entire time domain. While mathematically elegant, such a technique is not appropriate for analyzing a signal with indeterminate future behavior. For instance, one must presuppose some degree of indeterminate future behavior in any telecommunications systems to achieve non-zero entropy (if one already knows what the other person will say one cannot learn anything). To harness the power of a frequency representation without the need of a complete characterization in the time domain, one first obtains a time–frequency distribution of the signal, which represents the signal in both the time and frequency domains simultaneously. In such a representation the frequency domain will only reflect the behavior of a temporally localized version of the signal. This enables one to talk sensibly about signals whose component frequencies vary in time. For instance rather than using tempered distributions to globally transform the following function into the frequency domain one could instead use these methods to describe it as a signal with a time varying frequency. Once such a representation has been generated other techniques in time–frequency analysis may then be applied to the signal in order to extract information from the signal, to separate the signal from noise or interfering signals, etc. Time–frequency distribution functions Formulations There are several different ways to formulate a valid time–frequency distribution function, resulting in several well-known time–frequency distributions, such as: Short-time Fourier transform (including the Gabor transform), Wavelet transform, Bilinear time–frequency distribution function (Wigner distribution function, or WDF), Modified Wigner distribution function, Gabor–Wigner distribution function, and so on (see Gabor–Wigner transform). Hilbert–Huang transform More information about the history and the motivation of development of time–frequency distribution can be found in the entry Time–frequency representation. Ideal TF distribution function A time–frequency distribution function ideally has the following properties: High resolution in both time and frequency, to make it easier to be analyzed and interpreted. No cross-term to avoid confusing real components from artifacts or noise. A list of desirable mathematical properties to ensure such methods benefit real-life application. Lower computational complexity to ensure the time needed to represent and process a signal on a time–frequency plane allows real-time implementations. Below is a brief comparison of some selected time–frequency distribution functions. To analyze the signals well, choosing an appropriate time–frequency distribution function is important. Which time–frequency distribution function should be used depends on the application being considered, as shown by reviewing a list of applications. The high clarity of the