Signal Analyzer Lowpass filter overshoots input signal

Hi everyone,

i am trying to apply a lowpass filter from the signal analyzer app to a simulink signal.

As you can see in the screenshot, i am trying to allow frequencies only below 5 cycles/min - other than that i am using the default parameters.

When i apply the filter to the signal and compare it to the original signal, the filtered signal overshoots the original one.

As i am new to filtering, i would like to ask if there is a way to filter the signal without overshooting?

Thanks for any help

[Mathieu NOE]

hello

it's rather difficult to make an opinion and suggestion based only on this picture

can you share some data ?

[tired]

Hi,

yeah sure.

i had to zip the file cause its rather big

To use the data in the signal analyzer app i use a timeseries that is generated from "to workspace" block in simulink

Answer 1

[Mathieu NOE]

hello again

so here you can see your signals (in time and frequency domain) before and after low pass filtering (I used here filtfilt instead of filter to avoid phase distorsion if that is important for your application)

Zero-phase digital filtering - MATLAB filtfilt - MathWorks France

here a view on the first samples

code :

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% load signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
load('load_data.mat')  % Fs = 10 Hz
time = ans(1,:)'; % in s
signal = ans(2,:)';

dt = mean(diff(time)); % 
Fs = 1/dt;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% low pass  filter section %%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %allow frequencies only below 5 cycles/min (= 0.0833 Hz)
fc = 0.0833;      % Hz
N_bpf = 2;           % filter order

[b,a] = butter(N_bpf,2/Fs*fc);
signal_filtered = filtfilt(b,a,signal);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 1000;    % 
OVERLAP = 0.75;  % percentage of overlap

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 1 : time domain plot
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(1),
plot(time,signal,'b', time,signal_filtered,'r');grid on
title(['Time plot  / Fs = ' num2str(Fs) ' Hz / raw data ']);
xlabel('Time (s)');ylabel('Amplitude');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 2 : averaged FFT spectrum
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[freq, spectrum_raw] = myfft_peak(signal,Fs,NFFT,OVERLAP);
[freq, spectrum_filtered] = myfft_peak(signal_filtered,Fs,NFFT,OVERLAP);

figure(2),semilogx(freq,20*log10(spectrum_raw),'b',freq,20*log10(spectrum_filtered),'r');grid on
df = freq(2)-freq(1); % frequency resolution 
title(['Averaged FFT Spectrum  / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(df,3) ' Hz ']);
xlabel('Frequency (Hz)');ylabel('Amplitude (dB (L))');
legend('raw','filtered');


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function  [freq_vector,fft_spectrum] = myfft_peak(signal, Fs, nfft, Overlap)
% FFT peak spectrum of signal  (example sinus amplitude 1   = 0 dB after fft).
% Linear averaging
%   signal - input signal, 
%   Fs - Sampling frequency (Hz).
%   nfft - FFT window size
%   Overlap - buffer percentage of overlap % (between 0 and 0.95)

[samples,channels] = size(signal);

% fill signal with zeros if its length is lower than nfft
if samples<nfft
    s_tmp = zeros(nfft,channels);
    s_tmp((1:samples),:) = signal;
    signal = s_tmp;
    samples = nfft;
end

% window : hanning
window = hanning(nfft);
window = window(:);

%    compute fft with overlap 
 offset = fix((1-Overlap)*nfft);
 spectnum = 1+ fix((samples-nfft)/offset); % Number of windows
%     % for info is equivalent to : 
%     noverlap = Overlap*nfft;
%     spectnum = fix((samples-noverlap)/(nfft-noverlap));	% Number of windows

    % main loop
    fft_spectrum = 0;
    for i=1:spectnum
        start = (i-1)*offset;
        sw = signal((1+start):(start+nfft),:).*(window*ones(1,channels));
        fft_spectrum = fft_spectrum + (abs(fft(sw))*4/nfft);     % X=fft(x.*hanning(N))*4/N; % hanning only 
    end
    fft_spectrum = fft_spectrum/spectnum; % to do linear averaging scaling

% one sidded fft spectrum  % Select first half 
    if rem(nfft,2)    % nfft odd
        select = (1:(nfft+1)/2)';
    else
        select = (1:nfft/2+1)';
    end
fft_spectrum = fft_spectrum(select,:);
freq_vector = (select - 1)*Fs/nfft;
end

[tired]

hello,

thank you very much for your help - thats exactly what i needed.

