Spectrum

(Power) Spectrum

Let $\boldsymbol{s}$ a signal and $\hat \boldsymbol{s}$ its Fourier transform. The (power) spectrum of $\boldsymbol{s}$ is the (squared) modulus of $\hat \boldsymbol{s}$: $\text{Spectrum}(\boldsymbol{s}) = |\hat \boldsymbol{s}|\quad \text{PowerSpectrum}(\boldsymbol{s}) = |\hat \boldsymbol{s}|^2$

if $\boldsymbol{s}$ is real, the power spectrum is symmetric with respect to the frequency $0$