### Complexity of Exact Reverberation

For music, a typical reverberation time^{4.2}is on the order of one second. Suppose we choose exactly one second
for the reverberation time. At an audio
sampling rate of 50 kHz, each filter in
Fig.3.1 requires 50,000 multiplies and additions
per sample, or 2.5 *billion* multiply-adds per second. Handling
three sources and two listening points (ears), we reach 30 billion
operations per second for the reverberator. This computational load
would require at least 10 Pentium CPUs clocked at 3 Gigahertz,
assuming they were doing nothing else, and assuming both a multiply
and addition can be initiated each clock cycle, with no wait-states
caused by the three required memory accesses (input, output, and
filter coefficient). While these numbers can be improved using FFT
convolution instead of direct convolution (at the price of introducing
a throughput delay which can be a problem for real-time systems), it
remains the case that exact implementation of all relevant
point-to-point transfer functions in a reverberant space is very
expensive computationally.

While a tapped delay line FIR filter can provide an accurate model for any point-to-point transfer function in a reverberant environment, it is rarely used for this purpose in practice because of the extremely high computational expense. While there are specialized commercial products that implement reverberation via direct convolution of the input signal with the impulse response, the great majority of artificial reverberation systems use other methods to synthesize the late reverb more economically.

**Next Section:**

Possibility of a Physical Reverb Model

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Exact Reverb via Transfer-Function Modeling