An Introduction to Statistical Signal Processing and Spectrum Estimation

This chapter presents an overview of current signal processing techniques, most of which are applied to music transcription in the following chapters. The elements provided will hopefully help the reader. Some signal processing tools presented here are well known, and readers already familiar with these concepts may wish to skip ahead. As we only present an overview of various methods, readers interested in more depth may refer to the bibliographical references provided throughout the chapter.

This chapter is organized as follows. Section 2.1 presents the Fourier transform and some related tools: time-frequency representations and cepstral coefficients. Section 2.2 introduces basic statistical tools such as random variables, probability density functions, and likelihood functions. It also introduces estimation theory. Section 2.3 is about Bayesian estimation methods, including Monte Carlo techniques for numerical computations. Finally, Section 2.4 introduces pattern recognition methods, including support vector machines and hidden Markov models.