Hello Everyone, I need to pass a low pass filter in this plot and I can't find the best way to do that. Someone can help me? Thanks.

Hello Everyone, I need to pass a low pass filter in this plot and I can't find the best way to do that. Someone can help me? Thanks.

I'm using this filter and I'm not getting any results

[b,a] = butter(8,0.1,'low'); 
y = filtfilt(b,a,pz);

[Walter Roberson]

Can you attach your data, perhaps as .mat file ?

[Rita Gama]

Yes.

Answer 1

[Star Strider]

Use the freqz function (or freqs linked to in that documentation page, if it is a continuous-time filter) —

[b,a] = butter(8,0.1,'low'); 

figure
freqz(b, a, 2^16)

Or, if the intent is the impulse response, the impz function —

figure
impz(b,a)

.

[Walter Roberson]

It is not clear to me how this filters existing data stored in the variable pz ?

[Rita Gama]

The variable pz corresponds to the coordinates of a point cloud. But there is a lot of noise in them and what I'm trying to do is reduce that noise. But I'm not having any success.

[Star Strider]

Experiment with filters and other options —

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/764556/DATA.mat','filetype','text');
pz = T1.pz;
Fs = 1;                                             % Guess Sampling Frequency
Fn = 0.5;                                           % Nyquist Frequency
L = numel(pz);
FTpz = fft(pz)/L;
Fv = linspace(0, 1, fix(L/2)+1)*Fn;
Iv = 1:numel(Fv);

figure
semilogx(Fv, mag2db(abs(FTpz(Iv))*2))
grid
xlim([0  0.025])
xlabel('Frequency')
ylabel('Amplitude')

Wp = 2.0E-4;
Ws = 2.5E-4;
Rp =  1;
Rs = 75;
[n,Wp] = ellipord(Wp,Ws,Rp,Rs);
[z,p,k] = ellip(n,Rp,Rs,Wp);
[sos,g] = zp2sos(z,p,k);                            % Lowpass Is The Default For All Filters

figure
freqz(sos, 2^16, Fs)
set(subplot(2,1,1),'XLim',[0  0.001])
set(subplot(2,1,2),'XLim',[0  0.001])
sgtitle('Filter Bode Plot')

pzFilt = filtfilt(sos,g,pz);

figure
plot(pz)
hold on
plot(pzFilt)
hold off
legend('Original','Filtered')

So, there is no effective way to filter this using a frequency-selective filter, since that is simply not appropriate here.

A better option would be smoothdata (introduced in R2017b) —

Window = 5000;
pzSmooth = smoothdata(pz, 'sgolay', Window);

figure
plot(pz)
hold on
plot(pzSmooth, '-r', 'LineWidth',2)
hold off
legend('Original','Smoothed')

An alternative to smoothdata would be sgloayfilt.

Experiment with different values for ‘Window’ to get the desired result. Higher values will produce a smoother result, however sacrificing detail.

.

[Rita Gama]

Star....Thank you very much for your help. That's just what I wanted to get. You are the best.

[Star Strider]

As always, my pleasure!

Thank you!

.

Answer 2

[Walter Roberson]

You are getting differences near the sharp edges.

filename = 'https://www.mathworks.com/matlabcentral/answers/uploaded_files/764556/DATA.mat';
pz = readmatrix(filename, 'filetype', 'text');
[b,a] = butter(8,0.1,'low'); 
y = filtfilt(b,a,pz);
plot(pz, 'k.-', 'displayname', 'original');
hold on
plot(y, 'b+-', 'displayname', 'filtered');
hold off
legend show
xlim([6050 6199])

figure
plot(pz - y, 'displayname', 'pz-y')
legend show

[Rita Gama]

Thanks for your help Walter. Just more ne question, do you think this is the best filter to use here to reduce noise?

[Walter Roberson]

I am having difficulty at the moment figuring out how a vector of values might correspond to values from a point cloud, so I am having difficulty judging what kind of noise might be present or what an effective way of reducing it might be.

The only idea I have come up with so far is that you might possibly be scanning a linear structure with pits, such as for CDs.