Introduction

 This blog is about how to do speech science - how to collect, visualize, analyze, and understand speech data. A lot of speech data are signals such as microphone recordings, but image data are increasingly common in speech science, and we therefore need tools to work with both signals and images. We will start with smoothing operations, beginning with moving averages. The moving average will provide us with a conceptually simple and - generally - familiar analysis tool, which we will then expand upon and generalize from. Along the way, we will see that the generalized moving average is an incredibly powerful tool - and one that relies on nothing more than arithmetic. (We will make use of more than arithmetic as we learn how to generalize the moving average, but the final results will always be expressible in simple arithmetic terms - terms that a computer can work with!)

The "generalized moving average" is not a technical term in the field that I have ever heard, although I doubt that I'm the first to coin it. Generalized moving averages include convolutions, Fourier transforms, low-pass filters, high-pass filters, Gaussian filters, and many more common operations in signal and image processing.