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Butterworth Filters

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Butterworth Filters

by

Chad Greene (view profile)

 

11 Oct 2012 (Updated )

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

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Description

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

Required Products Signal Processing Toolbox
MATLAB
MATLAB release MATLAB 7.12 (R2011a)
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Comments and Ratings (3)
31 Oct 2013 Paul

Paul (view profile)

 
12 Oct 2012 Chad Greene

Chad Greene (view profile)

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

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12 Oct 2012 Jan Simon

Jan Simon (view profile)

You need the Signal Processing Toolbox for the BUTTER command.

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Updates
12 Oct 2012

Clarified that the signal processing toolbox is required.

12 Oct 2012

fixed typo in description text.

15 Oct 2012

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

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