# Why can the FFT always be mirrored in the middle of the x axis? [duplicate]

Plotting the FFT of a signal with Matlab e.g. by the code:

y_fft = abs(fft(y));
f = fs*(0:length(y)-1)/length(y);
plot(f,y_fft);


where y is the discrete signal and 'fs' is sample rate. creates a plot where the curve can be mirrored in the middle of the x-axis e.g.

Why can the FFT always be mirrored in the middle of the x axis?

## marked as duplicate by Jim Clay, Peter K.♦, sansuiso, Jason R, endolithApr 12 '13 at 0:02

The DFT of a real signal is conjugate symmetric. For example, if your DFT result at, say, 2Hz was $1+j5$, then your DFT result at -2Hz would be $1-j5$. This is conjugate symmetry.