Complexity of Exact Reverberation

Reverberation time is typically defined as $t_{60}$ , the time, in seconds, to decay by 60 dB.

Example:

• Let $t_{60}= 1$ second
• $f_s= 50$ kHz
• Each filter $h_{ij}$ requires 50,000 multiplies and additions per sample, or 2.5 billion multiply-adds per second.
• Three sources and two listening points (ears) $\Rightarrow$
  30 billion operations per second
  • 10 dedicated CPUs clocked at 3 Gigahertz
  • multiply and addition initiated each clock cycle
  • no wait-states for parallel input, output, and filter coefficient accesses
• FFT convolution is faster, if throughput delay is tolerable

Conclusion: Exact implementation of point-to-point transfer functions is generally too expensive for real-time computation.