Digital Signal Processing Syllabus

                                                       DIGITAL SIGNAL PROCESSING

Digital  Signal Processing

Objectives:

· To learn methodology to analyze signals and systems
· Study transformed domain representation of signals and systems
· Design of filters as DT systems
· To get acquainted with the DSP Processors and DSP applications

Signals and Systems

Continuous time (CT), Discrete-time (DT) and Digital signals, Basic DT signals and
Operations. Discrete-time Systems, Properties of DT Systems and Classification, Linear Time
Invariant (LTI) Systems, Impulse response, Linear convolution, Linear constant coefficient
difference equations, FIR and IIR systems, Periodic Sampling, Relationship between Analog
and DT frequencies, Aliasing, Sampling Theorem, A to D conversion Process: Sampling,
quantization and encoding. 

Frequency Domain Representation of Signal

Introduction to Fourier Series, Representation of DT signal by Fourier Transform (FT),
Properties of FT: Linearity, periodicity, time shifting, frequency shifting, time reversal,
differentiation, convolution theorem, windowing theorem .Discrete Fourier Transform (DFT),
DFT and FT, IDFT, Twiddle factor, DFT as linear transformation matrix, Properties of DFT,
circular shifting, Circular Convolution, DFT as Linear filtering, overlap save and add, DFT
spectral leakage 

Fast Fourier Transform (FFT) and Z-Transform (ZT)

Effective computation of DFT, Radix-2 FFT algorithms: DIT FFT, DIF FFT, Inverse DFT
using FFT, Z-transform (ZT) , ZT & FT, ZT &DFT , ROC and its properties, ZT Properties ,
Rational ZT, Pole Zero Plot, Behaviour of causal DT signals, Inverse Z Transform (IZT): power
series method, partial fraction expansion (PFE) , Residue method. 

Analysis of DT - LTI Systems:

System function H(z), H(z) in terms of Nth order general difference equation, all poll and all
zero systems, Analysis of LTI system using H(Z), Unilateral Z-transform: solution of difference
equation, Impulse and Step response from difference equation, Pole zero plot of H(Z) and
difference equation, Frequency response of system, Frequency response from pole-zero plot
using simple geometric construction, Ideal frequency selective filters, magnitude and phase
response 

Digital Filter Design

Concept of filtering, Ideal filters and approximations, specifications, FIR and IIR filters, linear
phase response, FIR filter Design: Fourier Series method, Windowing method, Gibbs
Phenomenon, desirable features of windows, Different window sequences and its analysis,
Design examples:
IIR filter design: Introduction, Mapping of S-plane to Z-plane, Impulse Invariance method,
Bilinear Z transformation (BLT) method, frequency warping, Prewarping, Design examples,
Practical filters e.g. Butterworth filters, Comparison of IIR and FIR Filters, Finite word length
effect

Filter Structures and DSP Processors

Basic Structures for FIR Systems: direct form, cascade form, structures for linear phase FIR
Systems, Examples
Filter structures for IIR Systems: direct form, cascade form, parallel form, examples.
DSP Processors Architecture Study: ADSP 21XX series: features, comparison with
conventional processor, Functional Block diagram: ALU, MAC, Barrel shifter, DAG, Registers
Introduction to Applications of DSP in speech and image processing