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