Fourier Transforms

Fourier Transforms

Addtional infromation:

Fourier Series and Fourier Transform

Fourier Series

Fourier series simply states that, periodic signals can be represented into sum of sines and cosines when multiplied with a certain weight. It further states that periodic signals can be broken down into further signals with the following properties.

• The signals are sines and cosines
• The signals are harmonics of each other

Although both Fourier series and Fourier transform are given by Fourier , but the difference between them is:

• Fourier series is applied on periodic signals
• Fourier transform is applied for non periodic signals

Fourier transform
The Fourier transform simply states that that the non periodic signals whose area under the curve is finite can also be represented into integrals of the sines and cosines after being multiplied by a certain weight.
The Fourier transform has many wide applications that include, image compression (e.g JPEG compression), filtering and image analysis.

Cite: Learn DIP^[1]

Hsuty; 傅里叶级数(Fourier series)与傅里叶变换(Fourier transform)
Fourier Transforms; Learn Signal System

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1. Fourier Series and Transform; Learn DIP ↩︎