Whittaker-Shannon Interpolation

#Math

$\displaystyle f(t)=\tilde{f}(t)*h(t)=\sum_{k = -\infty}^{\infty}f(kT),\text{sinc}(2Bt-k)$

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