» mathematics

Negative Zero

Howdy Pierce My wife brings up the following story any time she wants to make the point that I’m pedantic: When one of my daughters was in second grade, her math teacher told the class that any number divided by zero was one. I dashed off an impassioned email t…

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Why Sample Size and Random Sampling Matters

Mike Perkins Recently we tweeted an interesting article on big data, from the Financial Times. The author’s key point is that sampling bias and sampling error are possible even with large data sets. As illustration, the author discusses a classic case where the…

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Posted In: Perk, Theory

Big Data, Probability, and Birthdays: Part 2 of 2

Mike Perkins In Part One of this blog post I discussed how to state an experiment in the form of probability spaces. Determining the sample space and the event space is necessary to be able to talk intelligently about probability measures, which is the topic of t…

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Posted In: Perk, Theory

A C++ class to implement low-pass, high-pass, and band-pass filters

Mike Perkins We recently needed a simple C++ class for linear phase FIR filtering, and I figured it might be useful to others, as well. You can download it here. Here’s how to use this class: Specify the desired filter type (low-pass, high-pass, or band-pass)…

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Posted In: Perk, Theory

Transforms for Video Compression, part 3: The DCT and Why Transforming is Valuable

Mike Perkins The use of transforms in data compression algorithms is at least 40 years old. The goal of this three-part series of posts is to provide the mathematical background necessary for understanding transforms and to explain why they are a valuable part of…

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Transforms for Video Compression, part 2: Matrix Representation and 2D Transforms

Mike Perkins The use of transforms in data compression algorithms is at least 40 years old. The goal of this three-part series of posts is to provide the mathematical background necessary for understanding transforms and to explain why they are a valuable part of…

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Transforms for Video Compression, part 1: Vectors, the Dot Product, and Orthonormal Bases

Mike Perkins The use of transforms in data compression algorithms is at least 40 years old. The goal of this three-part series of posts is to provide the mathematical background necessary for understanding transforms and to explain why they are a valuable part of…

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