MATLAB: High Pass Butterworth Filter increases unwanted frequencies using Filtfilt

butterworthfftfilterfiltfiltfrequencyhigh passhighpassMATLAB

Hello,

I am trying to high-pass filter some data using filtfilt. For my application, I only need to effectively remove data close to DC, so I am using a fairly low frequency cutoff.

However, I have noticed that my implementation (butterworth filter using filtfilt) is causing increased spectral content around my cutoff.

Does anyone know why this is happening?

I am thinking it may be a result of having a small ensemble size (50 samples) or possible a filter ripple effect (?)

For example:

N = 50;
data = randn( N,1);
prf = 500;
cutoff = 2;
[B A ] = butter(2, cutoff/ (prf / 2), 'high');
data2 = filtfilt( B,A, data);
figure(); 
plot( linspace(-prf/2, prf/2, 5000), fftshift( abs( fft( data, 5000))), 'k')
hold on;
plot( linspace(-prf/2, prf/2, 5000), fftshift( abs( fft( data2, 5000))), 'b')

Thanks!

Best Answer

First, if you want to eliminate the D-C value, simply subtract the mean of your signal from your signal. You do not need to filter it. (Since you are using the randn function, the mean should already be close to 0.) Butterworth filters are popular because they are easier to design than others. However, using the Signal Processing Toolbox functions, this is no longer a significant problem. Elliptical filters are much more efficient. See the documentaion on ellip (link) and related functions (ellipord, zp2sos, and others) as well.

Second, an order 2 filter of any design is not likely to be very efficient. If you have R2018a or later, use the highpass (link) function, although the related bandpass function is usually a better option, since highpass filters amplify noise. If you use the second ‘d’ output from highpass (or any of the others), use it with filtfilt, not filter.

Related Solutions

MATLAB: How to Butterworth Filter with Bandpass [10 500] with sampling rate 1000

You have to divide your passband and stopband frequencies by the Nyquist frequency to normalise them:

Fs = 1000;                                          % Sampling Frequency
Fn = Fs/2;                                          % Nyquist Frequency
Wp = [10  495]/Fn;                                  % Norrmalised Passband Frequencies
Ws = [5   499]/Fn;                                  % Normalised Stopband Frequencies
Rp =  1;                                            % Passband Ripple (dB)
Rs = 25;                                            % Stopband Ripple (dB)
[n,Wn] = buttord(Wp, Ws, Rp, Rs);                   % Optimal Filter Order
[b,a] = butter(n, Wn);                              % Calculate Filter Coefficients
[sos,g] = tf2sos(b,a);                              % Convert To Second-Order Sections For Stability
figure(1)
freqz(sos, 4096, Fs)                                % Filter Bode Plot

You cannot have any frequency exactly at zero or exactly at the Nyquist frequency, so I designed your passband to be close enough to them to be stable. In your filter, you can also use a high-pass design with a lower cutoff of 10 Hz, since your upper passband is at the Nyquist frequency. The passband and stopband ripple values are necessary to specify in the design but irrelevant to a Butterworth filter. These are acceptable values for most filter designs (for example Chebyshev) that require them.

You would use the ‘sos’ and ‘g’ variables in your actual filter:

filtered_signal = filtfilt(sos, g, signal);

(This design works well in R2016a and should also work in earlier releases.)

MATLAB: Comparison of IIR filters

Your approach appears to be correct. Remember to divide your passband and stopband frequencies by your Nyquist frequency (here 125 Hz) to normalise them.

a. The fvtool graphics are telling you the characteristics of your filter, not the filtering process using filtfilt, that actually produces a maximally-flat-phase filter response.

b. The filter design you choose depends on the result you want. Your lower frequency (at 5 Hz) may make a Chebyshev design more practical, because you have a narrow stopband-to-passband transition in that region. An elliptic filter could give you the same benefits with that. A Butterworth filter can handle that, but takes a bit more effort to design. And then you have to consider the passband and stopband ripple you can tolerate, neither of which is a practical consideration with the flat passband and stopband of a Butterworth filter.

c. Whatever works best with your signal. Filter design (in my experience) is largely heuristic. I usually begin with a Butterworth design because of the flat passband and stopband characteristics. If I need a steep rolloff (for example as you do at the low end), and if the Butterworth filter cannot give the response I want, I consider a Chebyshev II filter because of the flat passband. Another possibility is a relatively high-order FIR filter (see the fir1 documentation).

Note that this is my approach. There is no one best approach, as there is no one best filter design. You have to decide what characteristics are most important, and choose the design that best meets your needs.

Best Answer

Related Solutions

MATLAB: How to Butterworth Filter with Bandpass [10 500] with sampling rate 1000

MATLAB: Comparison of IIR filters

Related Question