# Audio Signal Processing for Music Applications

### Description

In this course you will learn about audio signal processing methodologies that are specific for music and of use in real applications. We focus on the spectral processing techniques of relevance for the description and transformation of sounds, developing the basic theoretical and practical knowledge with which to analyze, synthesize, transform and describe audio signals in the context of music applications.

The course is based on open software and content. The demonstrations and programming exercises are done using Python under Ubuntu, and the references and materials for the course come from open online repositories. We are also distributing with open licenses the software and materials developed for the course.

### What you will learn

Introduction

Introduction to the course, to the field of Audio Signal Processing, and to the basic mathematics needed to start the course. Introductory demonstrations to some of the software applications and tools to be used. Introduction to Python and to the sms-tools package, the main programming tool for the course.

Discrete Fourier transform

The Discrete Fourier Transform equation; complex exponentials; scalar product in the DFT; DFT of complex sinusoids; DFT of real sinusoids; and inverse-DFT. Demonstrations on how to analyze a sound using the DFT; introduction to Freesound.org. Generating sinusoids and implementing the DFT in Python.

Fourier theorems

Linearity, shift, symmetry, convolution; energy conservation and decibels; phase unwrapping; zero padding; Fast Fourier Transform and zero-phase windowing; and analysis/synthesis. Demonstration of the analysis of simple periodic signals and of complex sounds; demonstration of spectrum analysis tools. Implementing the computation of the spectrum of a sound fragment using Python and presentation of the dftModel functions implemented in the sms-tools package.

Short-time Fourier transform

STFT equation; analysis window; FFT size and hop size; time-frequency compromise; inverse STFT. Demonstration of tools to compute the spectrogram of a sound and on how to analyze a sound using them. Implementation of the windowing of sounds using Python and presentation of the STFT functions from the sms-tools package, explaining how to use them.