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 个评论
采纳的回答
Paul
2021-1-23
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 个评论
Paul
2021-1-24
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
2021-1-24
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.
更多回答(1 个)
Walter Roberson
2021-1-23
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 个评论
Walter Roberson
2021-1-23
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.
另请参阅
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