Schroeder Reverb: Algorithmic Reverberation¶

The Schroeder reverb, introduced by Manfred Schroeder in 1960, is one of the earliest digital reverb algorithms. It simulates reverberation using a network of comb filters and all-pass filters.

Schroeder, Manfred R., and Benjamin F. Logan. "-Colorless-Artificial Reverberation." Audio Engineering Society Convention 12. Audio Engineering Society, 1960.
Schroeder, Manfred R., and Benjamin F. Logan. "" Colorless" artificial reverberation." IRE Transactions on Audio 6 (1961): 209-214.

Strengths:

Computationally efficient
Parametric - it can be tuned.

Drawbacks:

Artificial sound.

Filter Structure¶

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The Schroeder reverb above is composed of:

Four parallel comb filters, emulating the early reflections.
Two serial all-pass filters to create the diffuse reverberation.

The Allpass¶

The allpass filters $A$ in this Schroeder algorithm are defined as:

$$ A = \frac{-g + z^{-N}}{1 - g z^{-N}} $$

$N$ is the delay length in samples.
$g$ are the coefficients.

The Comb¶

$$ C = \frac{1}{1 - g z^{-N}} $$

$N$ is the delay length in samples.
$g$ are the coefficients.

See: Julius Smith's Schroeder explanation

The Impulse Response¶

The following impulse response has been created with these parameter settings:

Allpass¶

$g=0.805$
Delays = $0.0297, 0.0371, 0.0411, 0.0437$ (seconds)

Combs¶

$g_1=0.7$
Delay 1: $0.005$ (seconds)
$g_2=0.7$
Delay 2: $0.0017$ (seconds)

Impulse Response of Schroeder Reverb:

Sound Example¶

The following example shows how a violin sound (recorded in an anechoic chamber) sounds with the Schroeder reverb. Although it is still very artificial, it does a good job at emulating the reverb of a a medium sized room:

Dry Violin Recording:

Violin with Schroeder Reverb:

Exercise¶

1: Implement a Schroeder reverb with the signal flow shown above.
2: Download a solo: https://ringbuffer.org/download/audio/solo_instruments/
3: Apply the reverb and explore different parameter settings