FIltered signal not matching with the original signal.

Hello, im new to filter design, as you can probably tell. I have a signal from a wave guage measuring depth with time, The signal has very high low end frequencies so i am trying to apply a short low pass filter to smooth the signal, im not sure if it is my kernal or order choice but when i plot the original signal with the filtered signal, the filtered signal has lost magnitude. Its was originally intended to be a band stop filter so might not be consistant the whole way through. At this stage im completely stuck and any healp would greatly apreciated.

Thank you so much for your time,

clc



srate = 128;%Hz Sample Rate 
nyquist = srate/2;
coff = [7];%Cut off or range
transw = .1;% randomly set
shape = [1 1 0 0];
frex = [1 coff(1)-coff(1)*transw coff(1) nyquist]/nyquist;
hz = linspace(0,srate,8321);%8321 is the number of samples in the data

% Loop for best matching order
order1 = (.2*srate/coff(1))/(srate/1000);%randomly set as I was trying different orders
order2 = (.3*srate/coff(1))/(srate/1000);
orders = round(linspace(order1,order2,2));%step count

fkernx = zeros(length(orders),8321);

figure(1)
for k = 1:length(orders);
    
    fkern = firls(orders(k),frex,shape);
    n(k) = length(fkern);
    
    fkernx(k,:) = abs(fft(fkern,8321)).^2;
    
    subplot(2,1,1)
    hold on
    plot((1:n(k))-n(k)/2,fkern+.1*k)
end



subplot(2,2,3)
hold on
plot(hz,fkernx)
plot(frex*nyquist,shape,'ro-')
xlim([0 64])


% % Loop for best matching transwidth

transwidth = linspace(.1,.4,4);
fkerxx = zeros(length(transwidth),8321);
orderl = round(order1);
figure(2)
for t = 1:length(transwidth);
    
    frex2 = [1 coff(1)-coff(1)*transwidth(t) coff coff(2)+coff(2)*transwidth(t) nyquist]/nyquist;
    fkern2 = firls(2,frex2,shape);
    n(t) = length(fkern2);
    
    fkernxx(t,:) = abs(fft(fkern2,8321).^2);
    
    subplot(2,1,1)
    hold on
    plot((1:n(t))-n(t)/2,fkern2+0.1*t)
end

subplot(2,1,2)
hold on
plot(hz,fkernxx)
plot(frex2*nyquist,shape,'ro-') 

%Final Filter Design
orderx = round((.3*srate/coff(1))-(srate/1000));%Use best matchig order here
transwidthx = 0.1;
frex3 = [1 coff(1)-coff(1)*transw coff nyquist]/nyquist;
filt28 = firls(orderx,frex3,shape); 

%Apply filter design to signal (PDg1)
PDg1s = filtfilt(filt28,1,PDg1);
detfftp1 = detrend(PDg1s);
fftp1 = abs(fft(detfftp1));
%Frequency domain after filter 
figure(3)
semilogy(hz, fftp1)

figure(4)
hold on
plot(PT5, PDg1,'r');
plot(PT5, PDg1s,'b')%plot smoothed data
legend('Original','Filtered')
xlabel('TIme (s)')
ylabel('Depth (m)')
title('Depth Against Time')

Answer 1

[Mathieu NOE]

hello

I see that you are doing a detrend action on your data. This will remove the dc (mean) value of the signal , so no surprise that the output is shifted.

My suggestion :

T = csvread('ExampleData PDg1 and time.txt');
y = T(:,1);

Fs = 128;
dt = 1/Fs; 

samples = length(y);
t = (0:samples-1)*dt;

%%% filter data %%%
N = 250;
y_LP = smoothdata(y, 'gaussian' , N); % low pass filtered data

%%% plot data %%%
figure(1)
plot(t,y,t,y_LP);legend('Raw','low pass filtered');
title(['Data samples at Fs = ' num2str(Fs) ' Hz / filtered with smoothdata' ]);
xlabel('Time (hours) ')
ylabel('Depth (m) ')

[indigo fgo]

Thank you for taking the time to answer. I am only using the detrend function for the frequency domain and not for the plotting of the data. Do you know of way to set a non abritry window spacing for the smoothdata function?

[Mathieu NOE]

hello

the window length has been adjusted just by visual aspect... if you want something like a low pass filter with specific / controlled parameters like type / order / cut off frequency , we can use other approaches :

very similar plot :

%%% filter data with Butterworth low pass filter %%%
NN = 2; % filter order
flo = 0.5; % cut off LP frequency
Wn = 2/Fs*flo;
[B,A] = butter(NN,Wn);

y_LP = filtfilt(B,A,y - y(1)); % shift dc by removal of  first sample (to avoid initial transient)
y_LP = y_LP + y(1);  % put back the shifted value in the output after filtering
%%% plot data %%%
figure(2)
plot(t,y,t,y_LP);legend('Raw','low pass filtered');
title(['Data samples at Fs = ' num2str(Fs) ' Hz / filtered with smoothdata' ]);
xlabel('Time (hours) ')
ylabel('Depth (m) ')

[indigo fgo]

Thank you very much! Can I ask why you chose an order of 2 and a cut off of 0.5?

[Mathieu NOE]

you can modify the parameters if you want to see how that will affect the result

my selection is only because it smooth enough the signal without removing the global shape

[Mathieu NOE]

hello

if my answer has helped you, do you consider accepting it ?