How to filter signals properly?

Hi,

I have a .mat file which is given in the attachments. I'd like to apply low pass filter to it. So, I might be able to analyse it properly. For this purpose, I'd like to use designfilt() function. How can I properly construct a .m file to filter my signal?

Ts = 0.005;                                                     % Sampling Interval (s)
Fs = 1/Ts;                                                      % Sampling Frequency (Hz)

%d=designfilt('lowpassfir', 'FilterOrder', 100, 'CutoffFrequency', 20, 'SampleRate', Fs);
d=designfilt('lowpassfir','PassbandFrequency',0.25,'StopbandFrequency',0.35,'PassbandRipple',0.5,'StopbandAttenuation',65,'DesignMethod','kaiserwin');
y=filter(d,sampleSignal);
plot(x,'--');
hold on
plot(y)

Thank you.

[Walter Roberson]

What is x?

[Hasan Kaan Tuna]

x is the values inside the sampleSignal.mat

[Walter Roberson]

whos -file sampleSignal

  Name                   Size              Bytes  Class     Attributes

  sampleSignal      387196x1             3097568  double              

There is no x inside that .mat file.

[Hasan Kaan Tuna]

Just define x with the values inside the sampleSignal.mat...

Answer 1

[Star Strider]

The filter is not going to do much actual filtering.

Try this —

LD = load('sampleSignal.mat');
sampleSignal = LD.sampleSignal;
L = size(sampleSignal,1);
Ts = 0.005;                                                     % Sampling Interval (s)
Fs = 1/Ts;                                                      % Sampling Frequency (Hz)
t = linspace(0, L-1, L)/Fs;                                     % Time Vector


%d=designfilt('lowpassfir', 'FilterOrder', 100, 'CutoffFrequency', 20, 'SampleRate', Fs);
d=designfilt('lowpassfir','PassbandFrequency',0.25,'StopbandFrequency',0.35,'PassbandRipple',0.5,'StopbandAttenuation',65,'DesignMethod','kaiserwin');
y=filtfilt(d,sampleSignal);
lpfirc = d.Coefficients;

figure
freqz(lpfirc, 1, 2^16, Fs)

[FTs1,Fv] = FFT1(sampleSignal,t);

figure
plot(Fv, abs(FTs1)*2)
grid
xlabel('Frequency')
ylabel('Magnitude')
title('Fourier Transform Of ‘sampleSignal’')
xline(0.25*Fs/2, '--g', 'Passband Frequency')
xline(0.35*Fs/2, '--r', 'Stopband Frequency')

% xlim([0 50])

figure
plot(t, sampleSignal,'--', 'LineWidth',1)
grid
hold on
plot(t, y)
hold off

function [FTs1,Fv] = FFT1(s,t)
    s = s(:);
    t = t(:);
    L = numel(t);
    Fs = 1/mean(diff(t));
    Fn = Fs/2;
    NFFT = 2^nextpow2(L);
    FTs = fft((s - mean(s)).*hann(L), NFFT)/sum(hann(L));
    Fv = linspace(0, 1, NFFT/2+1)*Fn;
    Iv = 1:numel(Fv);
    FTs1 = FTs(Iv);
end

.

[Hasan Kaan Tuna]

Thank you for your answer. Could you please briefly explain your code? I am bit confused about passband and stopband freqs.

[Star Strider]

As always, my pleasure!

Sure!

The first part loads the file and creates a time vector using the available information.

The next part uses your designfilt call to design the filter and then specifically uses filtfilt rather than filter to do the actual filtering. I extracted the FIR filter denominator coefficients from ‘d’ to display the filter Bode plot using the freqz function.

I want to see what the signal spectrum looks like, so I used my ‘FFT1’ function to calculate the Fourier transform, and then plotted it, also with respect to the filter passband and stopband frequencies displayed using the xline calls.

The last plot is your plot of the filtered and unfiltered signals, slightly changed to make the unfiltered signal a bit easier to see.