 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

Introduction

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\$...

## Re: Slow fading channel & SNR

The SNR is a random variable in a fading environment, so have to think of it in terms of a distribution, from which you can derive summary statistics (e.g. mean...

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While noise can certainly be uniform, was your intent to generate Gaussian noise instead? in MATLAB rand produces uniformly distributed data (between 0 and 1) while...

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It looks like you have already computed the transfer function H(z) in z-domain. To compute the frequency response, you can simply set z = e^{jw) and compute H(e^jw)....

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You said they have low periodicity, but is the phenomenon periodic? The period could give you some clues about the source (e.g. any relation to the sampling rate...

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I'm not sure what "100% bad" means, but remember that rcosdesign can generate a square root raised cosine or a normal raised cosine (the latter is obtained by convolving...

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Every sinusoid has the following property: sin(x) = sin(x+2pi) = sin(x+4pi) ..., or compactly, sin(x) = sin(x + 2m*pi) for any integer m. Just think of the argument...

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