sampling Method, Design of Optimum Equiripple Linear-Phase FIR Filters, Design of FIR Differentiators, Design of Hilbert Transformers, Comparison of Design Methods for Linear-Phase FIR Filters

Design of IIR Filters From Analog Filters: IIR Filter Design by Approximation of Derivatives, IIR Filter Design by Impulse Invariance, IIR Filter Design by the Bilinear Transformation, The Matched-z Transformation, Characteristics of Commonly Used Analog Filters, Some Examples of Digital Filter Designs Based on the Bilinear Transformation.

Frequency Transformations: Frequency Transformations in the Analog Domain, Frequency Transformations in the Digital Domain.


Design of Digital Filters Based on Least-Squares Method: Padé Approximation Method, Least-Squares Design Methods, FIR Least-Squares Inverse (Wiener) Filters, Design of IIR Filters in the Frequency Domain.

Module-V: Adaptive Filtering [4 hr]
LMS Algorithm for Coefficient Adjustment, System Identification or System Modeling
Suppression of Narrowband Interference in a Wideband Signal, Adaptive Line Enhancement, Adaptive Channel Equalisation

To make students familiar with the inner-product space representation of signals.

To make students capable of applying the transformed method in the analysis of signals and systems

To make students familiar with different structures of Discrete-Time Systems.

To enable students to design FIR and IIR filters with various characteristics.

To make students capable of implementing adaptive filtering algorithms.

At the end of the course, students will be able to
CO1: use the inner-product space representation of signals

CO2: apply transformed methods in analysis of signals and systems

CO3: design different structures of Discrete-Time Systems

CO4: design FIR and IIR filters with different characteristics

CO5: implement adaptive filtering algorithms.

John G. Proakis and Dimitris G. Manolakis, Digital Signal Processing: Principles, Algorithms and Applications, 5th edition, Pearson Education , 19 June 2025

Ruye Wang, Introduction to Orthogonal Transforms With Applications in Data Processing and Analysis, CAMBRIDGE UNIVERSITY PRESS , 2012

G. Strang, Linear Algebra and its Applications, THE , 2006 or latest Ed.

Vinay K. Ingle and John G. Proakis , Digital Signal Processing Using MATLAB®: A Problem Solving Companion, Cengage India Private Limited , 1 January 2017