Re: [Discuss-gnuradio] CPM timing recovery

[Dan Halperin]

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Nothing that modulates data has constant envelope. Plot the amplitude of
a BPSK or GMSK signal (after transmission, not simulation) sometime.

- -Dan

Achilleas Anastasopoulos wrote:
> Bob,
> 
> this is not correct.
> 
> The CPM signal is by definition constant envelope.
> It is defined as
> s(t)=exp(j phi(t))
> where
> phi(t)= 2 pi int_0^t f(t') dt'
> where
> 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.
> 
> Achilleas
> 
> 
> ======================
> 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
> modulation.
> 
> Bob
> 
> 
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