Extracting from bit streams remains an active research area in modern cryptography. Recently, there has been renewed interest in debasing with structured linear mappings, namely by linear codes. Linear codes were proposed as extractors for independent but biased bits in the theory community . Decades later, they were popularized among the hardware designers , and …
Tag archives: Fourier analysis
Fourier integrals vanishing on large circles
When evaluating contour integrals, it is often of interest to prove that Fourier-type integrals vanish on large enough semicircles (see the figure). This holds under the following condition: Theorem. Suppose that $$f(z)=O(|z|^{-a}), \quad a>0$$ for in the upper half-plane. Then for any \(\lambda > 0\) we have $$\int_{\gamma_R} f(z)\mathrm{e}^{i\lambda z} \rightarrow 0, \quad R\to+\infty,$$ where …
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