The Page distribution Motivated by the construction of a causal energy density, Page proposed the following distribution (the Page distribution): $$\begin{eqnarray*} P_x(t,\nu) &=& {d\over dt}\, \left\{{ \vert\int_{-\infty}^t x(... ...t\ x(u)\ e^{-j2\pi \nu u}du\right)^* \ e^{-j2\pi \nu t}\right\}} \end{eqnarray*}$$ It is the derivative of the energy spectral density of the signal considered before time $t$. It corresponds to the element of the Cohen's class with parameterization function $f(\xi,\tau)=e^{-j\pi \xi \vert\tau\vert}$, and verifies the properties 1-5, 7-10 (see section 4.1.1). Actually, it is the only distribution of the Cohen's class which is simultaneously causal, unitary, compatible with modulations, and preserves time-support. The function tfrpage.m computes this distribution. A frequency-smoothed version of the Page distribution, called the pseudo-Page distribution, is also available (see the file tfrppage.m).
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