I have a signal:
$r(t) = \sum_k a_k g( lT/2 -k(T+\Delta T) )$ where $a_k \in \lbrace\pm 1\rbrace$, $g(t)=\frac {\sin(2\pi t/T)}{2\pi t/T}$, $T/2$ is the sampling period, and $\Delta T$ is a constant.
I want to recover my original bits $a_k$ from this signal but the problem is that: In this continuous-time signal, the bits $a_k$ occur at multiples of $(T+\Delta T)$ but the zero-crossings of $g$ functions happen at multiples of $T/2$. Therefore, at the positions of the bits, the $g$ functions will overlap and add up so that we cannot recover the bits by just re-sampling because the bits are distorted.
Let me also add that we are still within the Nyquist theorem so the information is there in the signal and can be recovered somehow. The question is how?? Does anybody know?