Emulate an analog nonlinear audio device, is it possible ?

(1)

Emulate an Analog Nonlinear Audio Device, is it Possible ?

ABAV, Belgium, 2016

Schmitz Thomas

Department of Electrical Engineering and Computer Science, University of Li`ege

24 janvier 2016

(2)

Communication Outline

1 Why nonlinear models are important ?

2 Non-linear modelling

IR measurement

3 Real audio devices emulation

Objective evaluation of the model Model limitations

(3)

Why nonlinear models are important ?

Section 1 Why nonlinear models are important ?

(4)

Nonlinear Devices

A system is nonlinear if :

it does not respect the principles of superposition (additivity) and homogeneity (scaling)

Almost all audio devices exhibit a nonlinear behavior

Loudspeakers. Amplifiers. Compressors.

Guitar and Keybord sound effects. Microphones.

Acoustic field :

More generally, the system equations governing fluid dynamics (for sound waves in liquid or gazes) and elasticity (for sound waves in solid) are nonlinear.

(5)

Why Try to Emulate Audio Devices

Figure:Home studio ?

Advantages of the simulation :

Wide variety of sounds and timbres. Weight and overcrowding.

Cheaper.

Figure:Home studio !

Figure:Objective of the work

(6)

Non-linear modelling

Section 2

(7)

Non-linear modelling IR measurement

Nonlinear Systems Identification Techniques

Autonomous models

Physical model (non black box). NARMAX model (difficult to identify). MISO model (difficult to identify). Volterra model (difficult to identify). Neural network (too many

parameters). ...

Non autonomous models

Extended Kalman filter. Particle filtering. ...

(8)

Nonlinear Emulation : Volterra Series

(9)

Miso to Hammerstein model

Power series model

x[n] (.)M (.)2 (.)1 _h 1[n] h2[n] hM[n] y[n]

Figure:Polynomial Hammerstein model

y [n] = x [n] ~ h1[n] + x [n]2~ h2[n] + ... + x [n]M~ hM[n] (1)

(10)

OHKISS method

From Identification to Emulation

Sine Sweep Exponential Under Test Device Guitar Signal Input Sine Sweep Inverse Hammerstein Kernels Computation Model Emulation Hammerstein Emulated Device Output OHKISS Emulation ss[n] ss[n] hm[n] y1[n] x [n] y2[n]

(11)

Deconvolved ESS Through a NL Device

z[n] = y [n] ~ x−1[n] (2) 15 16 17 18 19 20 21 −0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 Time(s) Amplitude h’3 h’5 h’4 h’2 h’1 ∆3=3.18s ∆2=2.01s

Figure:z[n], the deconvolution of the ESS through a Nonlinear device

From measured kernels to Hammerstein kernels (see [5])

h0m[n] compute

=⇒ hm[n] (3)

(12)

Real audio devices emulation

Section 3

(13)

Real audio devices emulation Objective evaluation of the model

Real Output Device Signal vs Emulated Signal

ss[n] Nonlinear y1 y2 ssm_[n] z[n] ss[n] Compute Volterra kernels (.)M hm[n] Convolution NL device under test 0 20 40 60 80 100 120 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 Sample [n] Amplitude y 1 y 2

Figure:Output signal from TSA15 (y1)and emulated

(14)

Real audio devices emulation Model limitations

So what ?

Figure:The Grail of emulation techniques ?

0 50 100 150 200 −1 −0.5 0 0.5 1 Sample [n] Amplitude y 1 y 2

Figure:Comparison between the real output signal

with an input amplitude of 0.5 (y1) and the simulated signal where Hammerstein kernel where calculated for a input amplitude of 1 (y2)

Principal limitation :

(15)

Conclusion

Section 4 Conclusion

(16)

Conclusion

Questions ?

Hammerstein model do not fits for all input amplitude but works well for a given

level.

Can we measure several models at different levels and switching between them ? Do we have to try others models and identification methods ?

(17)

Conclusion

Thank you for your attention !

(18)

Conclusion

Bibliography

M.Schetzen, The Volterra & Wiener Theory of Nonlinear Systems (John Wiley & Sons, 1980).

T.Ogunfunmi, Adaptive Nonlinear System Identification : The Volterra and Wiener Model Approaches (Springer, 2007).

F. Kadlec, P. Lotton, A. Novak, & L. Simon, ”A new method for identification of nonlinear systems using miso model with swept-sine technique : Application to loudspeaker analysis,” presented at 124th Convention of the Audio Engineering Society (2008 May), convention paper 7441.

A. Farina, A. Bellini, & E. Armelloni, ”Nonlinear Convolution : A New Approach for the Auralization of Distorting Systems,” presented at the 110th Convention of the Audio Engineering Society (2001 May), convention paper 5359.

T. Schmitz, J.J. Embrechts, ”Nonlinear Guitar Loudspeaker Simulation,” presented at the 134th Convention of the Audio Engineering Society (2013 May),convention e-Brief 96.