Sadly, when i run the code my plot still overshoots the original signal

[Mathieu NOE]

hello

that is true , forgot that point ! I was focusing only on the low pass filtering topic .

I changed from Butterworth to Bessel low pass filters to avoid overshoots , seems now much better :

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% load signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
load('load_data.mat')  % Fs = 10 Hz
time = ans(1,:)'; % in s
signal = ans(2,:)';

dt = mean(diff(time)); % 
Fs = 1/dt;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% low pass  filter section %%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %allow frequencies only below 5 cycles/min (= 0.0833 Hz)

% Bessel filter is analog filter
% Specify cut-off as rad/second
fc = 0.0833;      % Hz
w0 = 2*pi*fc;
N = 5;           % filter order
[z,p,k] = besself(N, w0,'low'); % zero, pole and gain form
% Convert to digital fileter
[zd,pd,kd] = bilinear(z,p,k,Fs);   % z-domain zero/pole/gain
[sos,g] = zp2sos(zd,pd,kd);        % convert to second order section 

signal_filtered = filtfilt(sos, g,signal);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 1000;    % 
OVERLAP = 0.75;  % percentage of overlap

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 1 : time domain plot
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(1),
plot(time,signal,'b', time,signal_filtered,'r');grid on
title(['Time plot  / Fs = ' num2str(Fs) ' Hz / raw data ']);
xlabel('Time (s)');ylabel('Amplitude');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 2 : averaged FFT spectrum
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[freq, spectrum_raw] = myfft_peak(signal,Fs,NFFT,OVERLAP);
[freq, spectrum_filtered] = myfft_peak(signal_filtered,Fs,NFFT,OVERLAP);

figure(2),semilogx(freq,20*log10(spectrum_raw),'b',freq,20*log10(spectrum_filtered),'r');grid on
df = freq(2)-freq(1); % frequency resolution 
title(['Averaged FFT Spectrum  / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(df,3) ' Hz ']);
xlabel('Frequency (Hz)');ylabel('Amplitude (dB (L))');
legend('raw','filtered');


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function  [freq_vector,fft_spectrum] = myfft_peak(signal, Fs, nfft, Overlap)
% FFT peak spectrum of signal  (example sinus amplitude 1   = 0 dB after fft).
% Linear averaging
%   signal - input signal, 
%   Fs - Sampling frequency (Hz).
%   nfft - FFT window size
%   Overlap - buffer percentage of overlap % (between 0 and 0.95)

[samples,channels] = size(signal);

% fill signal with zeros if its length is lower than nfft
if samples<nfft
    s_tmp = zeros(nfft,channels);
    s_tmp((1:samples),:) = signal;
    signal = s_tmp;
    samples = nfft;
end

% window : hanning
window = hanning(nfft);
window = window(:);

%    compute fft with overlap 
 offset = fix((1-Overlap)*nfft);
 spectnum = 1+ fix((samples-nfft)/offset); % Number of windows
%     % for info is equivalent to : 
%     noverlap = Overlap*nfft;
%     spectnum = fix((samples-noverlap)/(nfft-noverlap));	% Number of windows

    % main loop
    fft_spectrum = 0;
    for i=1:spectnum
        start = (i-1)*offset;
        sw = signal((1+start):(start+nfft),:).*(window*ones(1,channels));
        fft_spectrum = fft_spectrum + (abs(fft(sw))*4/nfft);     % X=fft(x.*hanning(N))*4/N; % hanning only 
    end
    fft_spectrum = fft_spectrum/spectnum; % to do linear averaging scaling

% one sidded fft spectrum  % Select first half 
    if rem(nfft,2)    % nfft odd
        select = (1:(nfft+1)/2)';
    else
        select = (1:nfft/2+1)';
    end
fft_spectrum = fft_spectrum(select,:);
freq_vector = (select - 1)*Fs/nfft;
end

[tired]

Hi,

thank you very much - that works like a charm!

Just for interest:

Is it also possible to design a filter that keeps the filtered signal always below the original Signal?

Meaning that the filtered signal approximates the originial signal at a lower amplitude?

