> -----Original Message-----
> From: piclist-bounces@mit.edu [mailto:piclist-bounces@mit.edu] On
Behalf
> Of M.L.
> Sent: 28 May 2009 18:41
> To: Microcontroller discussion list - Public.
> Subject: Re: [EE] WWVB CMAX Chip?
> 
> On Thu, May 28, 2009 at 1:10 PM, Peter Restall <pete@restall.net>
wrote:
> 
> >
> > On Thu, 28 May 2009 11:13:40 -0400, M.L. wrote:
> >
> > > Pete,
> > > You can't detect a 60kHz signal with a 26.7kHz sample rate. I just
ran
> an
> > > Octave simulation of the Goertzel algorithm and I was able to get
good
> > > results with something like this:
> > >
> > > [snip]
> > >
> > > --
> > > Martin K.
> >
> > Thanks for the input Martin - I'll have a play about with your
script a
> > little
> > later.  For the time being though, I've stuck my own octave script
at
> >
> 
> 
> Very simply, sampling theory says that you need to sample at least
twice
> as
> fast as the maximum frequency you want to look at. 

Only if you wish to completely re-construct the original signal without
loss of information!

> So if you sampled at
> 10kHz the maximum frequency you can see is 5kHz (with much
distortion).
> You
> will get numbers if your Goertzel code is trying to detect a frequency
>
> sample speed, but they won't be correct.

Undersampling aliases frequencies above the Nyquist rate, and folds them
back into the first Nyquist region.  Shannon understood this and told us
we need to sample at a rate of at least twice the signal bandwidth, not
the highest frequency component.  Providing you don't wish to
re-construct the carrier, then undersampling is a very useful way of
extracting information from a high frequency carrier using a low cost
ADC and DSP.

Regards

Mike

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