A signal analysis system and method for analyzing an input signal acquired from a mechanical system. The mechanical system may include at least one rotating apparatus. The signal analysis system may be configured to: (a) receive samples of the input signal, (b) perform an invertible joint time-frequency transform (e.g., a Gabor transform) on the samples of the input signal to produce a first array of coefficients which depend on time and frequency, (c) construct an order mask array in response to user input designed to select coefficients from the first array which correspond to one or more order components in the input signal, (d) mask the first array of coefficients with the order mask array to generate a second array of coefficients which depend on time and frequency, wherein the second array of coefficients correspond to the one or more order components in the input signal, (e) generate a time domain signal from the second array of coefficients, and (f) present the time domain signal to a user on a presentation device. The signal analysis system may generate the time domain signal from the first coefficients by performing an inverse joint time-frequency transform on the first coefficients. The time domain signal may then be useable in analyzing the mechanical system.