Direct signal recovery from threshold crossings

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