1. Sampling
Introduction, Discrete-Time Processing of Continuous Time Signals, Periodic Sampling Process (C/D-Conversion), Discrete-Time System H(ej?) (Conversion of x(n) to y(n)), Ideal Reconstruction System: (D/C-Conversion), Continuous Time Processing of Discrete Time Signals, Changing the Sampling Rate using Discrete Time Processing, Sampling Rate Reduction by an Integer Factor (Down Sampling Method), Increasing Sampling Rate by an Integer Factor, Changing the Sampling Rate by Non-Integer Factor, Numerical Problems, Review Questions.
2. Transform Analysis of LTI System
Objectives, Introduction, Frequency Response of LTI System, Symmetry Properties of the Magnitude and Phase Response, Concept of Group Delay in LTI Filter, System Functions for Systems Characterized by LCCD (Linear Constant Coefficient Difference) Equation, Stability and Causality of the LTI System, Inverse System, Minimum Phase System, All Pass System (Filter), Frequency Response of First Order All Pass Filter, The Group Delay of First Order All Pass Filter, Minimum Phase System, Decomposition of H(z) in Minimum Phase and All Pass System, Compensation of Frequency Response, Properties of Minimum Phase System, Linear System with Linear Phase, Types of Linear System with Linear Phase, z-Transform of Linear-Phase Systems (Locations of Zeros for FIR Linear-Phase Systems), Relation between FIR-Linear Phase Systems and Minimum Phase Systems, Numerical Problems, Review Questions.
3. Structures For Discrete Time Systems
Objectives, Introduction, Block Diagram Representation of Linear Constant Coefficient Difference Equation, Advantages of Block Diagram Representation, Signal Flow Graph Representation of Linear Constant Coefficient Difference Equations, System Function From the Signal Flow Graph (SFG), Basic Structures For IIR System, Direct Form Structure for IIR Filter, Cascade Form Structure for IIR Filter, Parallel Form Structure for IIR Filter, Lattice Form Structure for IIR Filter, Ladder Form Structure for IIR Filter, Basic Structures For FIR Systems, Direct Form Structure, Cascade-Form Structures for FIR System, Frequency Sampling Structure For FIR System, Lattice Structure for FIR System, Transposed Structures, Transposed Direct Form–II Structure for IIR System, Transposed Direct form Structure for FIR System, Numerical Problems, Review Questions.
4. Filter Design Techniques
Objectives, Introduction, Ideal and Practical Filters, Analog Filter Design (Analog Lowpass Filter Design), Filter Specifications, Approximation Techniques, Butterworth Approximation, Chebyshev Filter Approximation, Analog Frequency Transformation, Normalized Lowpass Filter to Desired Lowpass Filter Transformation, Normalized Lowpass Filter to Desired Highpass Filter Transformation, Normalized Lowpass Filter to Desired Bandpass Filter Transformation, Normalized Lowpass Filter to Desired Band Elimination (Bandstop) Filter Transformation, Infinite Impulse Response Filter Design (IIR Filter Design), An Introduction to Infinite Impulse Response Filters, Design of Digital IIR Filters, Designing Steps For Butterworth IIR Filter using Impulse Invariance or Bilinear z-Transform Method, Design Steps For Chebyshev IIR Filter by Using Bilinear Transformation or Impulse Invariance Transformation, Finite Impulse Response Filter (FIR Filter), Basic Fundamentals of FIR Filters, Design of Fir Filter by Windowing Techniques, Design Steps for FIR Filter with Windowing Technique (Calculation of FIR Filter Coefficients), Hanning Window, Hamming Window, Kaiser Window, Kaiser Window Technique for Highpass Filter, Kaiser Window for Band Pass Filter, Kaiser Window for Band Stop Filter, Algorithm for Designing the Ideal FIR Filter by Windowing Technique, Comparison of IIR and FIR Filter, Numerical Problems, Review Questions.
5. Discrete Fourier Transform (DFT)
Objectives, Introduction, Different Forms of Fourier Transform, Continuous Time and Continuous Frequency, Continuous-Time and Discrete-Frequency, Discrete-Time and Continuous Frequency, Discrete-Time and Discrete-Frequency, Discrete Fourier Transform (DFT), Relationship Between DFT and Other Transforms, Relationship between DFT and Fourier Series Coefficients of a Periodic Sequence, Relation between DFT and the Spectrum of Infinite Duration (Aperiodic) Signal, Relationship of the DFT and z-transform, Properties of DFT, Periodicity, Linearity, Symmetry Properties of DFT, Circular Shift (Time-Domain Property), Time Reversal Property, Circular Shift Property (Frequency-Domain), Complex-Conjugate Properties, Circular Correlation, Parseval’s Theorem, Multiplication of two Sequences, Convolution of two Sequence, Convolution, Linear Convolution using DFT-IDFT Method, Pitfalls in using DFT, Efficient Computation of Discrete Fourier Transform (FFT Algorithms), Radix-2 FFT Algorithms, Inverse Discrete Fourier Transform (IDFT), Processing of Speech Signals, Introduction, The Speech Chain (Process of Producing and Perceiving Speech), Speech Coding, Vocoders, Channel Vocoders, Formant Vocoders, Cepstrum Vocoders, Voice-Excited Vocoder, Linear Predictive Coders, LPC Vocoders, Multipulse Excited LPC, Code-Excited LPC, Residual Excited LPC, Numerical Problems, Review Questions.
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