Digital Signal Processing - intro

Hi Wallace, I'd like to know what algorithm, or kind of algorithm, you need to develop.

I made a post about convolution, but I think it's a good, and simple, subject for we start our studies.

Look the noised signal:

-->T = 100;

-->t = 1:T;

-->w = %pi/10;

-->s = cos(w*t); //pure signal

-->n = rand(1, T, 'normal')*0.1; //noise

-->x = s + n;

-->plot(t, x);


The result is:


Now, let's filter the signal using an average filter.

We have two options for apply the filtering:

The first

-->Tm = 5;

-->y = [];

-->for i = 1:Tm,
-->y(i) = mean(x(1:i));
-->end;

-->for i = (Tm + 1):T,
-->y(i) = mean(x((i - Tm):i));
-->end;

-->plot(t, y);


The result is:

The second

-->Tm = 5;

-->m = ones(1, Tm);

-->y = convol(x, m);

-->ty = 1:length(y);

-->plot(ty, y);


The result is:


If you make the math operations, you'll see the results are, numerically, the same for t = Tm + 1 until t = T.