# Minimum Shift Keying (In-phase, Quadrature Components derivation)

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 $\ -T_b <= t <=T_b$

$\ s_Q$=$\ \pm$ $\sqrt {2Eb/Tb}$ $\sin( \frac {\pi}{2T_b} t )$ 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?
• 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. – Dilip Sarwate Dec 26 '14 at 0:00