The 'fft(x)' function computes the discrete Fourier transform (DFT) of x using a fast Fourier transform (FFT) algorithm.
Please refer the following link for more information about the fft function.
The 'pspectrum(x)' function returns the power spectrum of x.
Please refer the following link for more information about the 'pspectrum' function.
A fast Fourier transform is an algorithm that computes the discrete Fourier transform of a sequence. Fourier Transform changes the domain of the signal from time or space to frequency domain. The DFT is obtained by decomposing a sequence of values into components of different frequencies.
The statistical average of a certain signal or sort of signal (including noise) as analyzed in terms of its frequency content, is called its spectrum. So, the power spectrum refers to the spectral energy distribution that would be found per unit time, since the total energy of such a signal over all time would generally be infinite.