Schroeders reverberator

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).

Figure 3.6 Combining early echoes and late reverberation [Schroeder, 1970b], B z) is a reverberator.

Figure 3.14 Schroeder s reverberator consisting of a parallel comb filter and a series allpass filter [Schroeder, 1962],...

Schroeder s original reverberator sounds quite good, particularly for short reverberation times and moderate reverberation levels. For longer reverberation times or higher levels, some sonic deficiencies become noticeable and these have been described by various authors [Moorer, 1979, Griesinger, 1989, Jot and Chaigne, 1991] ... 

The first artificial reverberators based on discrete-time signal processing were constructed by Schroeder in the early 1960 s [Schroeder, 1962], and most of the important ideas about reverberation algorithms can be traced to his original papers. Schroeder s original proposal was based on comb and allpass filters. The comb filter is shown in figure 3.12 and consists of a delay whose output is recirculated to the input. The z transform of the comb filter is given by ... 

Schroeder proposed a reverberator consisting of parallel comb filters and series allpass filters [Schroeder, 1962], shown in figure 3.14. The delays of the comb filters are chosen such that the ratio of largest to smallest is about 1.5 (Schroeder suggested... 

Schroeder chose the parameters of his reverberator to have an echo density of 1000 echoes per second, and a frequency density of 0.15 peaks per Hz (one peak per 6.7 Hz). Strictly applying equation 3.27 using these densities would require 12 comb filters with a mean delay of 12 msec. However, this ignores the two series allpass filters, which will increase the echo density by approximately a factor of 10 [Schroeder, 1962], Thus, only 4 comb filters are required with a mean delay of 40 msec. 

All reverberation algorithms are susceptible to one or more of these faults, which usually do not occur in real rooms, certainly not good sounding ones. In addition to these criticisms, there is the additional problem that Schroeder s original proposal does not provide a frequency dependent reverberation time. 

Schroeder, 1970b] Schroeder, M. R. (1970b). Digital simulation of sound transmission in reverberant spaces . J. Acoust. Soc. Am., 47(2) 424-431. 

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