Continuous phase modulation: Difference between revisions

Revision as of 12:25, 20 September 2015

Revision as of 19:03, 18 December 2015

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:<math>s(t) = A_c \cos\left(2 \pi f_c t + D_f \int_{-\infty}^{t} m(\alpha) d \alpha\right)\,</math>

where ''A_c'' represents the amplitude of the CPFSK signal, ''f_c'' is the base [[Carrier wave|carrier frequency]], and ''D_f'' is a parameter that controls the [[frequency deviation]] of the modulated signal. The [[integral]] located inside of the [[cosine]]'s argument is what gives the CPFSK signal its continuous phase; an integral over any finitely valued function (which ''m''(''t'') is assumed to be) will not contain any discontinuities. If the message signal is assumed to be [[causal]], then the limits on the integral change to a lower bound of zero and a higher bound of ''t''.

Note that this does not mean that ''m''(''t'') must be continuous; in fact, most ideal digital data waveforms contain discontinuities. However, even a discontinuous message signal will generate a proper CPFSK signal.