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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.
List of contents
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.
Summary
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.
