Signal Processing

I’ve been working on a fun problem lately that involves estimating a scalar parameter from a set of repeated observations. It turns out that in certain circumstances, the presence of noise in the system can actually make the estimate more accurate, which is a little counterintuitive and also kind of cool. In my case, I... View Article

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 Literary Digest incorrectly predicted that Alf Landon would beat FDR in the 1936 election.... View Article

We’re a little late in posting this, but I wrote a blog entry for EDN last week that discusses how to choose the correct video sampling format. An excerpt: To process signals digitally, they must first be sampled and quantized. Sampling refers to measuring the light intensity at discrete space-time points, while quantization is the... View Article

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 this post. Approach 1: Counting We’ve figured out the sample space... View Article

Cardinal Peak’s big data practice is expanding as we continue adding data scientists to our staff. In a recent discussion regarding a data set we’re analyzing, a probability problem conceptually equivalent to the following arose: In a room filled with N people, what is the probability that none of them have the same birthday? In... View Article

We needed a simple C++ class for linear phase FIR filtering, so our expert offers a how-to and a download to help others implement a FIR filter.

The Boulder County Business Report did a nice article about a recent project we did with a local Boulder startup, Clip Interactive: Local inventor Jeff Thramann hatched the idea and started Clip Interactive, originally contracting with Cardinal Peak for working space as well as help developing the technology. Cardinal Peak specializes in digital video and... View Article

In the first post of this three-part series, I listed four points that I hope my readers will agree with at the end of this series. The second post addressed the first two points of the four. In this post, Part Three of the series, I will demonstrate the final two points: Phase distortions generally... View Article

In this post I will demonstrate that dramatically different time domain waveforms can lead to virtually the same audio perception, and two waveforms with identical spectrograms can sound quite different.

You may have encountered spectral analysis. The basic idea is to take a waveform, in our case an audio clip, and determine which frequency components are in it. This post provides a very brief overview of the Discrete Fourier Transform (DFT), spectrograms and DFT spectral analysis.

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 many compression algorithms. I’m focusing on video since that’s my particular interest. Part... View Article

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 many compression algorithms. I’m focusing on video since that’s my particular interest. Part... View Article