I am trying to model the subsurface as a randomly layered medium, with stochastic acoustic attentuation that gives rise to a reflected waveform from an active source as the following signal: $$ x(t) = \sum_{n \in \mathbb{N}}^\infty c_n g(t-W_n) $$ where $c_n$ are random amplitudes (the distribution of which I have not determined yet) and $W_n$ are the samples of an exponential Brownian motion at times $t_n$. Here $t_n$ are uniformly spaced. The function $g$ is a Morlet wavelet. My question is: is this an FRI signal? Seems to me to be so.

  • $\begingroup$ So the question is: can the signal be represented by a finite number of parameters per unit time?. It's not clear to me the relationship between $W_n$ and $t_n$. And then $W_n$ being subtracted from $t$ seems odd. Can you explain that a little more? $\endgroup$
    – Peter K.
    Jul 13 at 0:55


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