Re: Zero Padding in radix 2 FFT

stevenj@xxxxxxxxxxxx wrote:
....
> When used to compute the Fourier-series coefficients by sampling an
> arbitrary periodic function, the DFT is a trapezoidal-rule
> approximation for the integral.

Perhaps this is some misunderstanding. Consider some 1-periodic,
band-limited function f defined by

f(t) := a_0 + sum_{k=1}^K (a_k cos(2 pi k t) + b_k sin(2 pi k t) )

for arbitrary real coefficients a_k and b_k.

The Fourier coeffcients a_k and b_k can be perfectly (not
approximately) computed with the DFT of a vector that represents a
sufficiently sampled version of f(t). I don't think you will dispute
this.

Or are you saying that for periodic *non-band-limited* functions, the
DFT coefficients only approximate the Fourier series coefficients?
Which would be obvious, as non-band-limited functions can't be sampled
without throwing away information about the function.

Regards,
Andor

.

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