1. Fourier Transform

convolution neutral networks is a hot spot in machine learning technique.

But is that convolution the same as the following convolution?


let us start with 1D signal.




function h can be called mask.


correlation




linear system


obviously, gradient operator is a linear system.



an example of non-linear system 


shift invariant


so, convolution defines a linear and shift-invariant system.


the equations above show that there are two formats of convolution formula. 

h(t) or h[n] can be called filter or mask.


I will show u some useful filters.

Box function


when a is near to 0, we have Dirac Function.


its area is always equal to 1.

Dirac Function has some properties.

Firstly, we talk about absorption property.


what happens when the input to an Linear Shift Invariant system is an Dirac Function?





Dirac description of sampling








review complex number.


atan2  (-pi, pi]






Fourier shift






sampling： convert analog time or space to digital 



















matlab functions


fftshif


fft  decomposes any periodic function or periodic signal into the sum of a (possibly infinite) set of simple oscillating functions, namely sines and cosines (or, equivalently, complex exponentials).


low pass filter




2.Image Convolution and Edge Detection

图片中边缘的形成：
1. depth discontinuity
2. illumination discontinuity
3. surface color discontinuity

Any 2D Array can be seen as an image.
































2D -filter








Edge detection















图像尺寸对边界检测的影响


非极大值抑制


留下的红点是局部极大值，作为边界点。
image processing codes in matlab






matlab 中数组的内存分布式按列排布的。