2. Syllabus

Chapter 1: Introduction to Signal & Systems

Signals: Definition of Signal, Various Types of Signals and its classification, Standard Test Signals, Representation of signals in continuous and discrete domain, Basic Signal Operations - Shifting, Time Scaling and Amplitude Scaling Operations, signal sampling and quantization, discretization of continuous time signals, Sampling Theorem, Nyquist Criteria, Aliasing and Quantization as a error in Sampling Process, Reconstruction of Sampled Signals, Various types of 1D and 2D signals. Systems: Definition of System, Types of Systems and its classification, Difference between continuous and discrete time domain systems Biomedical Aspects in Signal and Systems: Classification of Various Biosignals, Types of Biological systems, Types of 1D and 2D signals arising/captured from human body, Deciding Sampling Rate - Nyquist Criteria for various Biomedical Signals, Various Noises in Biomedical Signals

Chapter 2: Time Domain Analysis of Discrete Time System

Introduction of discrete time signal and systems, Properties of discrete time systems, Classification of discrete time systems, Systems characterized by Linear Time Invariance property, Convolution of LTI Systems using Mathematical method, Tabular method and Graphical method, Circular Convolution, LTI system characterized by differential equation: Homogeneous and Particular Solution of differential equation, Correlation of Signals - Cross correlation and Autocorrelation Biomedical Case Study: Convolution of 1D and 2D signals of Biomedical origin, Correlation of signals of Biomedical origin

Chapter 3: Frequency Domain Characterization of Signals & Systems by Transform Techniques (PART-I)

Frequency Domain analysis of First and Second Order LTI Systems. Z-Transform: Introduction to Z-Transform, Region of Convergence (ROC), Properties of Z – Transform, Z-Transform of Standard Sequences, one sided & Two sided Z –Transform, Solution of Differential Equation using Z-Transform, Frequency Response from poles and zero locations, Connection between Laplace Transform & Z - Transform, Inverse Z - Transform

Chapter 4: Frequency Domain Characterization of Signal & System by Transform Techniques (PART-II):

Discrete Fourier Transform: Representation of Periodic Sequence by Fourier Series, Introduction to Discrete Fourier Transform (DFT), Properties of DFT, DFT of Standard Signals, Implementation of DFT for Frequency domain analysis of discrete signals, Linear Convolution using DFT, Fast Fourier Transform: Introduction to Fast Fourier Transform, Radix-2 FFT algorithm, Radix-2 Decimation in Time FFT (DIT-FFT), Radix -2 Decimation in Frequency FFT (DIF-FFT), Goertzel Algorithm, Spectrum Power, Spectral Density and its Importance Relation between Discrete Fourier Transform (DFT) and Z- Transform, Importance of DFT and FFT as a primary tool for Biomedical Signal Analysis

Chapter 5: Structures for Linear Time Invariant System & system characterized by Linear Constant Coefficient Differential Equation (Structure for Digital Filters):

System classification based on the impulse response – IIR & FIR system, System classification bases on output response – Recursive & Non – Recursive System. IIR Filter Structure: Direct Form I & II Realizations, Cascade combination of Second Order System, Parallel combination of Second Order Systems. FIR Filter Structure: Direct form realization, Cascade form, Frequency Sampling form and Lattice Structure, Representation and dependency of Zero-pole plot on nature of IIR/FIR systems.