离散傅立叶变换 - 简单理解

前言

网络、书籍上有很多关于傅立叶变换的知识,屌丝总有一种感觉:知道这玩意名字N年了,但就是不知道它是啥玩意。

目的

可用。

关键点

1. 只需要掌握dft,其他傅立叶变换在程序里是无法实现的。
2. 时域与空域
When you see the term "time domain" in Fourier analysis, it may actually refer to samples taken over time, or it might be a general reference to any discrete signal that isbeing decomposed.
3. 实数部分-cos  虚数部分-sin
The names  real part  and  imaginary part  originate from the complex DFT, where they are used to distinguish between  real  and  imaginary numbers. Nothing so complicated is required for the real DFT. Until you get to Chapter 29, simply think that "real part" means the  cosine wave amplitudes,  while "imaginary part" means the  sine wave amplitudes . Don't let these suggestive names mislead you; everything here uses ordinary numbers.
4.opencv里的幅值
Rectangular and polar notation allow you to think of the DFT in two different ways. With rectangular notation, the DFT decomposes an  N point signal into  N /2 + 1 cosine waves and  N /2 + 1 sine waves, each with a specified  amplitude . In polar notation, the DFT decomposes an N  point signal into  N /2 + 1 cosine waves, each with a specified  amplitude  (called the  magnitude ) and  phase shift


opencv计算DFT的例子,是 polar notation的方式,例子中倾斜方向频率(u,v)的magnitude比其他频率高。

DFT物理意义的简单理解

一副图像可由不同频率的正弦、余弦波形( rectangular notation)构成,即可由不同频率的余弦波( polar notation)构成

Demo

http://bigwww.epfl.ch/demo/basisfft/demo.html



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