## Anything like a “shift delay”? Started by 3 years ago3 replieslatest reply 3 years ago159 views
We know that if the input signal is described by x(t) = a(t) cos(wt),

then the output is y(t) = |H(jw)|a(t-groupdelay)cos(w(t-phasedelay))

Now, what about if the input is: x(t) = cos(wt + s(t)), where s(t) is a slowly changing phase shift as a function of time.  Could we work out what would the output be? Is there anything like a “shift delay”?

Thanks.

[ - ] You should expand the cos(wt+s(t)) to cos(s(t)) cos (wt)-sin(s(t) sin(wt)... what you have ere is QPM (quadrature phase modulation) or CPM (continuous phase modulation). The amplitude is 1 and the phase is being shifted... if s(t) is a sinewave it is easy to find the closed form description of its spectrum in terms of Bessel functions. the approximate BW can be estimated by Carson's rule related to amplitude of s(t) and the frequency of s(t).

many manpack radios and many small low earth orbit satellites use CPM with its constant magnitude to keep their power amplifiers efficient and happy with extended battery life.

fred h

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