Total independent energy distance—A measure for choosing efficient spectrogram resolutions

Abstract

This paper describes a quantitative method for choosing the most efficient frequency resolution and window overlap when creating spectrograms. The method calculates the Euclidean distance, d, and the coefficient of determination, R2, between a pair of successive power spectra in the spectrogram. The quantity d × (1—R2) is the Euclidean distance between the windows' power spectra, discounted by the information redundancy between the spectra. The Total Independent Energy Distance (TIED) is then the sum of those distances along the entire spectrogram. The effectiveness of TIED is computed for a variety of artificial signals including white noise, sawtooth waveforms that vary in their frequency resolution, pulse trains, and amplitude-modulated signals that vary in their time distribution, and frequency sweeps that vary in both. The TIED is then calculated for human speech, bird song, and insect buzzes, demonstrating that it provides quantitative support to time- and frequency-resolutions for the spectrograms that closely adhere to the traditional resolutions that have been arrived at through generations of human pattern recognition.