Appendix A
559
The Effective Sampling Rate
In coherent under-sampling, the effective spacing is the spacing
obtained by shuffling the samples so as to get one single,
primitive, cycle of the waveform.
The effective or primitive spacing is T
p
= 1 / (F
s
* M).
The effective sampling rate F
s
’ = 1 / T
p
= M * F
s
= N * Fin.
In under-sampling, there is no lower limit to F
s
because there is no
inherent upper limit to M.
Example:
To capture a 10-MHz signal with a resolution of 100 ps (an
effective sampling rate of F
s
’ =10 GHz or 10000 MHz), you could
either
• capture one period of the signal with a sampling rate of 10 GHz
(which is usually not available)
– or –
• set the sampling rate to near 10 MHz as follows
In the second case, the actual sampling rate is
F
s
= F
s
’ / M = 10000 MHz / 1001 = 9.99 MHz,
and the signal frequency is
F
in
= F
s
’ / N = 10000 MHz / 1024 = 9.7656 MHz.
This makes it possible to look at risetimes, ringing, overshot, and
other high frequency phenomena.
(KP
(U
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