Re: nyquist sampling rate
- From: rickman <gnuarm@xxxxxxxxx>
- Date: Tue, 5 May 2009 08:27:19 -0700 (PDT)
On May 5, 6:01 am, aitezaz....@xxxxxxxxx wrote:
On May 5, 2:43 pm, "Alun" <no.spam.thank....@xxxxxxxxxxxxxxx> wrote:
<aitezaz....@xxxxxxxxx> wrote in message
news:e3e136be-68be-4e46-bc3e-5a2713463ebd@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i have a signal of bandwidth 2 MHz on a carrier of 5 MHz. That means
the Nyquist sampling rate is (5+2/2)*2 = 12 MHz.
If BW is 2 then Nyquist Rate is 4.
This is because you are interested only in reproducing the shape
of your original signal and have no interest in the shape of
the 5MHz carrier wave.
yes you are right. but i want to understand this thing in general for
nyquist sampling instead of bandpass sampling. i.e. consider 8 MHz of
bandwidth with 5 MHz carrier. Now i cannot use 16 MHz as sampling rate
because it will cause overlapping of the spectra. Please guide me for
the case when i am nyquist sampling the signal i.e. (5+4)x2=18 MHz. I
put my question again as follows.
Is it OK to sample at nyquist rate (2xmaximum frequency present in
signal) considering the sinx/x roll of characteristics of ADC or
should i oversample it a little bit. Or put it another way... is it
OK to have your spectrum tightly packed between -Fs/2 to Fs/2 ? (as in
this case the frequencies near the Fs/2 and -Fs/2 would suffer a loss
because of sinx/x characteristics.)
Thanks for your time
Talking about the spectum being between -Fs/2 to Fs/2 implies that you
are using quadrature sampling. With real sampling you need to limit
the signal bandwidth to 0 to Fs/2 to prevent aliasing.
When you talk about "sinx/x roll of charactersistics of ADC" I'm not
sure this is exactly the right way to put it. The problem with sample
rate is aliasing and filtering. If your signal is bandwidth limited
to 0 to Fs/2, then the sampled version will be accurate with no
aliasing. In the real world, filters are not perfect and a design
needs to allow for a transition band in the filter. So it works
better to use perhaps 80% ro 90% of the available bandwidth for your
signal.
In your example with a 5 MHz carrier and a 2 MHz wide signal, you
would do well to sample around 15 MHz or higher. If you sample at 4
MHz, the real signal would alias down to 0 to 2 MHz, however this does
not allow for the transition band of a real design. Another choice
might be to sample at 7 MHz bringing the signal to 1 to 3 MHz region.
But this presents an inverted spectrum which may or may not be an
issue for your application. Sampling above 12 MHz will give you a
spectrum that is entirely within the Nyquist bandwidth is not
inverted.
If the signal bandwidth were not so wide, say 1 MHz, you could sub-
sample at a rate just below the low end of the lowest frequency, say 4
MHz, to shift the band near 0 Hz and retain a non-inverted spectrum.
In this example the resulting spectrum would be between 0.5 and 1.5
MHz with a 2 MHz Nyquist rate. This would allow a reasonably wide
transition band on your anti-alias filter.
Rick
.
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