However, I don’t understand whyÂ they said the sample rate has to be at
least 400 kHz (after Nyquistâ€™s theorem).Â TheyÂ used a decimation of 128.
I think throughÂ the Nyquistâ€™s theorem, the sample rate should be 200kHz
(fs>2fmax, and fmax should be 100kHz). I think the decimation factor is
256.
I am confused. Could anyone please help me?

I am confused. Could anyone please help me?
Since the USRP performs quadrature downconversion to complex baseband
samples, the Nyquist limit is equal to the maximum passband
bandwidth. So a 200 KHz wide signal would need a minimum of 200K
(complex) samples per second to faithfully represent its spectral
content. This is different from dealing with real-valued signals,
which do require a sample rate of at least twice the frequency
content.

However, other factors come in to play. You will want to allow for
the fact that the USRP’s downsampler has a significant (6dB) droop at
the passband edges, and this would affect your signal fidelity. This
would call for having the baseband sample rate be something higher.

In addition, if you are going to actually start demodulating the
signal, you will need at some point in your signal processing chain to
resample to a sample rate that is related to GSM symbol rate. There
are a variety of choices that trade off CPU usage vs. complexity, and
one of the variables is the USRP decimation rate you start with.

Hi Johnathan,
Â
Thank you so much for your reply.Â I would like to make sure I don’t
misunderstand what you mentioned. Do you mean that I can chooseÂ a
decimation factor less than 320 (64M/200k) (without considering the 6dB
droop at the passband edges at this moment)? Then, I can tune the
decimation factorÂ lower to see whatÂ the differences are between them.

I am confused. Could anyone please help me?
Since the USRP performs quadrature downconversion to complex baseband
samples, the Nyquist limit is equal to the maximum passband
bandwidth.Â So a 200 KHz wide signal would need a minimum of 200K
(complex) samples per second to faithfully represent its spectral
content.Â This is different from dealing with real-valued signals,
which do require a sample rate of at least twice the frequency
content.

However, other factors come in to play.Â You will want to allow for
the fact that the USRP’s downsampler has a significant (6dB) droop at
the passband edges, and this would affect your signal fidelity.Â This
would call for having the baseband sample rate be something higher.

In addition, if you are going to actually start demodulating the
signal, you will need at some point in your signal processing chain to
resample to a sample rate that is related to GSM symbol rate.Â There
are a variety of choices that trade off CPU usage vs. complexity, and
one of the variables is the USRP decimation rate you start with.

Thank you so much for your reply. I would like to make sure I don’t
misunderstand what you mentioned. Do you mean that I can choose a
decimation factor less than 320 (64M/200k) (without considering the 6dB
droop at the passband edges at this moment)? Then, I can tune the decimation
factor lower to see what the differences are between them.

Yes.

Johnathan

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