MATLAB: A composite signal is defined as: x(t) = sin(2*pi*10*t) + sin(2*pi *40*t) + sin(2*pi *60*t) + sin(2*pi *50*t). Separate the four frequencies without using any of the transform techniques.

Question

Which Filtering should i employ for this question? Almost all filtering techniques employ fft in one way or the other, Is there any other way?

Answer 1

My way is all about converting this expression to a equivalent transfer function and let you see the frequency peaks in Bode plot. The following code does the trick:

syms t
x=sin(2*pi*10*t)+sin(2*pi*40*t)+sin(2*pi*50*t)+sin(2*pi*60*t);
Xs=laplace(x);
XsTf=syms2tf(Xs);
opts=bodeoptions;
opts.FreqUnits='Hz';
bode(XsTf,opts)

The first two line defines the x expression symbolically. Then, I took the laplace transform of the expression and the converted it to transfer function(the attached syms2tf function does it). Afterwards, since I obtain a transfer function expression, I expect to see peaks at those frequencies in Bode Plot and the attached figure contains it. Hope this helps to you.