Eyestrain Reduction in Stereoscopy by Leroy Laure;

Author:Leroy, Laure; [Leroy, Laure]
Language: eng
Format: epub
Publisher: Wiley
Published: 2016-06-30T00:00:00+00:00

6.2.1.1.1. Fourier transform

Definition of a Fourier transform

DEFINITION 6.1. (Fourier transform).– The Fourier transform F links spacetime with a dual space in which ω represents frequency. All temporal signals f can be linked with a Fourier transform :

[6.1]

Its inverse transform is written as:

[6.2]

Properties

The transform conserves the scalar product:

[6.3]

It conserves energy (Parseval’s identity):

[6.4]

There are also properties of expansion and translation:

[6.5]

Before stating the following property, let us remember the definition of a convolution.

DEFINITION 6.2.– The convolution r of two functions s and k is defined by:

[6.6]

where * denotes the convolution operator.

The product of temporal space is transformed into the convolution in frequential space and vice versa:

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