PasMatLib

Signal processing

by Nikolai V. Shokhirev

Definitions


Fourier Series

Fourier Integrals

Convolution


Fourier transform of convolution

Correlation

Fourier transform of the correlation function is

Fourier Interpolation

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

DUnit tests

in progress

 

Download

The PasMatLib units are available in Download section

 


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