# Digital Filters with GNU Octave

The following scripts use Octave's Signal Processing Toolbox; If you don't have the toolbox installed, get it from Octave-Forge.

It is easy to design a low pass filter:

% The sampling frequency in Hz. Fsam = 1500; % Nyquist frequency, in Hz. % The Nyquist frequency is half your sampling frequency. Fnyq = Fsam/2; % The cut-off frequency of your Low pass filter in Hz. % This frequency must be greater than 0 and less than Fnyq. Fc=1/4; % Create a first-order Butterworth low pass. % The returned vectors are of legth n. % Thus a first order filter is created with n = 2. [b,a]=butter(2, Fc/Fnyq); % clear unused variables clear("Fnyq", "Fc");

Now let's test the filter. First, let's generate a input signal containing components at 1 Hz, 200 Hz and Gaussian white noise.

% Create a 5 seconds signal with 3 components: % a 1 Hz and a 200 Hz sinusoidal component and some gaussian noise. t=0:1/Fsam:5; input=sin(2*pi*t) + sin(2*pi*200*t) + randn(size(t)); % Apply the filter to the input signal and plot input and output. output=filter(b,a,input); plot(t, [input; output])

You can also compare the input and output signals in the frequency domain:

plot([abs(fft(input)); abs(fft(output))]) find(abs(fft(input)) > 3000) find(abs(fft(output)) > 3000)

Thanks to Greg Locock for pointing out that rand() does not yield Gaussian noise.