As I know, the Fourier transform of the Gaussian function is also Gaussian.
The simple verification for that is shown below. http://mathworld.wolfram.com/FourierTransformGaussian.html
But fast Fourier transform(in Matlab) of the Gaussian function gives me some distribution, which oscillates its sign. However, its power spectrum looks like Gaussian. The results I got from Matlab are shown below.
(1) The Gaussian function in time domain
(2) fft of The Gaussian function in frequency domain
Why does the sign of fast Fourier transform of the Gaussian function oscillate? I appreciate your attention and answers in advance.