cross-terms may plague certain quadratic TFRs and they would need to be reduced. One way to do this is obtained by comparing the signal with a different function. Such resulting representations are known as linear TFRs because the representation is linear in the signal. An example of such a representation is the windowed Fourier transform (also known as the short-time Fourier transform) which localises the signal by modulating it with a window function, before performing the Fourier transform to obtain the frequency content of the signal in the region of the window. Wavelet transforms Wavelet transforms, in particular the continuous wavelet transform, expand the signal in terms of wavelet functions which are localised in both time and frequency. Thus the wavelet transform of a signal may be represented in terms of both time and frequency. The notions of time, frequency, and amplitude used to generate a TFR from a wavelet transform were originally developed intuitively. In 1992, a quantitative derivation of these relationships was published, based upon a stationary phase approximation. Linear canonical transformation Linear canonical transformations are the linear transforms of the time–frequency representation that preserve the symplectic form. These include and generalize the Fourier transform, fractional Fourier transform, and others, thus providing a unified view of these transforms in terms of their action on the time–frequency domain. See also Newland transform Reassignment method Time–frequency analysis for music signals References External links DiscreteTFDs — software for computing time–frequency distributions TFTB — Time–Frequency ToolBox Time stretched short time Fourier transform for time-frequency analysis of ultra wideband signals representation Signal estimation