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My question is easy one actually.
First, I generate a random signal using randn() function of MATLAB like this:
Then, I design a FIR filter of order 200 of pass-band characteristics with the pass-band $[0.2\pi, 0.4\pi]$ using the MATLAB function fir2():
My questions are:
The output signal will still be normally distributed, but its power spectrum, i.e. its frequency content, will obviously be different from the input signal. If $S_X(\omega)$ is the power spectrum of the input signal, which is approximately flat, then the power spectrum of the output signal is
$$S_Y(\omega)=|H(\omega)|^2S_X(\omega)$$
where $H(\omega)$ is the frequency response of the filter.
filter.m) or some other package. You can't just look at the filtered time-domain signal and say, well that looks good, probably my filter works as it should.
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h is the vector of filter coefficients returned from the function fir2(), and x is your random input signal, then you must use: y=filter(h,1,x);
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You will be creating a random band-pass signal.
What you are supposed to see for such a signal if you plot the time sequence, is a varying sinusoid of frequency $0.3 \pi$ (midpoint of the pass band). Amplitude and phase will vary randomly, depending on the signal bandwidth.
In your case, $0.2 \pi$ bandwidth is quite large compared to the carrier frequency of $0.3 \pi$, so the result should look quite erratic.
For a smaller bandwidth, amplitude and phase will vary more smoothly.
