Universidad EAFIT Contribution of the conditioning stage to the Total Harmonic Distortion in the Parametric Array Loudspeaker Andrés Yarce Botero Thesis to apply for the title of Master of Science in Applied Physics Advisor Olga Lucia Quintero. Ph.D. Master of Science in Applied Physics Science school Universidad EAFIT Medellín - Colombia 2017 1 Contents 1 Problem Statement 7 1.1 On sound artistic installations . 8 1.2 Objectives . 12 1.2.1 General Objective . 12 1.2.2 Specific Objectives . 12 1.3 Theoretical background . 13 1.3.1 Physics behind the Parametric Array Loudspeaker . 13 1.3.2 Maths behind of Parametric Array Loudspeakers . 19 1.3.3 About piezoelectric ultrasound transducers . 21 1.3.4 About the health and safety uses of the Parametric Array Loudspeaker Technology . 24 2 Acquisition of Sound from self-demodulation of Ultrasound 26 2.1 Acoustics . 26 2.1.1 Directionality of Sound . 28 2.2 On the non linearity of sound . 30 2.3 On the linearity of sound from ultrasound . 33 3 Signal distortion and modulation schemes 38 3.1 Introduction . 38 3.2 On Total Harmonic Distortion . 40 3.3 Effects on total harmonic distortion: Modulation techniques . 42 3.4 On Pulse Wave Modulation . 46 4 Loudspeaker Modelling by statistical design of experiments. 49 4.1 Characterization Parametric Array Loudspeaker . 51 4.2 Experimental setup . 52 4.2.1 Results of PAL radiation pattern . 53 4.3 Design of experiments . 56 4.3.1 Placket Burmann method . 59 4.3.2 Box Behnken methodology . 62 5 Digital filtering techniques and signal distortion analysis. 66 5.1 Chirp signal analysis . 66 5.1.1 Digital filter analysis . 69 5.1.2 Measurements of the harmonic content of a signal . 73 6 Conclusions 76 7 Acknowledgements 78 2 List of Figures 1.1 Design and construction of The Soundhouse ................................. 8 1.2 The SoundHouse, Marco Alunno 2015 . 9 1.3 The Forest and the Shadows projection . 10 1.4 The Forest of the Shadows, Marco Alunno 2016 . 11 1.5 Linear velocity acoustic dependence of temperature . 14 1.6 Deformation of a sinusoidal wave (black) into a sawtooth wave (red) due to local changes of speed during sound propagation . 14 1.7 Common signals and harmonic contents . 15 1.8 Audible frecuency by-product [1] . 16 1.9 Byproducts production due to the modulation of ultrasound in air . 16 1.10 Low frecuency wave generation . 17 1.11 Complete schematic operation PAL . 18 1.12 Constitutive equation to the KZK . 19 1.13 Soundlazer array . 22 1.14 Components of the PZT transducer and cone to couple the impedance [2] . 23 1.15 Cavities configuration to modify the frequency response of the PVDF transducer [3] . 23 1.16 Attenuation Characteristics of Sound Pressure by Distance . 24 2.1 Conical structures used to route the sound . 28 2.2 Commercial Sound Dome . 29 2.3 Other techniques to enroute sound . 29 2.4 Two-Frequency mutual interaction in a nonlinear medium . 30 2.5 First Parametric Array Loudspeaker Yoneyama . 31 2.6 Commercial Parametric Loudspeakers . 32 2.7 Close difference frequency wave addition . 34 2.8 Moiré pattern example . 35 2.9 Monaural and Binaural beats . 35 2.10 Graphical interpretation of a Linear and a Non linear system . 37 3.1 Common frequency spectrum of a signal . 39 3.2 Effect on the harmonic content of a signal caused for a Non Linear medium transformation . 39 3.3 Frequency spectrum Audiospot AS-24 The Soundhouse .......................... 41 3.4 Frequency spectrum Soundlazer Parametric Pro amp kit The Forest and the Shadows . 41 3.5 Pre-Distortion processing . 43 3.6 Comparison between the SRAM and the SBSAM . 45 3.7 PWM Output voltage frequency relation . 47 4.1 Cycle of the Design of Experiment methodology . 50 4.2 Soundlazer model SL-01 . 51 4.3 Electronic Schematic of the Soundlazer SL-01 . 52 4.4 Experimental setup for the radiation pattern characterization of the Loudspeaker . 53 4.5 Soundlazer SL-01 sound field characterization . 54 3 4.6 Testing of two microphones to choose the more appropriate one . 55 4.7 Controllable and non controllable factors for the DOE proposed . 56 4.8 Sigmastudio ™ digital signal processing stages . 57 4.9 Schematic Design of Experiment to measure the THD and the fundamental Intensity of the Parametric Array Loudspeaker . 58 4.10 Precondition stage DSP . 58 4.11 Placket Burmann second experiment, Response THD . 61 4.12 Placket Burmann response for the analysis of the fundamental . 61 4.13 Surface response plots of 3-factor Box Behnken analysis . 64 4.14 Contour plot of surface response . 65 5.1 Chirp Signal tested in the PAL . 67 5.2 GUI Interface for the signal analysis . 67 5.3 Time-dependent spectra of Chirp demodulated signal from Soundlazer PAL . 68 5.4 Time spectra of linear chirp signal demodulated 0-4500 Hz . 69 5.5 Software Designed Band-Pass filters . 70 5.6 Chime signal after and before filtered . 71 5.7 Band-Pass filter log chime signal . 72 5.8 Periodogram power spectrum 400 Hz . 73 5.9 THD and five first harmonics . 74 5.10 Signal to Noise Ratio 400 Hz . 74 5.11 Signal noise + distortion . 75 7.1 R Code for the Plackett Burmann Design . ..