The energy decay relief (EDR) is a time-frequency distribution which generalizes the EDC to multiple frequency bands [216]:
where denotes bin of the short-time Fourier transform (STFT) at time-frame [12,454], 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.3.2. For better correspondence with audio perception, the frequency axis is warped to the Bark frequency scale [461], 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 [154, p. 96].
The EDR is used to measure partial overtone dampings from recordings of a vibrating string in §6.11.5.