2D圆形卷积Vs卷积FFT [Matlab/Octave/Python] [英] 2D circular convolution Vs convolution FFT [Matlab/Octave/Python]
问题描述
我试图理解FTT和卷积(互相关)理论,因此我创建了以下代码来理解它.代码是Matlab/Octave,但是我也可以在Python中做到这一点.
I am trying to understand the FTT and convolution (cross-correlation) theory and for that reason I have created the following code to understand it. The code is Matlab/Octave, however I could also do it in Python.
在一维中:
x = [5 6 8 2 5];
y = [6 -1 3 5 1];
x1 = [x zeros(1,4)];
y1 = [y zeros(1,4)];
c1 = ifft(fft(x1).*fft(y1));
c2 = conv(x,y);
c1 = 30 31 57 47 87 47 33 27 5
c2 = 30 31 57 47 87 47 33 27 5
在2D模式下:
X=[1 2 3;4 5 6; 7 8 9]
y=[-1 1];
conv1 = conv2(x,y)
conv1 =
24 53 89 29 21
96 140 197 65 42
168 227 305 101 63
在这里我找到问题所在,填充矩阵和向量?我该怎么办?我可以在零附近填充x
吗?还是只在一侧?而y
呢?我知道,当x
和y
是向量时,卷积的长度应为M+L-1
,但是当它们是矩阵时呢?
我如何在这里继续我的例子?
Here is where I find the problem, padding a matrix and a vector? How should I do it? I could pad x
with zeros around? or just on one side? and what about y
? I know that the length of the convolution should be M+L-1
when x
and y
are vectors, but what about when they are matrices?
How could I continue my example here?
推荐答案
您需要使用以下方法对一个变量进行零填充:
You need to zero-pad one variable with:
- 与其他变量减的列数一样多的零列 一个.
- 零行与其他变量的行数减一一样.
- As many zero-columns as the number of columns of other variable minus one.
- As many zero-rows as the number of rows of the other variable minus one.
在Matlab中,它的显示方式如下:
In Matlab, it would look in the following way:
% 1D
x = [5 6 8 2 5];
y = [6 -1 3 5 1];
x1 = [x zeros(1,size(x,2))];
y1 = [y zeros(1,size(y,2))];
c1 = ifft(fft(x1).*fft(y1));
c2 = conv(x,y,'full');
% 2D
X = [1 2 3;4 5 6; 7 8 9];
Y = [-1 1];
X1 = [X zeros(size(X,1),size(Y,2)-1);zeros(size(Y,1)-1,size(X,2)+size(Y,2)-1)];
Y1 = zeros(size(X1)); Y1(1:size(Y,1),1:size(Y,2)) = Y;
c1 = ifft2(fft2(X1).*fft2(Y1));
c2 = conv2(X,Y,'full');
为了阐明卷积,还请看这张图片:
In order to clarify the convolution, look also at this picture:
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