## DIGITAL SIGNAL PROCESSING Introduction to Signals, Signal Processing, Types and Classification of Signals, Signal energy and power System and its properties.

Types of Systems, LTI Systems, Convolution and its properties, Auto & Cross Correlation. Analog to digital conversion: Sampling theorem, Quantization error, and aliasing.

Revision of Discrete Time Signal & Systems. Classification and its properties

Discrete Fourier Transforms: The Discrete Fourier Transform (DFT), DFT properties (Linearity, Circular shift of DFT input, Circular shift of DFT frequency output, periodicity, DFT of even and odd sequences, DFT of real sequence, complex-conjugate sequence/DFT relationship), Eight Point DFT example, DFT frequency response characteristics, frequency selectivity, spectral leakage, Gibbs phenomenon, Equivalent noise bandwidth, Overlap correlation. Fast Fourier transforms, Butter fly diagram, Decimation in Time and Frequency for FFT.

Revision of Z-transforms: The properties of Z-transform (Region of convergence, linearity, delay property, time scaling by complex exponential sequence, differentiation, multiplication, convolution property, Initial valuetheorem, Final value theorem). The inverse Z-transform, complex inversion integral, Inversion by partial fractions, inversion by divisions, complex convolution theorem. Solution of difference equation. Application of Z-transform to the analysis of discrete time systems.

Design & Analysis of Digital Filters (FIR & IIR): Realization structures for FIR and IIR filters. Direct form-I, Direct form II, Cascade, Parallel, Lattice, Frequency sampling and Fast Convolution method.

Design of Infinite Impulse Response (IIR) filters: Introduction to digital filter design, Analogue filter approximations (Analogue low pass Butterworth, Chebyshev, Elliptic filters) Frequency band transformation, Digital filter design equations (for low pass, high pass, band pass, band stop filters) IIR digital filter design techniques and procedure using Bilinear transformation, Impulse invariant and Pole placement methods.

Design of Finite Impulse Response (FIR) filters: Introduction to FIR filter and its characteristics, Properties of FIR filters, Window functions, FIR filter design using Hamminig, Hanning and Kaiser window methods. Introduction to digital image processing.