A class of positive isentropic time-frequency distributions

Abstract

Abstract-The Cohen-Posch-Zaparovanny class of positive time-frequency distributions is restricted to a Fourier subclass, and it is shown that besides invariance of the marginals, all members of this class exhibit the same entropy.

Copulas: a new insight into positive time-frequency distributions

“…Remark: In a recent publication [10], a class of isentropic positive TFDs is presented. The entropy of a given positive TFD is ; thus, the choice of a class of isentropic copulas leads to isentropic TFDs (for given marginals).…”

“…The entropy of a given positive TFD is ; thus, the choice of a class of isentropic copulas leads to isentropic TFDs (for given marginals). The copula corresponding to the parameterization function proposed in [10] is (23) where , and . For the special case , is symmetric, i.e., .…”

“…In [1] and [2], it is shown that all distributions such as in (1) can be written as (2) where (respectively, ) denotes 1 tively, ], and is a positive function such that (3) Positive TFDs are used in a variety of applications such as the analysis and synthesis of multicomponent signals [3], biomedical engineering [4], and speech processing [5]. Moreover, efficient recursive implementations have been proposed [6]- [10], most of which provide minimum cross-entropy (MCE) TFDs, which requires the definition of a prior estimate such as the spectrogram. Aside the work of Cohen and Posch [1], [2], statisticians [11], [12] have addressed the same problem, namely how to construct a joint probability distribution with imposed marginals?…”

Theoretical Study of Some Angle Parameter Trigonometric Copulas

“…The theory of the classical trigonometric copulas can be found in [5][6][7][8][9][10][11]. For practice, we refer to [12][13][14][15][16]. Furthermore, the R package named Cylcop, recently developed by [17], gives the trigonometric (and circular) copulas a new dimension of applicability.…”