Fast Fourier Transform Zero Padding
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Hi all,
I am using the code shown below to plot the FFT of some data. My issue is that the "resolution" seems poor, as the x axis is in increments of 0.2. I would like much finer plotting of points, and have recently seen the Zero Padding method. However, everytime I try to implement other solutions on MATLAB answers, I cannot seem to increase the resolution. Could anyone help me with the necessary code for my specific case?
O2_exp = [0.0247
0.2372
1.9171
1.5570
0.8016
0.5572
1.2185
1.3601
1.0067
0.7767
1.0244
1.1619
1.0210
0.8791
0.9595
1.0592
1.0274
0.9507
0.9735
1.0303
1.0286
0.9912
0.9924
1.0137
1.0143
0.9982
0.9996
1.0097
1.0174
1.0062
1.0052
1.0115
1.0177
1.0131
1.0150
1.0117
1.0182
1.0153
1.0206
1.0177
1.0243
1.0200
1.0221
1.0207
1.0235
1.0256
1.0275
1.0237
1.0248
1.0264];
figure
Fs = 1;
L = length(O2_exp);
Y = fft(O2_exp);
P2 = abs(Y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);
f = Fs*(0:(L/2))/L;
plot(f(2:end),P1(2:end)/max(P1(2:end)),'color','red','linewidth',4)
2 Comments
Accepted Answer
Paul
on 23 Jan 2021
Try changing these lines:
L = length(O2_exp);
Y = fft(O2_exp);
to
L = nfft; % select nfft > numel(O2_exp), preferable a power of 2
Y = fft(detrend(O2_exp),nfft)
4 Comments
Paul
on 24 Jan 2021
I'm not so sure I'd go so far as to say the output isn't physically meaningful, but I understand the sentiment.
I do agree that in order to get finer resolution, more data is needed.
However, I took the OP's question to not really mean frequency domain resolution in the technical sense (i.e, the ability the distinguish among frequency components); rather the OP was trying to get a reasonable interpolation in the frequency domain, of which zero padding is a reasonable approach among others. This link (and the Next pages) are a good discussion.
The results always need to be understood in the context of the underying samples of data.
Walter Roberson
on 24 Jan 2021
According to the comment at https://www.mathworks.com/matlabcentral/answers/724683-fast-fourier-transform-zero-padding#comment_1280732 the poster wanted to reduce the uncertainty in the interpretation of the frequency values. However, that is not something that you can do using zero padding.
More Answers (1)
Walter Roberson
on 23 Jan 2021
Pad_factor = 5;
O2_exp = [0.0247
0.2372
1.9171
1.5570
0.8016
0.5572
1.2185
1.3601
1.0067
0.7767
1.0244
1.1619
1.0210
0.8791
0.9595
1.0592
1.0274
0.9507
0.9735
1.0303
1.0286
0.9912
0.9924
1.0137
1.0143
0.9982
0.9996
1.0097
1.0174
1.0062
1.0052
1.0115
1.0177
1.0131
1.0150
1.0117
1.0182
1.0153
1.0206
1.0177
1.0243
1.0200
1.0221
1.0207
1.0235
1.0256
1.0275
1.0237
1.0248
1.0264];
plot(O2_exp); title('original');
nO2 = numel(O2_exp);
reconstructed = ifft(fft(O2_exp,2*nO2));
plot(reconstructed); title('reconstructed nfft')
%caution: the details that follow are only valid when the
%length of the signal is even, and the signal is purely real.
F = fft(O2_exp);
Fpad = [F(1); F(2:end/2+1); zeros(Pad_factor*nO2-1,1); flipud(conj(F(2:end/2+1)))];
reconstructed_center_padded = ifft(Fpad);
plot(reconstructed_center_padded); title('reconstructed center padded')
3 Comments
Walter Roberson
on 23 Jan 2021
You can change how you process to get it to plot at most any increment. The problem is that your output stops becoming meaningful. If you need finer resolution then you need more data.
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