The Fourier transform reads
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).
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
=\begin{cases}&space;0&space;&&space;\text{&space;if&space;}&space;x<0&space;&space;\\&space;&space;t&space;&&space;\text{&space;if&space;}&space;0\leq&space;x\leq&space;1&space;&space;\\&space;&space;2-t&space;&&space;\text{&space;if&space;}&space;1\leq&space;x\leq2&space;&space;\\&space;&space;0&space;&&space;\text{&space;if&space;}&space;x>2&space;&space;&space;\end{cases})
The Fourier transform reads
![s(\omega)=[4 \cos(\omega) \sin^2(\omega/2)] \; \frac{1}{\omega^2}](http://www.codecogs.com/eq.latex?s(\omega)=[4&space;\cos(\omega)&space;\sin^2(\omega/2)]&space;\;&space;\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).
The Fourier transform reads
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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