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 From: MacLeod, Matthew Subject: Re: [Discuss-gnuradio] USB2 <-> fast ADC & DAC Date: Tue, 3 Jun 2003 10:09:55 -0400

```Joseph-

I can't speak for Henrique's equations, but my gut feeling is this:

Basically this sampling technique divides the spectrum up into regions that
are fs wide. So if your sampling rate is say, 10 kHz, you can look at the
region from -5 kHz to 5 kHz, or from 5kHz to 15 kHz, or 15 to 25, etc. Now,
if your signal of interest (with a maximum width of 5 kHz) is centered at 0,
10, 20, 30, etc., you can get a 5 kHz wide signal, which uses your 10 kHz
sampling rate optimally (actually you'll always only be able to get a little
less than 5, but let's forget that for a moment). If you have a signal
centered at, say, 7 kHz, however, you'd only be able to get a 1 kHz wide
signal, as you couldn't touch anything above 7.5 reliably. So you'd have to
increase your sampling rate to get wider bands in order to capture it.

So basically the difference between optimum and minimum has to do with
whether your signal lies exactly in the middle of one of the bands you can
look at. If not, you won't be able to get optimum use of your sampling rate,
with optimum meaning being able to capture a signal as wide as slightly less
than half the sampling rate.

Matt MacLeod

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Dear Henrique,

No inconsistencies found. I had to brush up on my algebra of inequalities
(aarghh!) but I agree with your equations #1 & #2. Nicely done and thank you
again.

However, I must admit that I still don't fully appreciate what qualities
make a particular fs "optimum".

```