Unit 1 Introduction

6 lecture hours

• Discrete time systems
• Analysis of Discrete-time Linear time invariant systems
• Frequency analysis of Discrete time signals and Fourier Transform properties
• Frequency Response of LTI system
• The Z- transforms
• Inverse Z-transforms
• The Schur-Cohn stability test

Unit 2 Implementation of Discrete time systems

5 lecture hours

• Structures for FIR, IIR Systems
• Quantization of Filter Co-efficients
• Round-off Effects in Digital Filters

Unit 3 Discrete Fourier Transform and its applications

6 lecture hours

• Frequency domain Sampling
• Properties of DFT, Circular Convolution
• Linear Filtering Methods Based on the DFT, The discrete Cosine Transform
• frequency analysis of signals using the DFT

Unit 4 Fast Fourier Transform

6 lecture hours

• Efficient computation of DFT (FFT Algorithms-DIT and DIF)
• Application of FFT Algorithms
• The Goertzel Algorithm
• The Chirp-z Algorithm
• Quantization Effects in the Computation of DFT

Unit 5 Design of Digital Filters

8 lecture hours

• Design Techniques of FIR Filters – Windowing methods
• frequency sampling method
• Optimum Equiripple Linear Phase Filters
• FIR differentiators
• Hilbert Transformers
• design techniques of IIR filters : Impulse invariance
• Bilinear transformation
• finite difference
• Frequency Transformations

Unit 6 Discrete Wavelet Transform

• Introduction and applications 2 5

Unit 7 Power Spectrum Estimation

7 lecture hours

• Estimation of spectra from finite duration signals
• Periodogram Nonparametric methods - Bartlett
• Welch and Blackman-Tukey methods
• Parametric methods – ARMA
• AR and MA model based spectral estimation