Convolution of absolute magnitude =/= absolute magnitude of convolution?

I'd like to figure out what I'm doing wrong to cause this issue.

Consider the code below:

A = [0.008912 0.0008934 -0.002584 0.003039 -0.002209 0.0007542 0.0005372 -0.0003424 -0.009147 0.03952 -0.05169 -0.07655 0.3637 -0.5018 0.1533 0.4625 -0.7134 0.3894 0.06538 -0.2249 0.1327 -0.02629 -0.006015 0.003311 0.000262 -0.0007913 0.0005139 0 -0.0004398 0.0005598 -0.0003478];
B = [-0.0017 0.002354 -0.001407 -0.0003384 0.001932 -0.002653 0.002321 -0.0002952 -0.003325 -0.01342 0.09965 -0.219 0.149 0.2581 -0.682 0.597 -0.02179 -0.4432 0.42 -0.1383 -0.04043 0.05345 -0.01858 0.002102 0 0.0003302 0 0 0 0 0];

H = [0.1986 0.4934 0.6589 0.4934 0.1986];
C = A + B*1j;

plot(abs(conv(C,H,'same')));
hold on;
plot(conv(abs(C),H,'same'));

Why are the two plots different? I thought

Am I missing something simple? Thanks for the help!

Answer 1

[Rik]

Let's consider a minimal example:

data=[-3 0 3];
kernel=[1 1 1]/3;

Now it is easy to see that convolving first and then taking the absolute value will do something different than doing them in reversed order.

data=[-3 0 3];
kernel=[1 1 1]/3;

conv_first=conv(data,kernel,'same');%result: [-1 0 1]
conv_first=abs(conv_first)
%conv_first=[1 0 1]

data=abs(data);
abs_first=conv(data,kernel,'same')
%abs_first=[1 2 1]

I can't pinpoint where your math is wrong, but it must be wrong somewhere. Probably the second step, as you're doing multiple operations there at once, not all of which I understand.

Answer 2

[Shivam Sardana]

Please look at More About section of conv function.

Answer 3

[Nathan Jessurun]

That makes sense, thanks. It looks like I messed up when I put the magnitude operator in the summation.