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Re: [Discuss-gnuradio] CPM timing recovery

From: Achilleas Anastasopoulos
Subject: Re: [Discuss-gnuradio] CPM timing recovery
Date: Wed, 06 Jun 2007 10:17:09 -0400
User-agent: Mozilla Thunderbird 1.0.2 (Windows/20050317)


this is not correct.

The CPM signal is by definition constant envelope.
It is defined as
s(t)=exp(j phi(t))
phi(t)= 2 pi int_0^t f(t') dt'
f(t)= h sum_k a_k p(t-kT).
Selecting the approprate pulse shape p(t) shapes the spectrum of CPM,
but regardless of the selection it has continuous phase
(not abrupt transitions) as the name suggests ;-) and constant envelope.
Thus the method you suggested (looking at the envelope variations)
will not work.


Since the signal will not really have infinite bandwidth (instantaneous
transitions from one state to the next),  the envelope will not be of
constant modulus.  The signal will be amplitude modulated with a
component due to the data transitions.  Looking at the modulus or
modulus squared will reveal a line in the fft due to this amplitude


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