MATLAB: Fourier transformation input parameters

fourier transformationinput parameters

Hello,

I have a question about the Fourier transformation.

I have a matrix 290×2. The first column is time values in seconds. The second column are amplitudes in V.

Do I apply the Fourier transformation to the first + second column (data(:,1) + data(:,2)) or only to the second column (data(:,2)) or data(:,1:2)?

greetings

Christin

Best Answer

Only take the Fourier transform of the second column. Having the first column is necessary in order to calculate the frequency vector.

Example:

data = sortrows(rand(290,2));                       % Create ‘data’ (Use Your Own Data)
L = size(data,1);                                   % Matrix Length
Ts = mean(diff(data(:,1)));                         % Sampling Interval (Assumes Regular Sampling Interval)
Fs = 1/Ts;                                          % Sampling Frequency
Fn = Fs/2;                                          % Nyquist Frequency
FTdata = fft(data(:,2))/L;                          % Fourier Transform
Fv = linspace(0, 1, fix(L/2)+1)*Fn;                 % Frequency Vector (For One-Sided Spectrum)
Iv = 1:numel(Fv);                                   % Index Vector (For One-Sided Spectrum)
figure
plot(Fv, abs(FTdata(Iv))*2)
grid

That should work with your data, although you may first need to subtract the mean from ‘data(:,2)’ if you have a large d-c (constant) offset that obscures the other peaks.

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MATLAB: How to Butterworth Filter with Bandpass [10 500] with sampling rate 1000

You have to divide your passband and stopband frequencies by the Nyquist frequency to normalise them:

Fs = 1000;                                          % Sampling Frequency
Fn = Fs/2;                                          % Nyquist Frequency
Wp = [10  495]/Fn;                                  % Norrmalised Passband Frequencies
Ws = [5   499]/Fn;                                  % Normalised Stopband Frequencies
Rp =  1;                                            % Passband Ripple (dB)
Rs = 25;                                            % Stopband Ripple (dB)
[n,Wn] = buttord(Wp, Ws, Rp, Rs);                   % Optimal Filter Order
[b,a] = butter(n, Wn);                              % Calculate Filter Coefficients
[sos,g] = tf2sos(b,a);                              % Convert To Second-Order Sections For Stability
figure(1)
freqz(sos, 4096, Fs)                                % Filter Bode Plot

You cannot have any frequency exactly at zero or exactly at the Nyquist frequency, so I designed your passband to be close enough to them to be stable. In your filter, you can also use a high-pass design with a lower cutoff of 10 Hz, since your upper passband is at the Nyquist frequency. The passband and stopband ripple values are necessary to specify in the design but irrelevant to a Butterworth filter. These are acceptable values for most filter designs (for example Chebyshev) that require them.

You would use the ‘sos’ and ‘g’ variables in your actual filter:

filtered_signal = filtfilt(sos, g, signal);

(This design works well in R2016a and should also work in earlier releases.)

MATLAB: How to create low pass filter for audio file

You gave enough information for the Signal Processing Toolbox (with a bit of help from me) to be able to design your filter:

Fs  = 8000;                                 % Sampling Frequency (Hz)
Fn  = Fs/2;                                 % Nyquist Frequency
Fco =   20;                                 % Passband (Cutoff) Frequency
Fsb =   30;                                 % Stopband Frequency
Rp  =    1;                                 % Passband Ripple (dB)
Rs  =   10;                                 % Stopband Ripple (dB)
[n,Wn]  = buttord(Fco/Fn, Fsb/Fn, Rp, Rs);  % Filter Order & Wco
[b,a]   = butter(n,Wn);                     % Lowpass Is Default Design
[sos,g] = tf2sos(b,a);                      % Second-Order-Section For STability
figure(1)
freqz(sos, 2048, Fs)                         % Check Filter Performance

Then use the filtfilt function to filter your signal.

I chose a Butterworth design, but if you want a steeper cutoff, consider using a Chebychev design instead. You may want to experiment with the design to get the exact result you want with respect to your signal. See the relevant documentation for details.

Best Answer

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MATLAB: How to Butterworth Filter with Bandpass [10 500] with sampling rate 1000

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