In this thesis, a new algorithm, time–frequency component analyzer (TFCA), is proposed to analyze composite signals, whose components have compact time–frequency supports. Examples of this type of signals include biological, acoustic, seismic, speech, radar and sonar signals. By conducting its time–frequency analysis in an adaptively chosen warped fractional domain the method provides time–frequency distributions which are as sharp as the Wigner distribution, while suppressing the undesirable interference terms present in the Wigner distribution. Being almost fully automated, TFCA does not require any a priori information on the analyzed signal. By making use of recently developed fast Wigner slice computation algorithm, directionally smoothed Wigner distribution algorithm and fractional domain incision algorithm in the warped fractional domain, the method provides an overall time-frequency representation of the composite signals. It also provides time–frequency representations corresponding to the individual signal components constituting the composite signal. Since, TFCA based analysis enables the extraction of the identified components from the composite signals, it allows detailed post processing of the extracted signal components and their corresponding time–frequency distributions, as well.