MATLAB: Lowpass Filter with Linear Units

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I'm struggling to design a lowpass filter for data that is in a linear unit, not decibels. It's displacement data measured directly by a potentiometer. I'd like to remove noise above approximately 250hz, but I'll need to play around with that number I'm sure.

The data is in a vector.

I don't understand how all the different parameters work, like filter order, ripple, etc. Been frustrating myself all morning trying to sort it out. Any help is more than welcome.

Best Answer

The ‘decibel’ calculation simply converts amplitude to power, and scales it logarithmically. It is convenient with respect to plotting transfer functions and designing filters, and has no effect at all on the actual signal. If you give the filter your data in ‘linear’ amplitude units, the filtered result will be in the same units.

A prototype filter for your signal would be:

signal = ...;                                           % Signal Vector
tv = ...;                                               % Time Vector
Ts = mean(diff(tv));                                    % Sampling Interval
Fs = 1/Ts;                                              % Sampling Frequency (Hz)
Fn = Fs/2;                                              % Nyquist Frequency (Hz)
Wp = 250/Fn;                                            % Passband Frequency (Normalised)
Ws = 252/Fn;                                            % Stopband Frequency (Normalised)
Rp =   1;                                               % Passband Ripple (dB)
Rs =  50;                                               % Stopband Ripple (dB)
[n,Ws] = cheb2ord(Wp,Ws,Rp,Rs);                         % Filter Order
[z,p,k] = cheby2(n,Rs,Ws);                              % Filter Design
[soslp,glp] = zp2sos(z,p,k);                            % Convert To Second-Order-Section For Stability
figure(3)
freqz(soslp, 2^16, Fs)                                  % Filter Bode Plot
filtered_signal = filtfilt(soslp, glp, signal);         % Filter Signal

Note — Your sampling frequency ‘Fs’ must be at least 550 Hz for this filter to work. It has a passband ripple of 1 dB (that is irrelevant here with a Chebyshev Type II filter) and a stopband attenuation of 50 dB. Change those as necessary.

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MATLAB: Removing outliers in data

Although picture may be worth a thousand words, having your data to work with is worth a thousand pictures.

I would begin with a Fourier transform of your data (the fft (link) function) to determine what part of your data are your signal and what part are noise.

Once you have the frequency information, and you know you can filter out the high-frequency noise, a prototype lowpass filter design for you to experiment with is:

Fs = 1000;                                                  % Sampling Frequency (Hz)
Fn = Fs/2;                                                  % Nyquist Frequency (Hz)
Wp = 100/Fn;                                                % Passband Frequency (Normalised)
Ws = 105/Fn;                                                % Stopband Frequency (Normalised)
Rp =   1;                                                   % Passband Ripple (dB)
Rs = 150;                                                   % Stopband Ripple (dB)
[n,Ws] = cheb2ord(Wp,Ws,Rp,Rs);                             % Filter Order
[z,p,k] = cheby2(n,Rs,Ws);                                  % Filter Design
[soslp,glp] = zp2sos(z,p,k);                                % Convert To Second-Order-Section For Stability
figure(3)
freqz(soslp, 2^16, Fs)                                      % Filter Bode Plot
filtered_signal = filtfilt(soslp, glp, original_signal);    % Filter Signal

This design has a much steeper transition region than your Butterworth design, so it may have less effect on the part of your signal you want to retain. Make the appropriate changes in the parameters for your signal.

MATLAB: Design band pass filter

Here is prototype code I used for a different project that you can adapt, if you want an IIR filter:

Fs = 250;                                                       % Sampling Frequency
Fn = Fs/2;                                                      % Nyquist Frequency
Ts = 1/Fs;                                                      % Estimate Sampling Interval
t = linspace(0, numel(EKG), numel(EKG))/Fs;
Wp = [2  90]/Fn;                                                % Normalised Passband (Passband =  2 Hz To  90 Hz)
Ws = [1 100]/Fn;                                                % Normalised Stopband (Passband =  1 Hz To 100 Hz)
Rp =  1;                                                        % Passband Ripple/Attenuation
Rs = 50;                                                        % Stopband Ripple/Attenuation
[n,Wp] = ellipord(Wp, Ws, Rp, Rs);                              % Calculate Elliptic Filter Optimum Order
[z,p,k] = ellip(n, Rp, Rs, Wp,'bandpass');                      % Elliptic Filter
[sos,g] = zp2sos(z,p,k);                                        % Convert To Second-Order-Sections For Stability
figure
freqz(sos,2^16,Fs)
filtered_signal = filtfilt(sos,g,signal);

There are a number of FIR designs on Answers as well (I have posted many of them), although I usually reserve those for filters with multiple passbands and stopbands.

Best Answer

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MATLAB: Removing outliers in data

MATLAB: Design band pass filter

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