UNIT I
Review of discrete-time signals and systems: Time domain analysis of discrete-time signals & systems, Frequency domain analysis of discrete-time signals and systems.
Discrete Fourier Transform: Frequency-domain sampling and reconstruction of discretetime signals, Discrete Fourier Transform (DFT), The DFT as a linear transformation,
Relationship of the DFT to other transforms, Properties of DFT, Linear filtering methods based on DFT, Frequency analysis of signals using the DFT.

UNIT II
Efficient computation of the DFT – Direct computation of DFT, Divide and conquer approach to computation of DFT, Radix-2, Radix-4, and Split radix FFT algorithms,
Implementation of FFT algorithms, Applications of FFT algorithms – Efficient computation of the DFT of two real sequences, 2N point real sequences, Use of the FFT algorithm in
linear filtering and correlation, A linear filtering approach to computation of the DFT- the Goertzel, and the Chirp-z transform algorithms, Quantization errors in the computation of DFT.

UNIT III
Structures for the realization of discrete-time systems, Structures for FIR systems – Direct form, Cascade form, Frequency sampling, and Lattice structures, Structures for IIR systems –Direct form, Signal flow graphs & Transposed, Cascade form, Parallel form and Lattice structures, Conversion from Lattice structure to direct form, lattice – Ladder structure.

UNIT IV
IIR filter Design-Design of Infinite Impulse Response (IIR) filters from analog filters – IIR filter design by approximation of derivatives, by Impulse invariance, and by bilinear
transformation methods, Characteristics of commonly used analog filters, Design examples of both FIR and IIR filters, Frequency transformation in the analog and digital domains,
Illustrative problems.

UNIT V
FIR filter Design-Characteristics of practical Frequency Selective Filters, Design of Finite Impulse Response (FIR) filters –Symmetric and asymmetric FIR filters, Design of linear
phase FIR filters using windows, Design of linear phase FIR filters by the frequency sampling method, Design of optimum equi-ripple linear phase FIR filters, Comparison of
design methods for linear phase FIR filters,