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In the derivation of the minimum shift keying in-phase and quadrature components in Simon-Haykin Communication Systems 4th ed (p.387-390) we start off with the definition of the signal to be

$\ s(t) $= $\sqrt {2E_b/T_b}$ $\cos(2\pi f_c t+\theta(t))$

where $\theta(t) $ = $\theta(0) $ $\ \pm $ $\ \frac {\pi}{2T_b} t $

$\theta(0) $ is the phase of previous bit and $\ 0 <= t <=T_b$

but in the subsequent steps : for the in-phase component,

$\ s_I $=$\ \pm $ $\sqrt {2E_b/T_b}$ $\cos( \frac {\pi}{2T_b} t )$ and $\ -T_b <= t <=T_b$

for the quadrature-phase component,

$\ s_Q $=$\ \pm $ $\sqrt {2Eb/Tb}$ $\sin( \frac {\pi}{2T_b} t )$ and $\ 0 <= t <= 2T_b$

How did this change of the limits of t change from $\ 0 <= t <=T_b$ to $\ -T_b <= t <=T_b$ or $\ 0 <= t <= 2T_b$ ? How are we allowed to extend the definition like that?

Thanks in advance.

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  • $\begingroup$ What is $b$ in $Eb/Tb$? What are $E$ and $T$? If you want to understand the quadrature representation of MSK, I recommend throwing away all reading material except S. Pasupathy's article on Minimum Shift Keying published in IEEE Communications Magazine in 1979 or so. $\endgroup$ – Dilip Sarwate Dec 26 '14 at 0:00
  • $\begingroup$ Eb: bit energy , Tb : time of bit. Will check the article u mentioned thanks. $\endgroup$ – Dina Dec 26 '14 at 1:48
  • $\begingroup$ I've described the respresentation of MSK as offset QPSK (OPSK) in this blog post. $\endgroup$ – Matt L. Jan 7 '15 at 11:46

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