Use of the energy decay relief (EDR) to estimate partial-overtone decay times in a freely vibrating string

The energy decay relief (EDR) was proposed by J. M. Jot [IEEE, ICASSP (1992)] for displaying the impulse response of artificial reverberation systems. The EDR is a frequency-dependent generalization of Manfred Schroeder’s energy decay curve (EDC), defined at time n as the sum of squared impulse-response samples from time n until decay is complete. The EDR is similarly defined for each band in a uniform filter bank, typically implemented using the short-time Fourier transform (STFT). In this work, we apply the EDR to the problem of estimating decay times for the partials of a freely vibrating string. Previously, such decay times have been measured based on STFT magnitude data. We show that the EDR has certain advantages over the STFT, such as being less sensitive to ‘‘beating’’ in the amplitude envelopes of the partial overtones. Results in the context of virtual acoustic guitar modeling will be presented.