Hybrid Reverberation Algorithm:a Practical Approach

A. Primavera1, M. Gasparini1, S. Cecchi1, L. Romoli1 and F. Piazza1

1A3Lab - DII - Universita Politecnica delle MarcheVia Brecce Bianche 1, 60131 Ancona Italy

www.a3lab.dibet.univpm.it

Abstract

Reverberation is a well known effect that has an important role in our listening experience. Reverber-ation changes positively the perception of the sound, adding fullness and sense of space. Generally,two approaches are employed for artificial reverberation: the desired signal can be obtained by con-volving the input signal with a measured impulse response (IR) or by synthetic techniques based onrecursive filter structures. Taking into account the advantages of both approaches, a hybrid artificialreverberation algorithm is presented aiming to reproduce the acoustic behaviour of real environmentwith a low computational load. More in detail, the early reflections are derived from a real impulseresponse, truncated considering the calculated mixing time, and the reverberation tail is obtainedusing an IIR filter network. The parameters defining this structure are automatically derived fromthe analyzed impulse response, using a minimization criteria based on Simultaneous PerturbationStochastic Approximation (SPSA). The effectiveness of the proposed approach has been provedtaking into account a real Italian theatre impulse response providing comparison with the existingstate-of-art techniques in terms of objective and subjective measures.

Introduction

Reverberation is probably the most used audio effect employed by musician during live performancesand recording session.

• Synthetic Approach: the reverberation effect is achieved employing IIR structures (e.g., comband/or allpass) [1].Pros: Great flexibility and high computational efficiency.Cons: Low accuracy.• Fast Convolution: the desired signal is obtained convolving the input signal with a given IR [2].

Pros: Accurate reproduction of the acoustic environment.Cons: Computational complexity as a function to the IR length.•Hybrid Technique: reverberation is obtained taking into account the main advantages of the

aforementioned approaches [5] [6] [7].Pros: Low computational cost and audio quality comparable to the convolution approach.Cons: None.

State of the Art

To prove the effectiveness of hybrid reverberation algorithm [7] taking into account a real Italiantheatre impulse response (i.e., Le Muse Theatre of Ancona [11]).

Objective of this work

Hybrid Reverberation Algorithm - The Structure

The presented hybrid reverberator [7] is mainly composed of two parts as the Moorer’s reverberator[4].

+EARLY

REFLECTIONS

DEVICE

LATE

REFLECTIONS

DEVICE

DELAY ×x[n] y[n]

gain

Hybrid reverberator block diagram for the single channel case.

Based on the convolution with a real IR forthe reproduction of the early echoes.

Early reflections device

Based on IIR filters network (e.g., comband/or all-pass) and a FDN matrix [8] forthe simulation of the reverberation tail.

Late reflections device

LBCF

+x[n]

LBCF

LBCF

LBCF

AP AP

A

++

++

++

+

+y[n]

NAP filters

NLBCF filters

Late reflections device block diagram for the single channelcase.

Set the parameters of hybrid reverberator in order to emulate a real environment starting from itsimpulse response.

Autotuning procedure

Hybrid Reverberation Algorithm - The Autotuning Procedure

An offline procedure has been developed in order to determine all the parameters of the hybridreverberation algorithm starting from the IR of a real environment.

Evaluation of the mixing time to set theEarly reflection device:•Gaussianity estimators: Similarities

between IR behavior and gaussian noisecan be found in late reflections. Kurto-sis (k) and MAD/SD ratio (r) have beenused.

k =E (x− µ)4

σ4− 3→ 0

r =E (|x− µ|)

σ→

√2

π

• Phase distortion evaluation: The un-wrapped phase of the IR tends to be-come not linear with late reflections evo-lution.

Early Reflections Partitioning

An offline adaptation procedure, based onSPSA [10], has been used to iteratively findthe parameters set of the IIR structure.A single loss function computed in cepstraldomain [9] has been adopted in the mini-mization procedure.

L = max

max

√√√√ K∑

i=1

M∑j=1

[Tr(i, j)− Ta(i, j)]2

where:

• Tr is a matrix representing the Mel-Frequency Cepstral Coefficients (MFCC)derived from the real IR.

• Ta is the MFCC obtained by the artificialIR.

Late Reflections Analysis

Experimental Setup

The effectiveness of the presented technique [7] has been proved taking into account a real Italiantheatre impulse response (i.e., Le Muse Theatre).

Interior view of Le Muse Theatre.

The theatre impulse response has been de-rived using:• A logarithmic sweep signal excitation.• Sample rate of 48kHz.•Omnidirectional microphone

(Beyer-dynamic MM 1).• A professional soundcard

(MOTU MICROBOOK).

