Plot of fft of data is mirrored, unsure how to fix it

I have two sets of data that I have to compare by plotting each with fft on logarithmic axes. The data, however, keeps resulting in being mirrored which as far as I understand is due to not respecting the Nyquist limit.

My sample rate is 40,000 samples/sec and the time is 1 second. I have tried to use fftshift but it just shifts it to the mirroring point (around 20kHz). No matter if the x-axis data is time or freq (with array of 40000), it the y axis data plotted stays the same shape leading me to believe I need to do something to the y axis data?

My current code:

load data.dat

load data2.dat

t = data(4,:);

x = data(3,:);

y = data(1,:);

t2 = data2(4,:);

x2 = data2(3,:);

y2 = data2(1,:);

Fs = 40000;

Fn = Fs/2;

f = (0:length(t)-1)*Fs/length(t);

subplot(2,1,1)

h = fft(x);

semilogx(f,h)

subplot(2,1,2)

h2 = fft(x2/2);

semilogx(f,h2,"r");

Answer 1

[Star Strider]

It respects the Nyquist limit. If you use the fftshift function you will see the result as negative frequencies and positive frequencies (although you have to create the frequency vector to go from -Fn to +Fn, where ‘Fn’.is the Nyquist frequency).

To get a one-sided Fourier transform, I do something like this —

Fs = 1000;                                              % Sampling Frequency
t = linspace(0, Fs-1, Fs)/Fs;                           % Time Vector
s = sum(sin([1:50:460].'*2*pi*t)).';                    % Signal
t = t(:);

L = numel(t);
Fn = Fs/2;                                              % Nyquist Frequency
NFFT = 2^nextpow2(L);                                   % For Efficiency
FTs = fft(s.*hamming(L),NFFT)/L;                        % Windowed Fourier Transform
Fv = linspace(0, 1, NFFT/2+1)*Fn;                       % Frequency Vector
Iv = 1:numel (Fv);                                      % Index Vector

figure
plot(Fv, abs(FTs(Iv))*2)
grid
xlabel('Frequency')
ylabel('Magnitude')

Make appropriate changes to work with your signals.

.

[Clare Leverage]

Thanks I will try this out!!

[Star Strider]

My pleasure!

[Clare Leverage]

So the code definetly works but my data set is too large :( I get

Error using fft

Requested 40000x40000 (23.8GB) array exceeds maximum array size preference (15.9GB). This might cause MATLAB to become unresponsive.

(My data set already gives me time vector, signal vector and sampling frequency which are all sizes of 40k). Is there a way to do this that doesn't use so much RAM?

[Star Strider]

I am using a window to correct for the fft being finite, and the window is a column vector by default.

Your signal vector may be a row vector. Use the simple transpose operator (.') or the transpose, .' function to transpose it to a column vector, and the fft call should run without error.

If your signal vector is ‘s’, another way to force it to be a column vector (regardless of its original orientation) is:

s = s(:);

That should solve this problem. Please post back here with the result, so I can be sure that it does.

.

[Clare Leverage]

I had only used t=t(:) previously but also using it on my signal helped!! Thank you so much it completely solved the issue. It works perfectly now (:

[Star Strider]

As always, my pleasure!