I want to separate the signal from the noise with the help of a low pass filter.

Hello to everyone. I had many signals in the time domain. I first converted these signals to the frequency domain with fft. I am sharing the image of the signal in the frequency domain with you. What I need to do now is to separate the noise from the signal by passing this noisy signal through a low pass filter. but I don't know how to do it as I've never done it before. I would be very happy if you could help with this. They said I can use the firpm command for the filter.

    %the code I used to convert to frequency domain
    Tt = Time{i,m};
    x = signal{i,m};
    L = length(Tt);                                                         
    Ts = mean(diff(Tt));                                                   
    Fs = 1/Ts;                                                             
    Fn = Fs/2; 
    X = fftshift(fft(x)/L);                                                  
    Fv2 = linspace(-Fn, Fn, L);

[Star Strider]

I do not see any significant noise.

First, elimnate the D-C offset by changing the ‘X’ calculation to —

X = fftshift(fft(x - mean(x))/L);   

Then, it might be possible to see the noise.

You can then elimiinate frequency-limited noise with a frequency selective filter (the filter design depends on the noise spectrum), however it is not possible to eliminate broadband noise with a frequency--selective filter, and other techniques (wavelets, Savitzky-Golay filter) would be necessary to reduce it significantly.

[studentmatlaber]

I removed the offset from the signal before converting the signal to the frequency domain. now I don't know how to pass the low pass filter.

[Star Strider]

There is a significant peak near 0 Hz, so filtering it out with a lowpass filter would likely not work. I would have to have the original, un-processed time-domain signal to experiment with in order to provide a useful approach.

[studentmatlaber]

I can send the file from the contact section if you want.

[Star Strider]

I prefer that it be uploaded here. It is easier for me to work with.

[studentmatlaber]

@Star Strider Actually I have 24 .mat files, but I can throw 1 of them from here.

Answer 1

[Star Strider]

I could not figure out which of those signals you want to filter, so I arbitrarily chose ‘t1’ and ‘y1’.

They are not consistently sampled, so I used the resample function to correct that. This will eliminate the high-frequency noise, however I was not able to eliminate the baseline offset using a bandpass filter, since I do not know what constitutes the signal and what constitutes the baseline drift. I leave that to you to experiment with, using:

[yfilt,df] = bandpass(xr, [0.005 0.04], Fs, 'ImpulseResponse','iir');

Experiment with the lower passband frequency to get the result you want.

Try this —

LD = load('Data4.mat');

t = LD.t1;
y = LD.y1;

Tt = t;
x = y;
[xr,Ttr] = resample(x,Tt,4.5);
L = numel(Ttr);
Ts = mean(diff(Ttr));
Tsd = std(diff(Ttr));
Fs = 1/Ts;
Fn = Fs/2;
X = fftshift(fft(xr-mean(xr))/L);
Fv2 = linspace(-Fn, Fn, L);

figure;
plot(Fv2, abs(X));
grid;
xlabel('Frequency');
ylabel('Amplitude');
xlim([-0.25 0.25])

[yfilt,df] = lowpass(xr, 0.04, Fs, 'ImpulseResponse','iir');

figure
subplot(2,1,1)
plot(Ttr, xr, '-b')
grid
title('Original Signal')
subplot(2,1,2)
plot(Ttr, yfilt, '-r')
grid
title('Filtered Signal')

I cannot run this in the online application since I cannot load .mat files in it.

[Star Strider]

I did not realise that this is a homework assignment!

The documentation for firpm has all the information you need to use the function correctly. See specifically the section on Parks-McClellan Lowpass Filter .

Experiment to get the result you want.

[studentmatlaber]

this is not a homework. I'm doing my own project and getting help from my teacher. you don't need to be angry

[Star Strider]

I’m not angry! It’s just that the policy here on Answers is to give hints for homework problems, rather than complete code. If it is not a homework problem, I can provide more information.

I calculated and plotted the fft to understand where the optimal lowpass filter cutoff should be, that being at 0.4 frequency units. There is nothing particularly notable about that choice, since it simply seems to be appropriate to me. Experiment with other values to see what works best for that application. I would follow the documentation example, specifically starting with the firpmord function. (I usually use functions other than firpm to design filters, so I do not have extensive experience with it. I will help as I can if you have problems with it.)

Use freqz to visualise the filter Bode plot before you use it to filter the signals, so you know that the filter is designed correctly and is going to do what you want.

[studentmatlaber]

Hi. @Star StriderI wrote this code fpass=0.04hz fstop=0.5hz

[n, fo, ao, w] = firpmord ([0.04 0.5], [1 0], [0.001 0.01], Fs);
    b = firpm (n, fo, ao, w);
    Hd = dfilt.dffir(b);
    Filtered_signal = filter(Hd,signal{i,m});
    plot(Time{i,m},Filtered_signal,Time{i,m},signal{i,m});

fpass=0.04hz fstop=0.09hz

When I choose fstop value large, it is not ideal filter, but when I choose lower fstop value, the signal slips. How can I solve this problem?

[Star Strider]

The problem may be in using filter, since it causes phase delay and phase distortion. Use the filtfilt function instead.

[studentmatlaber]

@Star Strider Hello again, sorry for asking questions all the time. There was no phase difference when I used the filtfilt command. however, this command does not work with any value other than [0.04 0.5]. When you use these values, too much noise remains in the signal. I want to narrow this range. Do you have an idea?

[n, fo, ao, w] = firpmord ([0.04 0.5], [1 0], [0.001 0.001], Fs{i,m});

[Star Strider]

That vector defines the frequencies, and they are not allowed to be less than or equal to 0 or greater than ‘Fs/2’. Check Fs and make appropriate changes depending on that value.

That is the only possibility I can think of.

Answer 2

[Image Analyst]

What is i and m?

What I'd do it do just zero out the middle of the FFT signal to "zero out" high frequencies. Or zero out the beginning and end of the fft if you shifted it with fftshift() so that the zero frequency point is in the middle. Then inverse transform with ifft(). It's kind of old school and primitive and you have to know what range you want to zero out over (you can experiment). It's probably not as sohpisticated as what Star Strider recommended (certain special MATLAB functions), but this "manual" way might be fine for you.

Answer 3

[fyp matlab]

you can design low pass filter or any kind of filter using:

filterDesigner

command .