Computer Vision Foundations · 免费预览

离散傅里叶变换

复指数构成有限图像的正交基，向它们投影就得到 DFT 及其快速算法。

1. Waves become complex exponentials

Waves become complex exponentials

Orthogonality, the miracle that makes it work

The transform pair

Keeping only the biggest coefficients

Why does the orthogonality of the complex exponentials let the DFT read each coefficient independently of the others?

An image is constant, every pixel equal to 10. What does its DFT look like?

A $4 \times 4$ image has mean value $10$ in every pixel. Write the DC coefficient $\mathscr{L}[0,0]$ as a number.

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