James Richard Tyrer wrote:
I suppose that I will have to do the math for that since he didn't.
To state the problem:
With ideal sampling, we have a string of impulses (signed) at the
sampling frequency. The impulses contain power equal to the sampled
value at each sample but have a time duration of 0 (the definition of an
impulse). Yes, this is physically impossible, but the math is nice.
With PWM we have a wave form consisting of finite width pulses (signed)
one per sample that are centered around the sample (actually, there is a
finite but uniform delay) with a constant height but with varying width
so that they have exactly the same power as the corresponding impulses
in the impulse train.
First question is how the (periodic) Fourier transforms of these two
signals is different for an example sine wave at say 1/48th the sample
rate. E.G. sample rate 48Ks/s frequency of signal 1Khz. But normalize
it to 48s/s and 1Hz signal.
Second question is what you get when you run both wave forms through a
reconstruction filter with F0 at half the sample rate. E.G. normalized
to 24Hz.
Is their a mathematician among us, or do I start looking for text books
in my closet?
--
JRT
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