Digital Signal Processing and Application

Syllabus

1. Discrete time signals and systems (6 hours)
   1. Basic elements of Digital Signal Processing
   2. Need of Digital Signal Processing over Analog Signal Processing
   3. Sampling of continuous time signal, spectral properties of sampled signal
   4. Discrete time signal, basic signal types
   5. Transformation of independent variable
   6. Energy signal, power signal
   7. Periodicity of discrete time signal
   8. Discrete time Fourier transform and properties
   9. Discrete time system properties
   10. Linear time invariant (LTI) system convolution sum, properties of LTI system
2. Z-transform (3 hours)
   1. Definition, convergence 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 (5 hours)
   1. Frequency response of LTI system, response to complex exponential
   2. Linear constant co-efficient 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 (6 hours)
   1. FIR filter, structures for 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. Limit cycles and scaling
5. FIR filter design (9 hours)
   1. Filter design by window method, commonly used windows (rectangular, Hanning, Hamming, Bartlett, Blackman window)
   2. Filter design by Kaiser window
   3. Filter design using optimum approximation, Remez exchange algorithm
   4. Types of FIR filters (Type-1, Type-2, Type-3 and Type-4)
6. IIR filter design (9 hours)
   1. Filter design by impulse invariance method
   2. Filter design using bilinear transformation
   3. Design of digital low pass Butterworth filter
   4. Frequency transformation of lowpass IIR filters (transformation of lowpass digital filter prototype to highpass, bandpass and bandstop filters)
7. Discrete Fourier transform (5 hours)
   1. Discrete Fourier transform (DFT) representation, properties of DFT (linearity, time shift, 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. Computational complexity of FFT algorithm
8. Applications of Digital Signal Processing (2 hours)
   1. DSP application in Power System Monitoring and Diagnostics (Fault Detection, Power Quality Analysis)
   2. DSP application in Protection and Control Systems (Smart Grid Management)
   3. DSP application in Reliability and Maintenance