Convolution without any Built-in Commands

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?

[Matt Fig]

Sounds like homework. Please show the code you have written so far.

[SB]

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]

please do deconv() function using for loops

Answer 1

[Matt J]

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

[SB]

Alright thank you, ill check it out. Could you also possibly look at my code and let me know if my for loop attempt is correct? I'm just doing (x*h)(n) =y(n) with x and h being vectors, but I'm not sure if it totally works.

[Matt J]

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

[Image Analyst]

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.

Answer 2

[Jan]

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.