by Nikolai V. Shokhirev
Fourier Series
Fourier Integrals
Convolution
Fourier transform of convolution
Correlation
Fourier transform of the correlation function is
The “approximate” delta-symbol:
It is equal to 1 not only for n = 0 but for all n divisible by N.
Use of delta - interpolation
Discrete Fourier transform
Properties of the Discrete Fourier Transformation
here the asterisk denotes complex conjugation.
The interpolated function is a periodic with the period N h :
The case of pure harmonic function 
| k | K | K |
| 0 | 0 |  |
| 1 | 1 | -(N-1) |
| 2 | 2 | -(N-2) |
| . | . | . |
| N-2 | N-2 | -2 |
| N-1 | N-1 | -1 |
Non-zero Fourier coefficients.
is equivalent to 0
Relation between interpolation and integration
here
Correlation function
and
in progress
The PasMatLib units are available in Download section
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©Nikolai V. Shokhirev, 2002-2006