Digital Signal Processing and its Applications

1. Linear Algebra: Set of linear equations, rank, four subspaces and their relationships, uniqueness for overdetermined and underdetermined systems 2. Signal Representation: Basis representation, CT Fourier transform, Fourier series, existence and convergence analysis, Fourier transform for signals in L1, L2, and beyond, regularity- and decay properties, Dirac impulses, and the Poisson summation, uncertainty principle, time-limitedness & bandlimitedness 3. Analog to Digital Conversion: Sampling theory, quantization, oversampling - missing sample recovery, an introduction to sub-Nyquist sampling, projection onto a bandlimited space 4. Recap of - Discrete-Time Signals and Systems, System Analysis by z-Transform, LTI, DTFT, DFT, linear & circular convolutions 5. Relation between CTFT and DTFT, introduction to the problems of blind deconvolution, phase retrieval 6. FIR and IIR filter design: design of basic filters by pole-zero placements, Design of FIR Digital filters: Window method, Park-McClellan`s method; Design of IIR Digital Filters:Butterworth, Chebyshev and Elliptic Approximations; Lowpass, Bandpass, Bandstop and High pass filters 7. Frequency analysis of continuous-time signals, DFT, and resolution issues, linear prediction, high-resolution spectral estimation 8. Spectral Estimation: Parametric and Non-parametric