Magnitude spectrum and phase spectrum

The size $|\hat f(\omega)|$ and angle $\arg\hat f(\omega)$ of a complex-valued spectrum, plotted separately.

Because $\hat f(\omega)$ is generally complex, it is usually plotted as two separate real graphs: the magnitude spectrum $|\hat f(\omega)|$ (how much of each frequency is present) and the phase spectrum $\arg\hat f(\omega)$ (where in its cycle each frequency component starts). An equalizer that reshapes magnitude without disturbing phase is a familiar application of keeping the two separate.

Examples

Shifting a pulse in time changes its phase spectrum completely but leaves its magnitude spectrum unchanged.