Energy decay relief

Figure 3.4 Energy decay relief for occupied Boston Symphony Hall. The impulse response was measured at 25 kHz sampling rate using a balloon burst source on stage and a dummy-head microphone in the 14th row. The Schroeder integrals are shown in third octave bands with 40 msec time resolution. At higher frequencies there is a substantial early sound component, and the reverberation decays faster. The frequency response envelope at time 0 contains the non-uniform frequency response of the balloon burst and the dummy-head microphone. The late spectral shape is a consequence of integrating measurement noise. The SNR of this measurement is rather poor, particularly at low frequencies, but the reverberation time can be calculated accurately by linear regression over a portion of the decay which is exponential (linear in dB).

The late reverberation is characterized by a dense collection of echoes traveling in all directions, in other words a diffuse sound field. The time decay of the diffuse reverberation can be broadly described in terms of the mid frequency reverberation time. A more accurate description considers the energy decay relief of the room. This yields the frequency response envelope and the reverberation decay time, both functions of frequency. The modal approach reveals that reverberation can be described statistically for sufficiently high frequencies. Thus, certain statistical properties of rooms, such as the mean spacing and height of frequency maxima, are independent of the shape of the room. 

Thus, in order to simulate a perceptually convincing room reverberation, it is necessary to simulate both the pattern of early echoes, with particular concern for lateral echoes, and the late energy decay relief. The latter can be parameterized as the frequency response envelope and the reverberation time, both of which are functions of frequency. The challenge is to design an artificial reverberator which has sufficient echo density in the time domain, sufficient density of maxima in the frequency domain, and a natural colorless timbre. 

In order to take advantage of the full information contained in the AMOC data we use a two-dimensional fitting procedure A two-dimensional model function representing the number of counts as a function of positron age and energy of the annihilation quanta is fitted to the raw AMOC relief without prior data reduction. On the age axis, each positron state is represented by an exponential decay function convoluted with the time resolution function of... 

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