Transform Analysis of Linear Time Invariant System
Review of Z-transform and its properties, Response to sinusoidal and complex exponential signals, Steady-state response to periodic input signals, Response to aperiodic input signals, Relationships between the system function and the frequency response function, Computation of the frequency response function.
LTI systems as frequency-selective filters like - Low pass, High pass, Band pass, Notch, Comb, All-Pass filters and Digital resonators.
Invertibility of LTI systems, Minimum-phase, Maximum-phase, Mixed-phase systems.
The Discrete Fourier Transform and Efficient Computation
Frequency domain sampling and reconstruction of discrete time signals, Discrete Fourier Transform (DFT), DFT as a linear transformation, Properties of the DFT, Relationship of the DFT to other transforms.
Fast Fourier Transform : Radix-2 and split-radix Fast Fourier Transform (FFT) algorithms and their applications.
Quantization effects in the computation of the DFT.
Design of Digital Filters and Implementation
Design of Infinite Impulse Response (IIR) filters using impulse invariant method and bilinear transformation method, Butterworth and Chebyshev filter approximation.
Concepts of Finite Impulse Response (FIR) filter, Symmetric and anti symmetric FIR filter, FIR filter design using window method and frequency sampling method.
Realization structures for IIR and FIR filters using direct form structures, Cascade, Parallel structures and lattice, Ladder structure (only conceptual understanding).
Multirate Signal Processing
Decimation by a factor D, Interpolation by I, Sampling rate conversion by a rational factor I/D.
Polyphase filter structures, Interchange of filers and down samplers/up samplers, Sampling rate conversion with cascade integrator comb filters, Polyphase structures for decimation and interpolation filters, Structures for rational sampling rate conversion.
Multistage implementation of sampling rate conversion.
Sampling rate conversion of band pass signals.
Sampling rate conversion by an arbitrary factor - Arbitrary re-sampling with polyphase interpolators, Narrow band filter structures.
Application of multirate signal processing for design of phase shifters, Interfacing of digital systems with different sampling rates, Implementation of narrowband low pass filters, Sub band coding of speech signals.
Analysis of Finite Word Length Effects
Quantization process and errors, Quantization of fixed-point numbers, Quantization of floating-point numbers, Analysis of coefficient quantization effects.
A/D conversion noise analysis, Analysis of arithmetic round-off errors and dynamic range scaling.
Applications of Digital Signal Processing
Dual-tone multi frequency signal detection, Spectral analysis of sinusoidal signals, Spectral analysis of non stationary signals and spectral analysis of random signals.
Musical sound processing, Digital music synthesis, Discrete time analytic signal generation.
Trans-multiplexers, Oversampling ADC and DAC and sparse antenna array design.