Hi Everyone,
Suppose that I generate a time series x[n] as follows:
>>>
P is a constant value between 0 and 1
At each time step n (n is an integer):
r[n] = uniform_random(0, 1)
x[n] = (r[n] <= P) ? uniform_random(-1, 1) : x[n-1]
Where "(a) ? b : c" is the C ternary operator that takes on the value b
if a is true, and c otherwise.
<<<
What would be a good way to derive a closed-form expression for the
spectrum of x? (Assuming that the series is infinite.)
I'm guessing that the answer is an integral over the spectra of shifted
step functions, but I don't know how to deal with the random magnitude
of each step, or the random onsets. Please assume that I barely know how
to take the Fourier transform of a step function.
Maybe the spectrum of a train of randomly spaced, random amplitude
pulses is easier to model (i.e. w[n] = x[n] - x[n-1]). Either way, any
hints would be appreciated.
Thanks in advance,
Ross.
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