Using dynamic time warping to measure similarity between spectra

Many situations in acoustics and noise control involve comparing two or more spectra. For example, when tuning a numerical model to match measured data, the measured and predicted sound pressure spectra will be compared. In machine learning applications, it is useful to express the similarity between two spectra as a single number, which can then be incorporated into a cost function. It is common to use the mean square difference between the two spectra as this number. However, the mean square difference does not always reflect an acoustician's intuition of the similarity between two spectra. For example, if the natural frequencies of the two spectra are slightly misaligned, the mean square difference can be quite high, even though the underlying system parameters are similar. In this paper, several different similarity metrics for spectra are explored. Most notably, dynamic time warping (DTW) and its variants are applied to spectra and compared to more traditional metrics. Modifications to the DTW algorithm to handle logarithmic frequency and amplitude spacing as commonly arise when considering spectra are also addressed.