matlab - Filtering random Signal

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:

• What am I supposed to see when I filter a random signal using BPF?


• What change in the characteristics will be occur considering the theory?

Answer

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.