Processing sensor data with a convolution

We’ve talked about calculating an integral which reduces from a lot of data to a single value, and we’ve also explored sorting that likewise operates on our input data. Now we’ll explore an interesting but different concept called convolution.

A convolution is an operation that works like sliding a small window (called a filter) over our data and combining the data values with the weights on the filter to produce a transformed result. This kind of operation is very common in image and signal processing, and financial analysis as well. However, a simpler example is smoothing the values collected from sensors to filter out noise. That’s exactly what we are going to work on now.

Let’s suppose that in a factory there are machines bearing many sensors that measure the vibration of each piece of equipment. We can use a weighted moving average to process the last N measurements from each sensor and produce...