Module 1:

Discrete Fourier Transform and Fast Fourier Transform

Definition of DFT and IDFT

,

Twiddle factors and their properties

,

multiplication of DFTs

,

circular convolution, computation of circular convolution by graphical

,

DFT/IDFT and matrix methods

,

filtering of long data sequences using Overlap-Save and Overlap-Add methods

,

Parseval's Identity

,

Difference between DFT and FFT

,

Radix-2 algorithm

,

Decimation-In-Time, Decimation-In-Frequency algorithms

,

Bit reversal

Module 2:

Filter Design

Basic concepts of IIR and FIR filters

,

Moving average system

,

Autoregressive system

,

Pole- zero system

,

Non- recursive and recursive structures

,

Low pass FIR digital filters

,

High pass FIR digital filters

,

Band pass FIR digital filters

,

Notch FIR digital filters

,

Realization of Filters using Direct form

,

Cascade & Parallel Form

,

Factors influencing choice of structure

,

Design of IIR Filter using impulse invariant and bilinear transform

,

Design of analog Butterworth Filter

,

Design of Analog Low pass Chebyshev filters

,

Comparison between Butterworth Filter and Chebyshev filters

Module 3:

Finite word Length Effects in Digital Filters

Input Quantization error

,

Product Quantization error

,

Coefficient, Quantization error

,

Zero- input Limit cycle Oscillations

,

Dead band

,

limit cycle Oscillations