## How generating band limited white noise with matlab

on 30 Jun 2013

### Wayne King (view profile)

In matlab I use if true % code randn(1,length(N)) end to generate white noise... Now I would like to generate band limited white noise (e. g. from 240 to 435 Hz). How must I code that in matlab!?

## Products

### Wayne King (view profile)

on 2 Jul 2013

That's not a very good approximation to a bandpass filter between 240 and 435 Hz.

fvtool(B,A,'Fs',2000)

If you're going to use the window method, can you up the order significantly?

[B1,A1] = fir1(48,[fd fu]/fn);
fvtool(B1,A1,'Fs',2000)

Now you can do:

noise_limited = filter(B1,A1,white_noise);

### Wayne King (view profile)

on 30 Jun 2013
Edited by Wayne King

### Wayne King (view profile)

on 30 Jun 2013

band limited white noise is not possible. White noise by definition has a flat power spectral density function.

You can generate a white noise sequence and then filter that sequence to generate a band-limited noise but that noise will not be white.

You do not tell us what the sampling frequency is, which is a critical piece of information to have in designing the filter (you cannot design the filter without it), but I'll assume 2,000 Hz in the following example.

d = fdesign.bandpass('Fst1,Fp1,Fp2,Fst2,Ast1,Ap,Ast2', 150,240,435,550,60,0.5,60,2000);
Hd = design(d);
y = filter(Hd,randn(1000,1));

You can view the filter's magnitude response

fvtool(Hd)

I've also given you a minimum-order design with 60-dB of stopband attenuation. If you need less stopband attenuation, you can specify that, or if you wish to specify your filter with a certain order, you can also do that with fdesign.bandpass

Randy82

### Randy82 (view profile)

on 2 Jul 2013

Ok, there are a lot of parameters i need to design the filter... My sampling frequency is e.g.

fs = 2000;

What about to generate band limited noise in this way:

fn = 0.5*fs;
fd = 240;
fu = 435;
[B, A] = fir1(10,[fd fu]/fn);
noise_limited = filter(B, A, white_noise);
Randy82

### Randy82 (view profile)

on 2 Jul 2013

That works better - thanks!

MATLAB and Simulink resources for Arduino, LEGO, and Raspberry Pi