# Fft graphs exhibit symmetry on the x axis, but not around 0

4 views (last 30 days)
Sophie S on 6 Jul 2022
Commented: Star Strider on 12 Jul 2022
I'm pretty inexperienced with MatLab and Fourier transform. I'm trying to convert a matrix into a Fourier transform graph using the following code:
Y = fft(ppt1_female_dob_10_10_2020_20min_normal_colon_vid_05_10_2021matrx);
n = length(Y);
pwr = abs(Y(1:floor(n/2))).^2;
freq = (1:n/2)/(n/2) * 0.5;
plot(freq,pwr)
figure,plot(freq*100,pwr)
When I did this, I obtained bimodal data for every figure generated, and they were all symmetrical around an x value not equal to 0. (See attached files). Why might I be getting graphs that look like this?

Star Strider on 6 Jul 2022
It appears that you are plotting part of a two-sided Fourier transform.
I generally use this approach to plot a one-sided Fourier transform —
t = linspace(0, 20, 250); % Time Vector
s = sum(sin([1:5]'*2*pi*t)); % Signal Vector
Fs = 1/(t(2)-t(1)); % Sampling Frequency
Fs = 12.4500
Fn = Fs/2; % Nyquist Frequency
figure
plot(t, s)
grid
xlabel('t')
ylabel('s') L = numel(t);
NFFT = 2^nextpow2(L);
FTs = fft(s, NFFT)/L;
Fv = linspace(0, 1, NFFT/2+1)*Fn;
Iv = 1:numel(Fv);
figure
plot(Fv, abs(FTs(Iv))*2)
grid
xlabel('Frequency')
ylabel('Amplitude') There are other approaches as well that work. There is nothing particularly special about this approach, other than it generally works for me.
.
Star Strider on 12 Jul 2022
My pleasure!
The provided .mat file is a doouble matrix, not a table, so there are no variable names associated with any of the columns. There is also no time vector or sampling frequency provided.
My previous code would change to:
Mouse2 = LD.vid00232_Mouse2_05212022_Colon_3cm_matrx;
L = size(Mouse2,1);
t = linspace(0, L-1, L); % Create Time Vector
figure
subplot(3,1,1)
plot(t, Mouse2(:,1))
title(sprintf('Column %4d',1))
grid
subplot(3,1,2)
plot(t, Mouse2(:,640))
title(sprintf('Column %4d',640))
grid
subplot(3,1,3)
plot(t, Mouse2(:,1280))
title(sprintf('Column %4d',1280))
grid
xlabel('Time')
Fs = 1/(t(2)-t(1));
Fn = Fs/2;
NFFT = 2^nextpow2(L);
FT_Mouse2 = fft(Mouse2-mean(Mouse2), NFFT)/L;
Fv = linspace(0, 1, NFFT/2+1)*Fn;
Iv = 1:numel(Fv);
[maxpk,maxloc] = max(abs(FT_Mouse2)*2); % Maximum Peak Amplitude % Index For Each Column
PksLocs = table((1:size(Mouse2,2)).',maxpk(:),maxloc(:),Fv(maxloc(:)).', 'VariableNames',{'Column','Amplitude','Index','Frequency'});
figure
subplot(3,1,1)
plot(Fv, abs(FT_Mouse2(Iv,1))*2)
title(sprintf('Column %4d, Freq = %.6f',1,Fv(maxloc(1))))
grid
subplot(3,1,2)
plot(Fv, abs(FT_Mouse2(Iv,640))*2)
title(sprintf('Column %4d, Freq = %.6f',1,Fv(maxloc(640))))
grid
subplot(3,1,3)
plot(Fv, abs(FT_Mouse2(Iv,1280))*2)
title(sprintf('Column %4d, Freq = %.6f',1,Fv(maxloc(1280))))
grid
xlabel('Frequency')
This plots only a sample of the data, since there are too many to plot all of them. It calculates the Fourier transforms for each column and returns a table of the column number, maximum amplitude, row index of the maximum, and the corresponding frequency for each column. You can add the column names as a separate variable if you want. I did not because there were no column names provided.
If a common sampling frequency ‘Fs’ is provided, the time vector would change to:
t = linspace(0, L-1, L)/Fs; % Create Time Vector
This will also automatically change the frequencies for the peaks, and the frequency vector for the plots.
.