Input Filtering Algorithms for Digital Signal Processing

Extracting Signals from Noise and Other Distractions

- By Bob Japenga

FIGURE 1 Friden calculating machine.

Extracting an actual signal from real world noise is one of the most important skills of embedded software engineers. Noise, bias fluctuations based on temperature, and a plethora other distractions can stand between you and the data you need for your project. This month, Bob shows us how to extract the true signal without introducing other errors, through digital filtering.

When I first got out of college, I worked on the Apollo Lunar Excursion Module's (LEM) backup guidance system (later referred to as the Lunar Module or LM). My initial job was testing and analyzing the gyros used in our design. Gyro drift and noise were huge issues to be solved in maintaining the accuracy of these systems. I did my analysis on a Friden calculating machine (Figure 1). (You can watch a video of the Friden's inner workings, and playing the Friden March on YouTube [1]).

It was at that time that I was introduced to Kalman filters. Used extensively in navigation, guidance and vehicle control, the Kalman filter uses an algorithm that takes past inputs and a statistical knowledge of the noise footprint to predict the state of the system.

I was so ignorant of the actual workings and applicability of this filter that, in the mid-70s, I planned to create the first handheld musical instrument tuner using Kalman filtering. I explained my plan (without disclosing the “how”) to a technical editor from Byte magazine, while he was jamming with some friends at our house. He told me that creating such a tuner had been tried unsuccessfully many times before. The problem was filtering out the fundamental frequency. In a “smarter than thou” mode, I said that I planned to use a Kalman filter to extract the frequency—a completely bogus application of the filter. Thankfully he didn’t roll his eyes.