Butterworth Filters

Highpass, lowpass, bandpass, and bandstop Butterworth frequency filters.
4.8K Downloads
Updated 15 Oct 2012

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This set of functions is simply four built-in Matlab functions, repackaged for ease of use (Signal Processing Toolbox is required). If you don't want to go through the rigmarole of designing and implementing a filter with normalized frequencies and so forth every time you filter a signal, this package may be for you. If you are a Matlab pro and an expert in digital signal processing, you will probably not be impressed.

Each function takes the form [filtered_signal,filtb,filta] = bandstop_butterworth(inputsignal,cutoff_freqs,Fs,order)

INPUTS:
inputsignal = input time series
cutoff_freqs = filter corner frequencies in the form [f1 f2]
Fs = data sampling frequency
order = order of Butterworth filter

OUTPUTS:
filtered_signal = the filtered time series
filtb, filta = filter numerator and denominator (optional)

EXAMPLE 1:
load train
t = (1:length(y))/Fs;
y_filt = bandstop_butterworth(y,[800 1000],Fs,4); % cut off between 800 Hz and 1000 Hz

figure
plot(t,y,'b',t,y_filt,'r')
xlabel('time in seconds')
box off
legend('unfiltered','filtered')
sound(y,Fs) % play original time series
pause(2) % pause two seconds
sound(y_filt,Fs) % play filtered time series

EXAMPLE 2:
load train
t = (1:length(y))/Fs;
[y_filt,filtb,filta] =bandstop_butterworth(y,[800 1000],Fs,4); % cut off between 800 Hz and 1000 Hz
[h1,f1] = freqz(filtb,filta,256,Fs);

figure
subplot(3,1,1)
plot(t,y,'b',t,y_filt,'r')
xlabel('time in seconds')
box off
text(0,.1,' time series','units','normalized')

subplot(3,1,2)
AX = plotyy(f1,10*log10(abs(h1)),f1,angle(h1),'semilogx');
set(get(AX(1),'ylabel'),'string','gain (dB)')
set(get(AX(2),'ylabel'),'string','phase (rad)')
xlim(AX(1),[min(f1) max(f1)])
xlim(AX(2),[min(f1) max(f1)])
text(0,.1,' filter response','units','normalized')
box off

[Pxx,f] = pwelch(y,512,256,[],Fs,'onesided');
[Pxxf,f_f]= pwelch(y_filt,512,256,[],Fs,'onesided');
subplot(3,1,3)
semilogx(f,10*log10(Pxx))
hold on
semilogx(f_f,10*log10(Pxxf),'r')
xlabel('frequency (Hz)')
ylabel('PSD (dB)')
xlim([min(f1) max(f1)])
box off
legend('unfiltered','filtered','location','northwest')
legend boxoff

Cite As

Chad Greene (2024). Butterworth Filters (https://www.mathworks.com/matlabcentral/fileexchange/38584-butterworth-filters), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2011a
Compatible with any release
Platform Compatibility
Windows macOS Linux
Acknowledgements

Inspired: filter1, plotpsd

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Version Published Release Notes
1.3.0.0

Clarified in the text that the Signal Processing Toolbox is required.

1.2.0.0

Clarified that the signal processing toolbox is required.

1.1.0.0

fixed typo in description text.

1.0.0.0