How to filter? (Kalman, Narrow Bandpass , Low Pass)

Hello,

I have a signal which I need to filter them with three filters.

[Star Strider]

I’m not certain what you’re doing or what your objective is. I would instead use two serial cascaded digital filters, the first a bandpass filter with a low-frequency cutoff of 0.5-1.5 Hz and a high-frequency cutoff of 30 Hz, then the notch (narrow bandstop) filter with a normalised frequency of 1. A Chebyshev Type II design would likely be best.

Give that a go and see if it does what you want.

[Bob]

Thanks for your answer,

Could you provide me a code or an example since I don't know many things about filters?

Answer 1

[Star Strider]

Filter design, implementation, and plots:

D = load('Xaris load.mat');
t = D.t;
Xs_ddot = D.Xs_ddot;
Xu_ddot = D.Xu_ddot;

Ts = mean(diff(t));                                         % Sampling Interval
Fs = 1/Ts;                                                  % Sampling Frequency
Fn = Fs/2;                                                  % Nyquist Frequency

Wp = [3  25]/Fn;                                            % Normalised Paassband
Ws = Wp .* [0.2  1.1];                                      % Normalised Stopband
Rp =  1;                                                    % Passband Ripple
Rs = 30;                                                    % Stopband Ripple
[n, Wn] = buttord(Wp,Ws,Rp,Rs);                             % Bandpass Filter Design
[b,a]   = butter(n,Wn,'bandpass');                          % Choose Butterworth
[bp_sos,bp_g] = tf2sos(b,a);                                % Use SOS For Stability

Rs = 10;
Rp = 20;
Ws = [9.95  10.05]/Fn;
n = 2;
[b,a] = cheby2(n,Rs,Ws,'stop');                             % Bandstop (Notch) Filter Design
[bs_sos,bs_g] = tf2sos(b,a);

figure(1)
freqz(bp_sos,1024,Fs)                                       % Bandpass Filter Bode Plot

figure(2)
freqz(bs_sos,1024,Fs)                                       % Bandstop Filter Bode Plot

Xs_bp  = filtfilt(bp_sos, bp_g, Xs_ddot);                   % Filter Signals
Xs_out = filtfilt(bs_sos, bs_g, Xs_bp);

Xu_bp  = filtfilt(bp_sos, bp_g, Xu_ddot);
Xu_out = filtfilt(bs_sos, bs_g, Xu_bp);

figure(3)
subplot(2,1,1)
plot(t, Xs_ddot)
title('Unfiltered  ‘Xs\_ddot’')
grid
subplot(2,1,2)
plot(t, Xs_out)
title('Filtered ‘Xs\_ddot’')
grid

figure(4)
subplot(2,1,1)
plot(t, Xu_ddot)
title('Unfiltered ‘Xu\_ddot’')
grid
subplot(2,1,2)
plot(t, Xu_out)
title('Filtered ‘Xu\_ddot’')
grid