Imitating the Shazam App with Wavelets

Abstract

Like searching for a needle in a haystack, suppose that we have a large set of signals (finite sequences of numbers) {s 1 , s 2 , s 3 ,. .. }, and a special signal q that may or may not be in the collection. How can we find signals in the collection that are similar if not identical to q, and how can we do this quickly? A solution to this question is the basis of the Shazam smartphone app, where a listener captures a short excerpt of a recorded song with the smartphone's microphone, and in a matter of moments the app reports the name of the song and the artist [12]. There the "needle" is the excerpt, and the "haystack" is a vast corpus of popular music. The Shazam algorithm is powered by Fourier analysis [15], and the purpose of this paper is to present a simpler, waveletbased method that captures the basic process used by the app. Solutions to this problem are useful in situations where the description of the "needle" might not be precise or may have noise in it, such as the Shazam problem, and where there will be frequent searches of the "haystack." For this presentation, we will use a "haystack" of comparable and accessible signals. The Jaeb Center for Health Research has made a large database of continuous glucose monitor (CGM) data available to the public *. The data comes from a recent study of type-1 diabetes (an autoimmune disorder characterized by the destruction of the islet beta cells in the pancreas by the body's own immune system) that involved 451 patients wearing a CGM for 6 or 12 months [9]. In Figure 1 we see an example of a "CGM day" from a type-1 diabetic patient: 288 readings of positive integers-one every five minutes.