Sine Wave autocorrelation, interpolation of phase

<herrmannsfeldt@gmail.com> wrote:

>On Monday, July 31, 2017 at 9:38:26 PM UTC-7, robert bristow-johnson wrote:

>> your sample rate still needs to be faster than twice that of the sinusoid.

>This is almost the perfect case for bandpass sampling.
>(That is, with a bandwidth of zero.)

>If you have a sine of known frequency, but unknown phase and
>amplitude, two samples are in theory enough.  If things aren't
>quite that perfect, you should have more samples.  For one,
>you can average out noise, which might some in. 

>Next, consider the case where you know the fundamental
>exactly, but not the spectrum. You could sample a signal
>of period T every 10.001 T for thousands of samples. 
>With just 1000 samples, you have the equivalent of 1000
>samples over one period. 

You can't have a measurable, variable non-zero phase component unless 
there is some modulation that causes frequency spread, so it's not zero
bandwidth.

But you're right it does not have to be sampled at 2x the carrier
frequency.  It potentially needs to be sampled at some lower rate
but for much longer.


S.

On Friday, August 4, 2017 at 4:16:36 AM UTC-4, herrman...@gmail.com wrote:
> On Monday, July 31, 2017 at 9:38:26 PM UTC-7, robert bristow-johnson wrote:
> 
> (snip)
> 
> > your sample rate still needs to be faster than twice that of the sinusoid.
> 
> No.
> 
> This is almost the perfect case for bandpass sampling.
> (That is, with a bandwidth of zero.)

i stand (or sit) corrected.

bandpass sampling just didn't occur to me when i replied to that.

r b-j