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The ansatz

One wants to approximate the trigonometric polynomial $ f$ in (2.6) by a linear combination of shifted 1-periodic window functions $ \tilde \varphi$ as

$\displaystyle s_1\left(x\right) := \sum_{l \in I_n} g_{l} \; \tilde \varphi\left(x - \frac{l}{n}\right) \, .$ (2.7)

With the help of an oversampling factor $ \sigma >1$ the fft-length is given by $ n:=\sigma N$.

Stefan Kunis 2004-09-03