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Butterworth Filters

version 1.3 (120 KB) by

Highpass, lowpass, bandpass, and bandstop Butterworth frequency filters.



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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)

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

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

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

  xlabel('time in seconds')
  box off
  sound(y,Fs) % play original time series
  pause(2) % pause two seconds
  sound(y_filt,Fs) % play filtered time series

  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);

  xlabel('time in seconds')
  box off
  text(0,.1,' time series','units','normalized')

  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');
  hold on
  xlabel('frequency (Hz)')
  ylabel('PSD (dB)')
  xlim([min(f1) max(f1)])
  box off
  legend boxoff

Comments and Ratings (6)

sam zhpour

I downloaded that file and I don't know where to paste those files..

Chad Greene

Chad Greene (view profile)

I have rewritten these filters as a better single function called filter1. The new filter1 function has better error checking and is a bit more user friendly. I recommend using filter1 instead of the filters on this page. Get filter1 here:


Paul (view profile)

Chad Greene

Chad Greene (view profile)

Oh shoot! I forgot about that! Thanks for letting us know, Jan.

Jan Simon

Jan Simon (view profile)

You need the Signal Processing Toolbox for the BUTTER command.



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


fixed typo in description text.


Clarified that the signal processing toolbox is required.

MATLAB Release
MATLAB 7.12 (R2011a)

Inspired: plotpsd, filter1

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