Direct signal recovery from threshold crossings

We present a method for directly obtaining the $2M$ equally sampled amplitude values of the analog input signal $s(t)$ from the $2M$ locations ${{t}_{i}}$ where it intersects with a reference signal $r(t)=A\mathrm{cos}(2\ensuremath{\pi}{f}_{r}t).$ Until now, high-accuracy signal recovery in sinusoid-crossing sampling had been achieved only indirectly using spectral methods. The recovery requirements are (1) $|s(t)|lA$ and (2) $Wl~2{f}_{r}$ where W is the bandwidth of $s(t).$ The recovery method is evaluated as a function of the accuracy in which the crossings are located, and the sampling period $T=2M\ensuremath{\Delta},$ where $\ensuremath{\Delta}=1/2{f}_{r}.$ Its performance is also compared with other direct interpolation schemes.