I have a Ph.D. in Electrical Engineering from Stanford University, where my dissertation focused on applying optimization methods to resource scheduling problems in networking. After my Ph.D., I worked at Qualcomm for 6 years, designing signal processing algorithms for 3G/4G cellular modems, then led a team of engineers at Proteus Digital Health for 5 years, working on detecting signals from a proprietary ingestible sensor. Currently, I work on health sensing related algorithms at Apple.

Smaller DFTs from bigger DFTs

Aditya Dua January 22, 20198 comments

Let's consider the following hypothetical situation: You have a sequence $x$ with $N/2$ points and a black box which can compute the DFT (Discrete Fourier Transform) of an $N$ point sequence. How will you use the black box to compute the $N/2$ point DFT of $x$? While the problem may appear to be a bit contrived, the answer(s) shed light on some basic yet insightful and useful properties of the DFT.

On a related note, the reverse problem of computing an $N$...

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