Different tests have been carried out in order to evaluate the reverberation quality, providing com-parison with the existing state-of-art techniques in terms of objective and subjective measures alsoconsidering a real-time implementation on an embedded platform.

Experimental Results - EDRs and IRs evaluation

0 0.5 1 1.5 2 2.5 3-1

-0.5

0

0.5

1

Time [sec]

Am

plitu

de

(a)

0 0.5 1 1.5 2 2.5 3-1

-0.5

0

0.5

1

Time [sec]

Am

plitu

de

(b)

(a) Real impulse response of Le Muse Theatre. (b) Artificial impulse response derived with the proposed approach.

(a) (b)

Energy decay relief. (a) Le Muse Theatre impulse response. (b) Artificial impulse response derived with the proposed approach.

Experimental Results - Comparison with Fast Convolution

The presented hybrid reverberation algorithm [7] has been compared with a fast convolution algo-rithm based on the non uniform partitioning of the IR [3].

A real-time implementation of the presented algorithms has been realized on the OMAPL137 plat-form (DSP+ARM Texas Instruments) taking into account several design constraints (i.e., stereo im-plementation, sample rate of 48 kHz, and frame size of 64 samples).

WorkloadHybrid Reverberator [7] 26 %

Fast convolution [3] 36 %

Internal memoryHybrid Reverberator [7] 10 kB

Fast convolution [3] 100 kB

The obtained results confirm the improvement in terms of required computational resourcesachieved using the hybrid reverberation structure.

Consideration

The artificial effect produced using the presented hybrid reverberation algorithms is really similarto the natural one confirming the effectiveness of the presented approach.

Audio Quality Evaluation

Conclusions

• A hybrid reverberation algorithm with an automatic procedure for the parameters setting has been presented.

• The automatic procedure is based on the evaluation of the mixing time and the minimization of a single loss functioncomputed in the cepstral domain using the SPSA criterium.

• The effectiveness of the presented approach has been proved taking into account a real Italian theatre impulseresponse (i.e., Le Muse Theatre of Ancona).

• Different tests have been carried out in order to evaluate the reverberation quality, providing comparison with theexisting state-of-art techniques in terms of objective and subjective measures also considering a real-time imple-mentation on an embedded platform.

• The hybrid reverberator introduces a remarkable improvement in terms of computational complexity reduction withrespect to fast convolution algorithm.

• As confirmed by informal listening tests the artificial effect generated using the hybrid reverberation algorithmsounds really similar to the natural one validating the presented approach.

References

[1] M.R. Schroeder, Natural Sounding Artificial Reverberation, Journal of the Audio Engineering Society, vol. 10, pp. 219223, 1962.[2] W. G. Gardner, Efficient Convolution without Input-Output Delay, Journal of the Audio Engineering Society, vol. 43, pp. 127136, Mar. 1995.[3] A. Primavera, S. Cecchi, L. Romoli, , F. Piazza, and M. Moschetti, An Efficient DSP-Based Implementation of a Fast Convolution Approach with Non Uniform Partitioning, in Proc. of EDERC 2012,

Amsterdam, NL, Sep. 2012.[4] J.A. Moorer, About This Reverberation Business, Computer Music Journal, vol. 3, pp. 13-28, 1979.[5] R. Stewart and D. Murphy, Hybrid Artificial Reverberation Algorithm, in Proc. of 122nd AES Convention, Vienna, AU, May. 2007.[6] G. Constantini and A. Uncini, Real-time Room Acoustic Response Simulation by an IIR Adaptive Filter, Electronics Letters, vol. 39, pp. 330-332, 2003.[7] A. Primavera, S. Cecchi, L. Romoli, P. Peretti and F. Piazza, An Advanced Implementation of a Digital Artificial Reverberator, in Proc. of 130th AES Convention, London, UK, May. 2011.[8] J. Jot, Digital Delay Networks for designing artificial reverberator, in Proc. of 90th AES Convention, Paris, FR, Feb. 1991.[9] S. Heise, M. Hlatky, and J. Loviscach, Automatic Adjustment of Off-the-Shelf Reverberation Effects, in Proc. of 126th AES Convention, Munich, DE, May. 2009.[10] J.C. Spall, Implementation of the Simultaneous Perturbation Algorithm for Stochastic Optimization, in IEEE Transactions on Aerospace and Electronic Systems, vol. 34, pp. 817-823, 1998.[11] Reference to the Teatro delle Muse homepage. URL: http://www.teatrodellemuse.org/