Universitat Pompeu Fabra, Barcelona
This is an intermediate course in
audio signal processing thought for the third year undergraduate
students of the degree of Audiovisual Systems Engineering of the
Polytechnic School of the UPF. The course is a continuation of Signals
and Systems, where we focus on the analysis, transformation and
synthesis of musical sounds.
The course is offered in 10 weeks, with 20 hours of
lectures and 20 hours of labs. The evaluation of the students is
based on the lab assignments (15%) and final exam (85%).
All the labs of the course are done using Python and all the materials
and code used in the class are available under open licenses (Creative
Commons and GPL). All the materials prepared for the class are
available in: https://github.com/MTG/sms-tools
Introduction to audio signal processing for music applications; Music
applications examples. Introduction to needed math: Sinusoids, Complex
numbers, Euler's identity, Complex sinusoids, Inner product of signals,
- Discrete Fourier
Transform: DFT equation; Complex exponentials; Inner product; DFT of
complex sinusoids; DFT of real sinusoids; Inverse-DFT.
- Fourier transform
theorems and properties: Linearity; Shift; Evenness; Convolution; Phase
unwrapping; Zero padding; Power & amplitude in dB; Fast Fourier
Transform (FFT); FFT and zero-phase.
- Short-Time Fourier
Transform: STFT equation; Window type; Window size; FFT size; Hop size;
Time-frequency compromise; Inverse STFT; STFT implementation.
- Sinusoidal model: Sinusoidal Model; Sinewave spectrum; Sinusoidal detection; Sinusoidal synthesis.
- Harmonic model: Harmonic Model; Sinusoids-Partials-Harmonics; F0 detection; Harmonic tracking.
- Sinusoidal plus
residual model: Sinusoidal plus residual model; Sinusoidal subtraction;
Stochastic model; Sinusoidal plus stochastic model.
- Spectral-based sound transformations: Filtering; Morphing; Frequency scaling and pitch transposition; Time stretching.
Materials and references