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Q: Fast algorithm for computing certain signal transformations

RamiLet $f,g,h:\mathbb Z\to\mathbb C$ supported on $[-n,n]$.  For $\tau\in \mathbb Z$, let $\operatorname{sh}_\tau f$ be the shift of $f$ by $\tau$ (i.e. $(\operatorname{sh}_\tau f)(t) = f(t-\tau)$). Define $$k(\tau)=\lVert((\operatorname{sh}_\tau f) \cdot g)*h\rVert_2.$$ Here $*$ stands for convolu...

 

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