Gasquet C. Fourier Analysis and Applications...1999

Textbook in PDF format

This applied mathematic text focuses on Fourier analysis, filters and signal analysis. Scientists and engineers are confronted by the necessity of using classical mathematics such as Fourier transforms, convolution, distribution and more recently wavelet analysis in all areas of modelling. The object of this book is two-fold - on the one hand to convey to the mathematical reader a rigorous presentation and exploration of the important applications of analysis leading to numerical calculations and on the other hand to convey to the physics reader a body of theory in which the well-known formulae find their justification. The reader will find the basic study of fundamental notions such as Lebesgue integration and theory of distribution and these permit the establishment of the following areas: Fourier analysis and convolution Filters and signal analysis time-frequency analysis (gabor transforms and wavelets) The book is aimed at engineers and scientists and contains a large number of exercises as well as selected worked out solutions. The words `Translated by Robert D Ryan' should be included in ALL promotion material regarding the book.
Signals and Systems
Periodic Signals
The Discrete Fourier Transform and Numerical Computations
The Lebesgue Integral
Spaces -
Convolution and the Fourier Transform of Functions
Analog Filters
Distributions
Convolution and the Fourier Transform of Distributions
Filters and Distributions
Sampling and Discrete Filters
Current Trends: Time-Frequency Analysis