Using butterworth filter

[StandardOctaveUser]

What you need is a butterworth filter 
which is supplied with signal processing 
package. 

Say you have N data points and 
a sampling frequency of SF (in Hz). Then 
you have T seconds of record.

T=N/SF;

Assume uuu is your data and it is 
as zigzaggy as it gets, its random.

uuu=rand(N,1).-0.5;

Suppose you are interested in data 
that has a maximum of 18 rad*Hz 
frequency and above that is noise 
for your purposes.

wc=18;
n=10;
[b,a]=butter(n,wc/(N*pi/T));
uuu2=filter(b,a,uuu);

uuu2 is the filtered data that you want.
n is a parameter that designates the 
sharpness of the butterworth filter. 

Consider having an equal amount of 
each frequency. 

uw=ones(N,1);
uuu1=ifft(uw).*(N/T);

now at this point uuu1 is your problematic 
data.

wc=18;
n=10;
[b,a]=butter(n,wc/(N*pi/T));
uuu2=filter(b,a,uuu1);

w=(0:2*pi/T:(N-1)*2*pi/T)';

subplot(2,2,1):plot(w,abs(fft(uuu2)).*(T/N));
title('Filtered Spectra')
subplot(2,2,2):plot(w,abs(fft(uuu1)).*(T/N));
title('Unfiltered Spectra')
subplot(2,2,3):plot(uuu2);
title('Filtered Series')
subplot(2,2,4):plot(uuu1);
title('Unfiltered Series')

Try playing with wc and n and replotting 
several times. When you are satisfied 
with the filter you are about to apply, 
apply it to the real data. 

As you will see n increases sharpness of the 
fall but it also causes some wiggles in the 
frequencies that you want to keep depending 
on what your wc is the degree to this effect 
will change. The idea is to keep the frequencies 
you want to pass as close to 1 in that plot and 
the ones you want to get rid off falling to zero
as fast as possible. 

To have an idea which frequency will look 
how much zigzaggy in time series, make a 
plot out of it and decide if you want to keep 
it or not. ie.

SF=200;
dt=1/SF;
T=10;
w=5;
t=(0:dt:T-dt)';
Ft=sin(w*t);

plot(t,Ft);

Note: This will not filter signals according to 
         amplitude range as in the subject but will
         filter them based on their frequency which 
         what you want as I understand. 



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