Whittaker-Shannon Interpolation

$f(t)=\tilde{f}(t)\ast h(t)=\sum _{k=-\infty }^{\infty }f(kT)\text{sinc}(2Bt-k)$

• $\tilde{f}(t)$ is the sampled version of $f(t)$
• $h(t)$ is the impulse response of the low-pass filter (it removes the periodic repeats in reciprocal space)
• $T$ is the sampling period
• $B$ is the bandwidth
  
• The sum of green waves will equal the red function $f(t)$