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# deep-dive posts

## Fourier's Finches: A Primer on Digital Audio

As far as I know, Jean-Baptiste Joseph Fourier never took an interest in birds, but he was a legendary mathematician who’s work enabled our modern techniques for digital audio. Fourier discovered a mathematical transformation that converts a time signal into a frequency signal. This would let us, for example, record a finch’s birdsong and decompose it to find the major frequencies. This would be useful for compressing the audio file. By studying the anatomy of the ear, you can throw away all the frequencies that the ear wouldn’t hear anyway.

## PCI Device passthrough on Harvester

I want to share something that I’ve been working on for the last three months. Release 1.1.0-rc3 now has working PCI passthrough. Any PCI device in your cluster can now be passed through the hypervisor directly to a VM. This allows virtual machines to directly control a device, like a GPU, without any expensive virtualization layer in the way. In the diagram above, the guest (VM) has direct memory access to the host’s memory for the device.

## The SIR Model on novel coronavirus

Since a deadly virus appears to be spreading across the globe, I thought it would be useful to explore how this spread is modeled mathematically, and make some predictions about how quickly this can grow. The simplest model of disease spreading starts by breaking a population up into compartments: S (Susceptible) I (Infected) R (Removedī¸) Then, the model describes the flow between these compartments. NOTE: This version of the model works over short periods and ignores births and natural deaths.

## Imaginary Numbers Are Real

Numbers solve problems. Some problems are so precisely specified that they can be written as equations. When you learn to count, you start being able to solve problems like “how long until the weekend?”, which can produce equations like $$x + 2 = 5$$ Natural number equations give rise to a solution space that looks like this: When we learn how to subtract, we learn how to solve equations like $$x + 1 = 0$$, and when we learn to divide, we learn to solve equations like $$x * 3 = 1$$.

## Lossy Image Compression

Every time you take a picture on your phone, most of the data is thrown away. Lossy image compression is the art of throwing away what your eyes won’t notice. Note: at no point will this blog cover middle-out compression the pixels on most screens emit three different colors of light: red , green and blue . The reason those colors where chosen is that human color perception is enabled by cone cells, with cells that respond to red, green and blue light.