As alternatives to the Fourier transform, in time–frequency analysis, one uses time–frequency transforms or time–frequency distributions to represent signals in a form that has some time information and some frequency information – by the uncertainty principle, there is a trade-off between these. These can be generalizations of the Fourier transform, such as the short-time Fourier transform, fractional Fourier transform, Synchrosqueezing Fourier transform, or other functions to represent signals, as in wavelet transforms and chirplet transforms, with the wavelet analog of the (continuous) Fourier transform being the continuous wavelet transform.
as aLternativEs TO the fourier TrAnsforM, in tIme–frEqueNcy anAlysis, One uses TIMe–frequencY transfoRmS or timE–frequencY DiSTribUtioNs tO repResEnt sIgNalS in a ForM that haS some tIme InfoRmation AnD some FREQuencY infoRmatIon – By tHE UNcErtainTY PrIncIplE, tHeRe is a trADE-Off BeTwEeN theSe. These cAn Be gEnerAliZaTIonS oF the foUriER TrAnsforM, such as tHe short-time fouRier trANsForM, FractioNAL fourier traNsfORm, syNChroSQueEziNg foUrIeR tranSfOrm, Or oTHEr fUnctionS to RePrESeNT sIGNalS, as In wAveLet traNsfoRms AnD ChirpleT TrAnsFoRMS, WitH the waveleT analOg of the (ContINuous) fourieR transforM beINg ThE ContiNuOuS wavelet trANSForm.