In practice, from a computational, data storage, and display point of view, the chirplet transform is unwieldy. Therefore, we consider subspaces of the entire parameter space. Planes are particularly attractive choices in this regard both because of the ease with which they may be printed or displayed on a computer screen, and the fact that they lend themselves to finite-energy parameter spaces.
Well-known examples are the TF and TS planes discussed previously. Other subspaces, however, correspond to entirely new transforms. For example, consider the chirprate-frequency (CF) plane, computed with a Gaussian window (Gaussian so that chirprate and dispersionrate do not need to be dealt with separately). It turns out to be useful in two cases: (1) when we have only a short segment of data we wish to analyze (and therefore do not wish to partition it into even smaller time segments by the STFT), or (2) when we have a longer time-series, but are not interested in the time axis. In the latter case, the CF plane lets us average out time, and observe long-term slowly-varying frequency trends.