# DIGITAL SIGNAL ANALYSIS AND PROCESSING

### CT 704

Lecture:3                                                                                                                                        Year: IV
Tutorial: 1                                                                                                                                         Part: I
Practical: 3/2

#### Course Objectives:

To introduce digital signal Processing techniques and algorithms

1. Discrete-time signals and systems
1.  Discrete-time signal, basic signal types
2. Energy signal, power signal
3. Periodicity of discrete-time signal
4. Transformation of independent variable
5. Discrete-time Fourier series and properties
6. Discrete-time Fourier transform and properties
7. Discrete-time system properties
8. Linear Time-Invariant (LTI) System convolution sum, Properties of LTI system
9. Frequency response of LTI system
10. Sampling of continuous-time signal, spectral properties of sampled signal
2. Z-transform
1. Definition, Converge of Z-transform and region of convergence
2. Properties of Z-transform (linearity, time shift, multiplication by exponential sequence, differentiation, time reversal, convolution, multiplication)
3. Inverse z-transform by long division and partial fraction expansion
3. Analysis of LTI system in frequency Domain
1. Frequency Response of LTI system, responsive to complex exponential
2. Linear constant coefficient difference equation and corresponding system function
3. Relationship of frequency response to pole-zero of system
4. Linear phase of LTI system and its relationship to causality
4. Discrete Filter Structures
1. FIR filter, Structures of FIR filter (direct form, cascade, frequency sampling, lattice)
2. IIR filter, Structures for IIR Filter (direct form I, direct form II, cascade, Lattice, Lattice Ladder)
3. Quantization effect ( truncation, rounding), limit cycles, and scaling
5. FIR Filter Design
1. Filter Design by window method, commonly used windows ( rectangular window, Hanning Window, Hamming Window)
2. Filter Design by Kaiser Window
3. Filter Design by frequency sampling method
4. Filter Design using optimum approximation, Remez exchange algorithm
6. IIR filter Design
1. Filter design by impulse invariance method
2. Filter design using bilinear transformation
3. Design of digital low pass Butterworth filter
4. Properties of Chebyshev FIlter, Properties of elliptic filter, properties of Bassel filter, SPectral transformation
7. Discrete Fourier Transform
1. Discrete Fourier Transform (DFT) representation, properties of DFT (linearity, timeshift, frequency shift, conjugation and conjugate symmetry, duality, convolution, multiplication),circular convolution
2. Fast Fourier Transform (FFT) algorithm (decimation in time algorithm, decimation in frequency algorithm)
3. Computation Complexity of FFT algorithm

#### Practical:

• Introduction to DSP tools
• Signal Generation and manipulation
• Convolution