Thursday, April 17, 2008

[MT 5] PSD of ramp-like random processes

In the same way as [MT 4] we can consider single "steps" of a different form. Most relevant for our CSK fluctuation models are sawtooth-like pulses of the form

<br />0 & \text{ if } x<0  \\ 
<br />t & \text{ if } 0\leq x\leq 1  \\ 
<br />2-t & \text{ if } 1\leq x\leq2  \\ 
<br />0 & \text{ if } x>2  
<br />\end{cases}

The Fourier transform reads

s(\omega)=[4 \cos(\omega) \sin^2(\omega/2)] \; \frac{1}{\omega^2}

I didn't perform the calulations analogous to [MT 4] yet, but probably the asymptotic power spectrum would now be like 1/w^4 for large frequencies (short times).

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