ABSTRACT
This chapter addresses some of the main issues concerning time–frequency distributions and in particular positive distributions. It discusses how the positive distributions are constructed. The chapter describes the properties of these distributions. Bilinear distributions produce so-called cross terms and it has been a very important development in the field to understand these cross terms and to develop bilinear distributions that minimize them. Just as with the bilinear distributions, the positive distributions can also be applied to random signals. The property is summarized in the “support” property of the distribution, and, in particular, the strong finite support property, so named to contrast it to the usual finite support property. The finite support property is well known and was touted as an advantage of the Wigner distribution over the spectrogram. Like the Wigner distribution of the signal, the positive distribution also exhibits high concentration along the instantaneous frequency, and its conditional mean frequency is equal to the instantaneous frequency of the signal.
