Review of Signals and Systems (Discrete time processing of continuous signals - Frequency domain analysis of a digital filter, Quantization error, Sigma and Sigma Delta Modulation. Fourier Analysis – DFT, DTFT, DFT as an estimate of the DTFT for Spectral estimation. DFT for convolution, DFT/DCT for compression, FFT. Ideal vs non ideal filters, FIR and IIR Filters Digital Filter Implementation). Digital Filters (State Space realization, Robust implementation of Digital Filters, Robust implementation of equi – ripple FIR digital filters). Multirate Systems and Signal Processing (Fundamentals – Problems and definitions, Upsampling and downsampling, Sampling rate conversion). Multistage implementation of digital filters (Efficient implementation of multirate systems). DFT filter banks and Transmultiplexers (DFT filter banks, Maximally Decimated DFT filter banks and Transmultiplexers. Application of transmultiplexers in communications Modulation). Maximally Decimated Filter banks (Vector spaces, Two Channel Perfect Reconstruction conditions, Design of PR filters Lattice Implementations of Orthonormal Filter Banks, Applications of Maximally Decimated filter banks to an audio signal). Introduction to Time Frequency Expansion (The STFT, The Gabor Transform, The Wavelet Transform, Recursive Multiresolution Decomposition).

Course Code: 44