Fourier Analysis
eBook - ePub

Fourier Analysis

  1. English
  2. ePUB (mobile friendly)
  3. Available on iOS & Android
eBook - ePub

About this book

This book aims to learn to use the basic concepts in signal processing. Each chapter is a reminder of the basic principles is presented followed by a series of corrected exercises. After resolution of these exercises, the reader can pretend to know those principles that are the basis of this theme. "We do not learn anything by word, but by example."

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Yes, you can access Fourier Analysis by Roger Ceschi,Jean-Luc Gautier,Jean-Luc Gautier in PDF and/or ePUB format, as well as other popular books in Technology & Engineering & Signals & Signal Processing. We have over one million books available in our catalogue for you to explore.

1
Fourier Series

1.1. Theoretical background

1.1.1. Orthogonal functions

1.1.1.1. Orthogonal vectors

Let us consider a vector space with n dimensions and vectors x1, x2,....xn as the orthogonal basis.
[1.1]
image
ki is the norm for vector xi.
image
is the Hermitian vector (conjugate and transposed) of vector xi.
This collection of vectors is assumed to be complete once there is no way of finding any more values for xk such as
image
Consider vector A within this space and A1,A2,....An this vector’s components in relation to n basis vectors. If the basis is complete, we can pose:
[1.2]
image
We obtain coefficients Ai using to the following relation:
[1.3]
image

1.1.1.2. Vector-function analogy

Consider two functions fi(t) and fj(t) that are orthogonal on interval [t1,t2] if:
[1.4]
image
ki is the squared norm of function fi(t).
The vector space is complete if we can no longer find any further functions f(t) that are orthogonal to the previous ones.
When this space is complete and infinite, we can establish an exact representation of any function as a series on interv...

Table of contents

  1. Cover
  2. Table of Contents
  3. Title
  4. Copyright
  5. Preface
  6. 1 Fourier Series
  7. 2 Fourier Transform
  8. 3 Laplace Transform
  9. 4 Integrals and Convolution Product
  10. 5 Correlation
  11. 6 Signal Sampling
  12. Bibliography
  13. Index
  14. End User License Agreement