Convolution without any Built-in Commands

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SB 2012-11-24

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https://ww2.mathworks.cn/matlabcentral/answers/54698-convolution-without-any-built-in-commands

评论： SM60 2019-3-7

Hey guys, I'm trying to learn how convolution works without any built in fft or

conv commands, and I'm not quite sure how to write it. I'm starting at index 1 in

this case, so y(n) =(x*h)(n)= sum from 1 to infinity of (x(k)h(n-k+1)), and

trying to use just arrays and no loops, while also creating a stem plot. The lack

of a for loop is giving me the most trouble, any suggestions?

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SB 2012-11-24

编辑：Image Analyst 2012-11-25

在 MATLAB Online 中打开

It's actually not homework, but anyways (I'm trying to implement convolution in the MathScript Node, which is similar to Matlab, for LabView):

% 
m = length(x);
n = length(h);
X = [x,zeros(1,n)]; 
H = [h,zeros(1,m)]; 
for i = 1 : n+m-1
  Y(i)=0;
  for j=1:m
      if(i-j+1>0)
          Y(i)=Y(i)+X(j)*H(i-j+1);
      else
      end
  end
end
Y
stem(Y);
ylabel('Y[n]');
xlabel('----->n');

x and h are inputs on the node, so I haven't really provided them.

SM60 2019-3-7

please do deconv() function using for loops

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Answer 1

Matt J 2012-11-24

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TOEPLITZ isn't a built-in command. You could use that to implement convolution, e.g.,

    >> A=toeplitz([2 3, zeros(1,8)],[2 1 0 0 0 0 0 0 0 0 ]), b=rand(10,1);
    A =
         2     1     0     0     0     0     0     0     0     0
         3     2     1     0     0     0     0     0     0     0
         0     3     2     1     0     0     0     0     0     0
         0     0     3     2     1     0     0     0     0     0
         0     0     0     3     2     1     0     0     0     0
         0     0     0     0     3     2     1     0     0     0
         0     0     0     0     0     3     2     1     0     0
         0     0     0     0     0     0     3     2     1     0
         0     0     0     0     0     0     0     3     2     1
         0     0     0     0     0     0     0     0     3     2
    >> A*b-conv(b,1:3,'same')
    ans =
       1.0e-15 *
             0
        0.4441
        0.8882
             0
             0
        0.8882
       -0.4441
             0
             0
             0

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Matt J 2012-11-25

Why don't you test it against the output of conv() to see if you get the same results?

Image Analyst 2012-11-25

I think you mean x(n) ** h(n), which is the usual textbook notation for convolution, rather than (x*h)(n). The code it's not exactly the way I'd do it (padding with zeros, etc.) but it's easy enough to test, like Matt suggested. I would use the double for loop though.

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Answer 2

Jan 2012-11-25

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Even CONV is not a built-in function. But it calls conv2(), which is built-in now.

conv(a,b) can be calculated using:

c = filter(a, 1, b);

when the shorter of the inputs is padded by zeros. And filter() can by run as M-file also, see http://www.mathworks.com/matlabcentral/answers/9900#answer_13623. And considering the special inputs, this code can be improved.