(I tried to visualize what i mean by drawing a line into the screenshot)

[Mathieu NOE]

sure

I introduces a scale factor (0.9) on the y data so the filtered line is below

see these lines

%apply a y scale factor (will shift the filtered curve downwards)
ysc_factor = 0.9;
signal_filtered = ysc_factor*signal_filtered;

full code

    
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% load signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
load('load_data.mat')  % Fs = 10 Hz
time = ans(1,:)'; % in s
signal = ans(2,:)';

dt = mean(diff(time)); % 
Fs = 1/dt;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% low pass  filter section %%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %allow frequencies only below 5 cycles/min (= 0.0833 Hz)

% Bessel filter is analog filter
% Specify cut-off as rad/second
fc = 0.0833;      % Hz
w0 = 2*pi*fc;
N = 5;           % filter order
[z,p,k] = besself(N, w0,'low'); % zero, pole and gain form
% Convert to digital fileter
[zd,pd,kd] = bilinear(z,p,k,Fs);   % z-domain zero/pole/gain
[sos,g] = zp2sos(zd,pd,kd);        % convert to second order section 

signal_filtered = filtfilt(sos, g,signal);

%apply a y scale factor (will shift the filtered curve downwards)
ysc_factor = 0.9;
signal_filtered = ysc_factor*signal_filtered;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 1000;    % 
OVERLAP = 0.75;  % percentage of overlap

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 1 : time domain plot
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(1),
plot(time,signal,'b', time,signal_filtered,'r');grid on
title(['Time plot  / Fs = ' num2str(Fs) ' Hz / raw data ']);
xlabel('Time (s)');ylabel('Amplitude');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 2 : averaged FFT spectrum
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[freq, spectrum_raw] = myfft_peak(signal,Fs,NFFT,OVERLAP);
[freq, spectrum_filtered] = myfft_peak(signal_filtered,Fs,NFFT,OVERLAP);

figure(2),semilogx(freq,20*log10(spectrum_raw),'b',freq,20*log10(spectrum_filtered),'r');grid on
df = freq(2)-freq(1); % frequency resolution 
title(['Averaged FFT Spectrum  / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(df,3) ' Hz ']);
xlabel('Frequency (Hz)');ylabel('Amplitude (dB (L))');
legend('raw','filtered');


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function  [freq_vector,fft_spectrum] = myfft_peak(signal, Fs, nfft, Overlap)
% FFT peak spectrum of signal  (example sinus amplitude 1   = 0 dB after fft).
% Linear averaging
%   signal - input signal, 
%   Fs - Sampling frequency (Hz).
%   nfft - FFT window size
%   Overlap - buffer percentage of overlap % (between 0 and 0.95)

[samples,channels] = size(signal);

% fill signal with zeros if its length is lower than nfft
if samples<nfft
    s_tmp = zeros(nfft,channels);
    s_tmp((1:samples),:) = signal;
    signal = s_tmp;
    samples = nfft;
end

% window : hanning
window = hanning(nfft);
window = window(:);

%    compute fft with overlap 
 offset = fix((1-Overlap)*nfft);
 spectnum = 1+ fix((samples-nfft)/offset); % Number of windows
%     % for info is equivalent to : 
%     noverlap = Overlap*nfft;
%     spectnum = fix((samples-noverlap)/(nfft-noverlap));	% Number of windows

    % main loop
    fft_spectrum = 0;
    for i=1:spectnum
        start = (i-1)*offset;
        sw = signal((1+start):(start+nfft),:).*(window*ones(1,channels));
        fft_spectrum = fft_spectrum + (abs(fft(sw))*4/nfft);     % X=fft(x.*hanning(N))*4/N; % hanning only 
    end
    fft_spectrum = fft_spectrum/spectnum; % to do linear averaging scaling

% one sidded fft spectrum  % Select first half 
    if rem(nfft,2)    % nfft odd
        select = (1:(nfft+1)/2)';
    else
        select = (1:nfft/2+1)';
    end
fft_spectrum = fft_spectrum(select,:);
freq_vector = (select - 1)*Fs/nfft;
end

[tired]

okay, i see.

Thanks again for your help and the detailed information that you provided!

Very much appreciated!

Have a great weekend.

[Mathieu NOE]

as always, my pleasure

and have a nice week end too