Filtering signal noise using Fourier Transforms and MATLAB

Question

So, I've been given three different MATLAB (I'm using MATLAB R2014b) files with signals containing noise. I simply just plotted the values I was given for the first part. For example, the plot of the first signal looks like the one below.

enter image description here

Then, I did the Fourier Transform of the signal and plotted those values as well to determine where the noise and signal occur in the frequency spectrum. To show this, I added the plot image of the first signal below.

enter image description here

Finally, I am supposed to create a filter using the basic MATLAB commands and filter the noise out of the plot of the signal and then do the Fourier Transform of the signal again and plot the results. The filter portion will look something like this...

b = fir1(n,w,'type');
freqz(b,1,512);
in = filter(b,1,in);

Where n is the order of the filter, w is the cutoff frequency (cutoff frequency divided by half the sampling rate), and 'type' is something to the effect of low/high/stop/etc... So, my question is how do I figure out what the n, w, and type values of the filter I am creating are supposed to be?! Thanks in advance for any help!

Rashid Rashid · Accepted Answer · 2014-12-03T12:45:53

I believe your high frequency components are noise, but it actually depends on your data.

See this example,

Fs = 2000;
L = 200;
t = (0 : L - 1)/Fs;
data = chirp(t,20,.05,50) + chirp(t,500,.1,700);
subplot(411)
plot(t,data,'LineWidth',2);
title('Original Data') 
N = 2^nextpow2(L);
y = fft(data,N)/L;
f = Fs/2 * linspace(0,1,N/2+1);
subplot(412)
plot(f,abs(y(1:N/2+1)))
title('Spectrum of Original Data')
b = fir1(40,2*[1 200]/Fs); 
newd = filter(b,1,data);
subplot(413)
plot(t,newd)
title('Filtered Data')
newy = fft(newd,N)/L;
subplot(414)
plot(f,abs(newy(1:N/2+1)))
title('Spectrum of Filtered Data')

enter image description here

You can use b = fir1(40,2*[200 800]/Fs); for high-pass filter.

Filtering signal noise using Fourier Transforms and MATLAB

2 Answers