Objectives
To give the students: - A comprehension of the concepts of discrete-time signals and systems, - A comprehension of the Z- and the Fourier transform and their inverse, - A comprehension of the relation between digital filters, difference equations and system functions, - The knowledge about the most important issues in sampling and reconstruction, - The knowledge about the principles behind the discrete Fourier transform (DFT) and its fast computation, - The knowledge about the basics of estimation theory, - The knowledge about adaptive filtering for parameter estimation. To make the students able to: - Perform digital filtering according to known filter specifications, - Work with the Fourier analysis of stochastic signals using the DFT, - Use programming and numeric computing software for digital signal processing problems, - Apply adaptive filtering algorithms to real-world problems such as channel equalization, channel estimation, echo cancellation, etc.
Course program
Analog-to-digital conversion: sampling of signals and signal reconstruction, sampling rate conversion, quantization. The Z- and Fourier transforms: definition and properties. Discrete-time systems: difference equations and Auto-Regressive Moving Average (ARMA) systems. Discrete-time filter design: direct forms, cascade forms, parallel form, linear phase forms; Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) filter approximations. Design of linear FIR filters using windowing. Discrete Fourier Transform (DFT): definition and properties, Fast Fourier Transform (FFT), filtering using the DFT, spectral analysis using the DFT. Introduction to bayesian parameter estimation. Linear MMSE estimation, and Iterative LMMSE estimation: the steepest descent rule. Least Mean Square (LMS) and Recursive Least Square (RLS) adaptive filtering.
