Schroeder Reverb

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.

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Filter Structure¶

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.

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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.

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The Comb¶

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

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

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See: Julius Smith's Schroeder explanation

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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)

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: