Syllabus
(1) Discrete periodic signals. Discrete Fourier Transform and its properties (Parseval's theorem, convolution theorem). (2) FFT algorithm, fast multiplication of polynomials, fast convolution. (3) Fourier series and discrete non-periodic signals. (4) Operations with signals (modulation, convolution, non-linear distortion). (5) Linear Time-Invariant systems. Digital filters and their general form. IIR and FIR parts. Theorem on existence and uniqueness of digital filter solution. Invertibility, two-way filters. (6) Bode plot. Magnitude and phase. Phase delay, group delay, wave delay. (7) Implementing IIR filters (canonic forms). Round-off errors, stability and noise. (8) Minimum phase filters. Magnitude vs. group delay theorem. (9) Filter design methods. (10) Hilbert transform, analytic signal. (11) Sampling theorem, aliasing. Band-limited signals, Gibbs phenomenon. Resampling. A/D and D/A converters. Kell phenomenon. (12) Uncertainty principle and time-frequency representation. (13) Linear prediction (LPC). ASR front-ends. (14) Deconvolution, Wiener filter. Blind deconvolution. Echo suppression by temporal masking. (15) Frame of the vector space. Reconstruction theorem. (16) Signal restoration (denoising). (17) Biological sound processing: Human auditory system and pathways. Exercises will have a form of practical application examples (e.g. equalizer, speaker location, principle of active and passive radar (sonar), signal restoration (denoising), etc.). These would be selected so as to exercise the theory just learned.
Annotation
Introductory course in one-dimensional (mostly sound) signal processing. Complements lectures NPFL079 (Algorithms in
Speech Recognition) but can be taken separately as well. The lectures cover the theory of digital filters, FFT and its application in implementing fast convolution, sampling theorem, time-frequency signal representation and its connection with overcomplete representation via frame of the respective vector space, deconvolution and signal restoration.