Energy Decay Relief

The energy decay relief (EDR) is a time-frequency distribution which generalizes the EDC to multiple frequency bands [218]:

where denotes bin of the short-time Fourier transform (STFT) at time-frame [16,462], and denotes the total number of time frames. The FFT within the STFT is typically used with a window, such as a Hann window of length 30 or 40 ms.

Thus, is the total amount of signal energy remaining in the reverberator's impulse response at time in a frequency band centered about Hz, where denotes the FFT length.

The EDR of a violin-body impulse response is shown in Fig.2.2. For better correspondence with audio perception, the frequency axis is warped to the Bark frequency scale [467], and energy is summed within each Bark band (one critical band of hearing equals one Bark). A violin body can be regarded as a very small reverberant room, with correspondingly ``magnified'' spectral structure relative to reverberant rooms.

The EDR of the Boston Symphony Hall is displayed in [156, p. 96].

The EDR is used to measure partial overtone dampings from recordings of a vibrating string in §4.11.5.

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.