Re: Sampling theorem for narrow band signals
- From: "mnentwig" <mnentwig@xxxxxxxxxxx>
- Date: Wed, 12 Dec 2007 08:39:32 -0600
I hope this sheds some light:
Assume my signal is periodic, it repeats once per second.
Further, let its bandwidth be one kHz.
Since you asked for narrowband signals, it starts for example at 10 kHz
upwards.
Because of periodicity, there exists only a finite number of sine waves
with a full number of cycles within that bandwidth:
The first one is 10 kHz - 10000 cycles per second.
The second one goes through exactly one more cycle more within the same
time, in other words 10001 Hz.
Then 10002 Hz and so on. The last one within the BW is 10999 Hz.
Each "sine wave" requires an amplitude and a phase (or use sin/cos
amplitude, if that is more convenient). We have two parameters per wave.
Result: 1000 Hz bandwidth, 2000 samples required for one second of
signal.
Two real-valued samples can be replaced by one complex valued sample, in
other words, 1 kHz bandwidth, 1000 complex valued samples per second.
-mn
.
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