When the function to be interpolated is a function with a period of 2π, the n-th order trigonometric polynomial is usually used as the interpolation function and expressed by Gaussian trigonometric interpolation.
Sinker Interpolation We use Sinker interpolation in the sampled signal, which can perfectly reconstruct the original signal from the sample value. The famous sampling theorem states that for the correct sampled signal s(t), the original signal can be reconstructed from the sampled value sk. The formula is:
s(t) = ∑ sksincπ(t-tk) (Note: k is a subscript)
Here sk represents the sampling value at time tk=t0+k*T, T is the sampling time, and its reciprocal 1/T is called the sampling frequency. This formula means that if we know the sampling value sk in the regular distribution interval, we can first measure the sampling value according to the Sinker function, and then add them, so as to calculate the value at any time t.