### Allen Downey (@AllenDowney)

I am a professor at Olin College in Needham, MA, author of several books, including Think Bayes and Think DSP, and I write a blog called "Probably Overthinking It".

## In Search of The Fourth Wave

September 25, 20214 comments

Last year I participated in the first DSP Related online conference, where I presented a short talk called "In Search of The Fourth Wave". It's based on a small mystery I encountered when I was working on Think DSP.  As you might know:

A sawtooth wave contains harmonics at integer multiples of the fundamental frequency, and their amplitudes drop off in proportion to 1/f.  A square wave contains only odd multiples of the fundamental, but they also drop off...

## Autocorrelation and the case of the missing fundamental

January 21, 201610 comments

[UPDATED January 25, 2016:  One of the examples was broken, also the IPython notebook links now point to nbviewer, where you can hear the examples.]

For sounds with simple harmonic structure, the pitch we perceive is usually the fundamental frequency, even if it is not dominant.  For example, here's the spectrum of a half-second recording of a saxophone.

The first three peaks are at 464, 928, and 1392 Hz.  The pitch we perceive is the fundamental, 464 Hz, which is close to...

## Generating pink noise

January 20, 20161 comment

In one of his most famous columns for Scientific American, Martin Gardner wrote about pink noise and its relation to fractal music.  The article was based on a 1978 paper by Voss and Clarke, which presents, among other things, a simple algorithm for generating pink noise, also known as 1/f noise.

The fundamental idea of the algorithm is to add up several sequences of uniform random numbers that get updated at different rates. The first source gets updated at...

## Amplitude modulation and the sampling theorem

December 18, 20156 comments

I am working on the 11th and probably final chapter of Think DSP, which follows material my colleague Siddhartan Govindasamy developed for a class at Olin College.  He introduces amplitude modulation as a clever way to sneak up on the Nyquist–Shannon sampling theorem.

Most of the code for the chapter is done: you can check it out in this IPython notebook.  I haven't written the text yet, but I'll outline it here, and paste in the key figures.

Convolution...

## Differentiating and integrating discrete signals

December 14, 20152 comments

I am back at work on Think DSP, adding a new chapter on differentiation and integration.  In the previous chapter (which you can read here) I present Gaussian smoothing, show how smoothing in the time domain corresponds to a low-pass filter in the frequency domain, and present the Convolution Theorem.

In the current chapter, I start with the first difference operation (diff in Numpy) and show that it corresponds to a high-pass filter in the frequency domain.  I use historical stock...

## Bayes meets Fourier

October 26, 2015

Joseph Fourier never met Thomas Bayes—Fourier was born in 1768, seven years after Bayes died.  But recently I have been exploring connections between the Bayes filter and the Fourier transform.

By "Bayes filter", I don't mean spam filtering using a Bayesian classifier, but rather recursive Bayesian estimation, which is used in robotics and other domains to estimate the state of a system that evolves over time, for example, the position of a moving robot.  My interest in...

## Re: DSP project suggestion

How about making a karaoke machine with your own implementation of AutoTune?

## Re: DFT of a signal and system

Nope, it's the same DFT, whether you are applying it to a signal or an impulse response.

## Re: Understanding maths behind DFT?

It depends on what you are planning to do.  If you are using DFT to do spectral analysis and you are more interested in what the results tell you about the problem...

## Re: PID without a PhD

This looks very good.  Thanks!I also recommend this book: http://www.amazon.com/Feedback-Control-Computer-Sy...

## Re: Learning DSP with Python

@stephaneb Thanks for mentioning Think DSP!  Everyone else: You can download the PDF or read it online at http://think-dsp.comThink DSP is in technical review...

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