Iby and Aladar Fleischman
Courses I teach
to Statistical Signal Processing
Discrete-time Random Processes; Wide-sense stationary (WSS) processes and their properties; Linear parametric processes: Auto-Regressive (AR), Moving Average (MA), ARMA; Spectral estimation: nonparametric methods (periodogram, correlogram, Blackman-Tukey, Welch), parametric methods, Yule-Walker (YW) and Modified YW equations; Detection of deterministic signals in noise: matched filter; Optimal linear filtering: causal and non-causal Wiener filters, Kalman filter; Introduction to adaptive filtering.
Basic concepts of communication systems, frequency-domain analysis of deterministic signals vs. stochastic processes; Digital communication: Pulse-Amplitude Modulation (PAM) and Pulse-Coding Modulation (PCM), quantization and quantization-noise; Matched Filter; Inter-Symbol Interference (ISI) and eye-patterns; Line Codes; Delta Modulation; Analog communication: Baseband signals, Noise Figure, Narrowband Noise Characterization; Amplitude-modulation methods: Double-SideBand (DSB), Amplitude Modulation (AM), Single SideBand (SSB), Hilbert Transform and its use; Phase-modulation methods: Phase Modulation (PM), Frequency Modulation (FM), NarrowBand FM (NBFM); Phase-Locked Loops (PLL).
Design of Finite Impulse Response (FIR) discrete-time filters: Generalized Linear Phase (GLP) filters and their four types; Coefficients design methods: Impulse-response Truncation (IRT), windowing, “optimal” windows, Least-squares (LS) weighting approaches, the Alternation Theorem and related algorithms (Parks-McClellan, Remez Exchange). Implementation approaches, computational efficiency and finite word-length considerations. Multi-rate signal processing, sampling rate conversion, Polyphase filters, Multi-stage filtering, Filter banks, Quadrature Mirror Filters (QMF), conditions for perfect reconstruction. Concepts in Linear Time-Varying (LTV) systems: Tellegen’s theorem; generalization of filter-banks to time-frequency analysis, introduction to Wavelets.
Processing of Single- And Multi-Dimensional Signals
Single-Dimensional signals: Digital filtering principles, phase and amplitude relations, minimum phase, linear phase, group delay vs. phase delay, Generalized Linear Phase (GLP) filters; Multi-Dimensional (MD) signals and systems: MD Fourier transform, MD Z-transform, MD extensions of the Region of Convergence (ROC) concept, stability issues; FIR coefficients design: Single-dimensional: Impulse Response Truncation (IRT), windowing, Least-Squares approaches, Parks-McClellan and Remez exchange algorithms; Multi-Dimensional: zero-phase filters, MD windowing, frequency sampling, transformation approaches, extensions of single-dimensional tools; Muti-rate processing of single-dimensional signals, Polyphase filters, filter banks, perfect reconstruction, generalization of filter-banks to time-frequency analysis, the relation to wavelets; Wavelets in MD signal processing, pyramid representations; Interpolation with splines.
Digital Signal Processing Lab
The lab is based on TI’s TMS320UC6416, and features five DSP experiments aimed at demonstrating and exploring both theoretical and practical considerations in real-time implementation of DSP algorithms. The experiments include basic introductory functions, as well as more elaborate tasks such as real-time spectral analysis, FIR and IIR filtering and adaptive notch filtering.
to Signal Processing
Discrete and continuous signals and systems, classification, transformations, representation of signals in terms of an orthonormal basis; Linear, time-invariant (LTI) systems, impulse response, convolution, exponential signals as eigen-signals of LTI systems; Analysis of continuous-time periodic signals in terms of Fourier series, "continuous-discrete" signals and discrete signals, analysis of discrete-time periodic signals using a discrete-time Fourier series; Analysis of non-periodic continuous-time and discrete-time signals; The sampling theorem, reconstruction of continuous signals; Unilateral and bilateral Z-transform, its relation of the Discrete-Time Fourier Transform, rational LTI systems and their representation using difference equations.