Audio Tempo Extraction Presenter: Simon de Leon Date: February 9, 2006 Course: MUMT611

Agenda Introduction Algorithm Onset extraction Periodicity detection Temporal estimation of beat locations Examples Conclusion Discussion

Introduction Tempo extraction is useful for Automatic rhythm alignment Beat-driven effects Cut & paste operations in audio editing Tempo extraction in general is mature for straightforward, rhythmic music (rock, rap, reggae, etc.) The challenge is to be accurate across the widest range of genres

Introduction We will focus on the winning algorithm for MIREX 2005 [1] The top algorithms belong to the class that performs the following: Time-freq. analysis to determine beat onset Pitch detection and autocorrelation techniques for periodicity estimation Evaluation of algorithms is difficult due to different perceptions of rhythm

Algorithm Divided into three sections Onset extraction Where are the exact locations of the musical salient features? Periodicity estimation What is the tempo of the beats found? Temporal estimation of beat locations We found the onset locations in the spectral domain, but they are not all necessarily the beats

Algorithm – Onset extraction Idea is that the beat onsets correspond with Note changes Harmonic changes Percussive events Define spectral energy flux Time derivative of the frequency component magnitudes Technique of [1] assumes onsets correspond to the fastest change of frequency component magnitudes

Algorithm – Onset extraction Step 1: Take STFT of signal Step 2: Take time derivative of frequency components (spectral energy flux) a) Low-pass filter STFT magnitude b) Apply logarithmic compression [2] c) Pass through FIR filter differentiator [3] Step 3: Use dynamic threshold and remove the smallest onset spectral energy flux “spikes” from previous step

Algorithm – Onset extraction Top left: Piano signal. Bottom left: STFT Top right: Spectral energy flux. Bottom right: Detection function

Algorithm – Onset extraction Top left: Violin signal. Bottom left: STFT Top right: Spectral energy flux. Bottom right: Detection function

Algorithm – Periodicity Detection Two techniques studied in [1] Spectral product Autocorrelation function Assume tempo T is between 60bpm and 200bpm Spectral product Step 1) Take FFT of detection function Step 2) For each frequency, multiply it by all of it’s integer multiples Step 3) Largest product corresponds to frequency of periodicity

Algorithm – Periodicity Detection Autocorrelation function Classical periodicity estimation, slightly outperforms spectral product method It is the cross-correlation of a signal with itself Three largest peaks of cross-correlation are analyzed for a multiplicity relationship

Algorithm – Beat location Given the tempo extracted from previous steps, we need to align the beat in phase Step 1) Create pulse train q(t) with period T derived from periodicity algorithm Step 2) Find phase by cross-correlating q(t) with detection function, evaluating only at indices corresponding to detection function maximas Step 3) For successive beats in an analysis window, simply add T and search for peak in detection function in vicinity Repeat (2) to re-align phase if peak not found

Examples Let’s listen to some demos of the algorithm in action Jazz – very good to good Rock – very good Classical – very bad to good Soul – very good Latin – satisfactory to good

Conclusion This algorithm represents the state-of-the-art in tempo extraction, the majority of the work focusing on onset detection Problem areas Long fading attacks and decays produce false onsets Many instruments playing continuously with no stable regions produces too many false onsets Cannot keep up when tempo varies quickly

Conclusion Results from [1] indicate roughly 80-90% accuracy for classical, jazz, rock % for latin, pop, reggae, soul, rap, techno Results from [1] using MIREX database 95% of the time gave correct tempo

Discussion Can evaluation methods be improved? How can we avoid the subjective nature of tempo perception? Any suggestions on how we might improve the onset detection algorithm? How about the periodicity algorithm?

References [1] Alonso, Miguel, Bertrand David, and Gael Richard Tempo and Beat Estimation of Musical Signals. Proceedings of the 5th International Conference on Music Information Retrieval. [2] Klapuri, Anssi Sound Onset Detection by Applying Psychoacoustic Knowledge. Proceedings of the IEEE International Conference of Acoustics, Speech and Signal Processing: [3] Proakis, John G., and Dimitris K. Manolakis Digital Signal Processing: Principles, Algorithms and Applications. 3rd Ed. New York: Prentice Hall.