Fig. 3
From: From raw audio to a seamless mix: creating an automated DJ system for Drum and Bass
Illustration of the beat tracking algorithm. a Audio waveform extract. b Half-wave rectified onset detection function ΓHWR(m). c Autocorrelation function AΓ(l) of the ODF. d Tempo detection curve \(\mathcal {B}(\tau)\). e Phase detection curve Φ(ϕ). Our algorithm’s estimate of the beat period \(\hat {\tau }\) and the beat phase \(\hat {\phi }\) are annotated. This figure was created by applying the algorithm to a piece of audio of 4 m 30 s long. For illustrative purposes, only the first few seconds of the audio waveform, ODF and autocorrelation function are shown. Note that the described algorithm detects the beats between 160 and 190 BPM, and a larger tempo range is shown in d for illustrative purposes