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) select first coefficients from the first array which correspond to a first subset of one or more order components in the input signal, (d) generate a time domain signal from the first coefficients, and (e) present the time domain signal to a user on a presentation device. The signal analysis system generate the time domain signal from the first coefficients by performing an inverse joint time-frequency transform on the first coefficients. The signal analysis system extract the one or more order components for presentation to the user by masking out all coefficients except those corresponding to the one or more components. Conversely, the signal analysis system may suppress the one or more order components, i.e. present to the user the input signal minus the one or more order components by masking out coefficients corresponding to the one or more components and keeping the remaining coefficients.