 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.

## Filtering Noise: The Basics (Part 1)

Introduction

Finding signals in the presence of noise is one of the fundamental quests of the discipline of signal processing. Noise is inherently random by nature, so a probability oriented approach is needed to develop a mathematical framework for filtering (i.e. removing/suppressing) noise. This framework or discipline, formally referred to as stochastic signal processing, is often taught in graduate level engineering programs and is covered from different perspectives in excellent...

## 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 $N$...

## Blog editor issues

I am really struggling with the blog editor! In addition to MathJax equations rendering inconsistently (or not rendering at all). Additionally, I keep hitting this...

## Re: Can you find the illegal step?

As a corollary, 2 = 0.

## Re: Can you find the illegal step?

If $x^2 = y^2$, taking square root on both sides gives $x = +/- y$. In this case accepting the solution $x = -y$ would not have caused a contradiction.Alternatively, \$x^2...

## Re: Sensor data

Your professor is absolutely correct. The key to eqn 12 is the expected value operator E. If you just generate a random z and compute zz^T, there is no guarantee...

## Re: Sensor data

A sample covariance computed from 10 random samples is not going to be the identity matrix.

## Re: Covariance Matrix diagonal or not?

One example is not going to verify the literature. And calling a result "wrong" doesn't make sense if the example you have constructed is itself wrong. Anyway,...

## Re: Covariance Matrix diagonal or not?

I should have clarified. The N=24 suggestion was for your first case only. For the last case, try N=8.Are you starting to see a pattern here? You need to pick an...

...

## 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...

...

## Re: Help on Noise Correlation Matrix

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...

## Re: Understanding the Comb Filter Frequency Response

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)....

## Re: Time domain signal slikes

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...

## Re: raised-cosine filter paramiters.

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...

## Re: Not understanding digital signal processing

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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