Motivation and Introduction to Digital Signal Processing
Short Mathematical reminder – Vector spaces and inner products. Orthogonal families. Example: Fourier series
Continuous time Signals and Systems - The Dirac impulse function, System characterization: memory, linearity, time-dependence, causality, Fourier and Laplace analysis, Impulse response and Convolution, Differential equations as an I/O system. Time and Frequency domains
Discrete time Signals and Systems - System characterization: memory, linearity, time-dependence, causality, FIR vs. IIR, Fourier and Z analysis, Unit sample response and Convolution, Difference equations as an I/O. Time and Frequency domains
Sampling – Shannon-Nyquist sampling and reconstruction. Practical considerations. A/D, D/A, Quantization.
The Discrete Fourier Transform and the FFT algorithms. Spectral Analysis for random and deterministic signals. Windows
Filtering – Concepts and design methods
FIR filters – Linear phase, Window design methods, Park McLellan algorithm.
IIR filters – Families: Butterworth, Chebychev, Elliptic, Bessel. Bilinear transform design method
If time permits – Short Time Fourier Transform, Gabor Transform, Wavelets and Multi resolution analysis, Multi-rate systems