A transient waveform to be analysed is made periodic by repetition. The resulting Fourier series components are simply related to the continuous frequency distribution of the original transient waveform. The film on which the transient to be analysed is recorded is placed in a variable speed revolving lucite drum. A photoelectric system regenerates the signal, which is applied to fixed tuned amplifier circuits. Changing the speed of rotation has exactly the same effect as changing the tuning of the analyser. Hence the analysis is performed by allowing the drum to slow down from maximum speed under frictional forces. By this means a large number of points on the frequency spectrum can be rapidly obtained and presented in the form of a permanent ink record.