An optical spectrum analyzer and a method of spectrally analyzing an optical signal. The optical spectrum analyzer includes a wave shaper such as an optical modulator that shapes an optical signal, a dispersive element such as a dispersive fiber in which the shaped optical signal is dispersed, a detector that provides an output signal indicative of the dispersed shaped optical signal, and a signal processor that analyzes the output signal, for example by calculating a transform such as an inverse Fourier transform or a Fourier transform of the output signal, to provide a frequency spectrum of the optical signal.