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## Re: [Discuss-gnuradio] decimation rate of GSM

 From: Johnathan Corgan Subject: Re: [Discuss-gnuradio] decimation rate of GSM Date: Wed, 4 Feb 2009 18:45:26 -0800

```2009/2/4 Jane Chen <address@hidden>:

> I have a question about the decimation rate of GSM (channel is 200kHz wide).
>
> I search the decimation rate of GSM for GNURadio on the Google.  I got some
> information from
> http://www.segfault.net/gsm/The_Beginners_Guide_to_analyzing_GSM_data_in_MatLab.pdf
>
> However, I don't understand why they said the sample rate has to be at least
> 400 kHz (after Nyquist's theorem).  They used a decimation of 128.
> I think through the Nyquist's theorem, the sample rate should be 200kHz
> (fs>2fmax, and fmax should be 100kHz). I think the decimation factor is 256.

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.

Johnathan

```