Amplitude Distribution of Shot Noise

A shot noise, I(t), is a superposition of impulses occurring at random times · · · , t-, to, h , ti, · · · . If the impulses all have the same shape, F(t), then i{t) = E / ' U - u). (i) More generally, the impulse shapes may be randomly chosen from a family of shapes, F(a, t), depending on a parameter a. Then I(t) = » - li). (2) We assume that the times t, form a Poisson sequence with rate n impulses per second. In the case of (2), we assume that the parameters a, are chosen independently from a common distribution. We study the amplitude distribution function Q ( I ) = P r [ / « ) /].