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From: email@example.com (Tom Bruhns)
Subject: Re: Newbie DSP/frequency resolution question
Date: 24 Oct 2002 15:55:06 -0700
NNTP-Posting-Date: 24 Oct 2002 22:55:06 GMT
"Thomas Magma" wrote in message news:...
> I'm having a hard time finding the answer to this one on the internet. I
> have a bad text book that tells me that frequency resolution is "one over
> the sample period". Is this right? So if you sample a 1MHz signal for 100ms
> the best you can resolve the absolute frequency is to with in +/-10Hz? Surly
> this can be correct... how could they ever rate a oscillator for short term
> stability if this was correct? And what about sample rate and bit resolution
> how does that fit in?
I see some other good answers posted. Perhaps this will help a bit
more. It seems to me that the passage you quoted is not stated in a
way that gives you quite the right picture. Be sure to not confuse
the sampling period with the duration over which you conduct the
sampling. For example, if you perform an FFT on 81.92msec worth of
points sampled at 1e5 points per second, you'll have output "bins"
spaced at 1/81.92msec = 12.2Hz, and you'll have 4096 complex points
representing frequencies up to 50kHz, 1/2 the sample rate. In this
particular case, your example 1MHz input signal would alias to DC, but
in general any input signal will cause a response in only one "bin" if
it's right on that bin's frequency, or in lots of bins (actually all
of them to some degree) if it's not. You can think of each "bin" as
having a particular response to any input frequency. If your input is
a sinusoid (relate this to what Tom L. posted!), you can easily
calculate the frequency on which the input must have been to result in
the particular distribtion of responses which you see. But if the
input is non-sinusoidal, then each harmonic will also have responses
from all the bins, and sorting it all out is much more difficult.
Also, if the input is not a time-invariant fixed frequency, you are
likely to see confusing results.
The passage you quoted is confusing to me because "sample period" to
most people means "1/sampling rate". But I _think_ your book means it
as you suggested in your example, which is "the length of time for
which you sample." As has been pointed out, if you know enough about
your input waveform, you can determine a lot more about it than just
1/sampling-duration frequency resolution. And, I presume your book
also talks about needing to band-limit the input so you don't get
confused by aliasing.
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