Continuous-time reconstruction using Fourier series

Summary

A periodic signal can be interpolated at any point in time with arbitrary accuracy by evaluating its Fourier series form.
On a non-periodic signal, accurate reconstruction would require both an infinitely long signal and impulse response.

A bandlimited periodic signal can be written as a Fourier series, with a finite number of terms:
$f(x)=\frac{a_0}{2}+\sum_{n>0}(a_n\cos(n x)+b_n\sin(n x)).$
To interpolate points between the samples,

is then evaluated as needed.
The coefficients

and

are found using discrete Fourier transform, in particular FFT.

© Markus Nentwig 2007-2008
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