Klappentext

This book is intended to be used both by undergraduate and graduate students with an interest in signal processing and

applications of Fourier Analysis. The book describes Signal Processing from a formal viewpoint.The mathematical tools used are

Fourier Analysis and the Karhunen-Loève theorem. Other contents required to formally define the Fourier transform or the

Karhunen-Loève expansion are also treated, such as Measure Theory, Functional Analysis, Operator Theory, Probability Theory

and Matrix Theory to mention a few. Practical examples are also given using MATLAB.

Inhalt

Introduction. Signals. Measure spaces and integration. Hilbert spaces. The Discrete Fourier Transform (DFT) and the Fast Fourier

Transform (FFT). The Fourier Transform. Sampling. Generalized Functions. Stochastic Processes. Filters. Matrices.

Operators on a Hilbert Space. The Karhunen-Loeve (KL) expansion.