Allen Downey Blog on DSPRelated.com
https://www.dsprelated.com/blogs-1/nf/Allen_Downey.php
Allen Downey Blog on DSPRelated.com
https://www.dsprelated.com/blogs-1/nf/Allen_Downey.php
https://d23s79tivgl8me.cloudfront.net/user/profilepictures/103119.jpgen-USSat, 28 Jan 2023 17:36:46 +00001674927406In Search of The Fourth Wave
https://www.dsprelated.com/showarticle/1419.php
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...]]>
Sat, 25 Sep 2021 17:40:54 +0000Allen DowneyAutocorrelation and the case of the missing fundamental
https://www.dsprelated.com/showarticle/909.php
[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...]]>
Thu, 21 Jan 2016 19:53:20 +0000Allen DowneyGenerating pink noise
https://www.dsprelated.com/showarticle/908.php
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...]]>
Wed, 20 Jan 2016 20:24:05 +0000Allen DowneyAmplitude modulation and the sampling theorem
https://www.dsprelated.com/showarticle/897.php
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 Nyquistâ€“Shannon sampling theorem.

Most of the code for the chapter is done: Fri, 18 Dec 2015 16:24:27 +0000Allen DowneyDifferentiating and integrating discrete signals
https://www.dsprelated.com/showarticle/895.php
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...]]>
Mon, 14 Dec 2015 15:05:50 +0000Allen DowneyBayes meets Fourier
https://www.dsprelated.com/showarticle/836.php
Joseph Fourier never met Thomas Bayesâ€”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...]]>
Mon, 26 Oct 2015 19:20:34 +0000Allen Downey