applied sciences Article Experimental Evaluation of Distortion in Amplitude Modulation Techniques for Parametric Loudspeakers Ricardo San Martín 1,* , Pablo Tello 1, Ana Valencia 1 and Asier Marzo 2 1 Acoustics Group, Institute for Advanced Materials and Mathematics—INAMAT, Universidad Pública de Navarra, 31006 Pamplona, Spain; [email protected] (P.T.); [email protected] (A.V.) 2 UpnaLab, Institute of Smart Cities—ISC, Universidad Pública de Navarra, 31006 Pamplona, Spain; [email protected] * Correspondence: [email protected] Received: 19 February 2020; Accepted: 16 March 2020; Published: 19 March 2020 Abstract: Parametric loudspeakers can generate a highly directional beam of sound, having applications in targeted audio delivery. Audible sound modulated into an ultrasonic carrier will get self-demodulated along the highly directive beam due to the non-linearity of air. This non-linear demodularization should be compensated to reduce audio distortion, different amplitude modulation techniques have been developed during the last years. However, some studies are only theoretical whereas others do not analyze the audio distortion in depth. Here, we present a detailed experimental evaluation of the frequency response, harmonic distortion and intermodulation distortion for various amplitude modulation techniques applied with different indices of modulation. We used a simple method to measure the audible signal that prevents the saturation of the microphones when the high levels of the ultrasonic carrier are present. This work could be useful for selecting predistortion techniques and indices of modulation for regular parametric arrays. Keywords: parametric arrays; predistortion techniques; amplitude modulation; directional speakers; harmonic distortion; intermodulation distortion 1. Introduction Parametric loudspeakers exploit the non-linear behavior of acoustic waves travelling through air to generate audible sound along a highly directive path due to the self-demodulation property of finite-amplitude ultrasonic waves [1]. The audible components are more directional than sounds produced by conventional loudspeakers, hence they can find application in contexts where audio must be targeted precisely in space. The directional nature of parametric speakers has been used for directing users towards specific objects [2], and a hand-held directional speaker was used to provide targeted information about the objects pointed by the user [3]. Additionally, sound landscapes in which the audience receives sound stimuli from specific locations can be created with directional speakers [4]. In general, directional speakers enable the targeted delivery of audio for applications in advertising, dual-language systems or notifications [5]. In 1963, Westervelt [6] theoretically described the generation of difference frequency waves from two high-frequency collimated beams referred to as primary waves. Berktay [7] extended this approach and evaluated some possible applications in underwater acoustic transmission. His analysis was not limited to two primary waves and could be applied to a single self-demodulated primary wave. If the primary wave p1 is a generic carrier modulated in amplitude such that: p1(t) = E(t)P0sin!ct, (1) Appl. Sci. 2020, 10, 2070; doi:10.3390/app10062070 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, x FOR PEER REVIEW 2 of 11 Appl. Sci. 2020, 10, 2070 2 of 11 1 where and ω are the amplitude and the angular frequency of the carrier, and () is the 2 envelope function, then Berktay’s farfield solution predicts a self-demodulated wave where P0 and !c are the amplitude and the angular frequency of the carrier, and E(t) is the envelope 3 proportional to the second time derivative of the square of the modulation envelope: function, then Berktay’s farfield solution predicts a self-demodulated wave p2 proportional to the second time derivative of the square of() the∝ modulation ∂ ()/∂ envelope:, (2) 4 2 2 2 2 5 This dependence implies that the self-demodulatedp (t) P @ E (wavet)/@t (,) is not linear to () and that it will (2) 2 / 0 6 suffer from high levels of distortion due to the generated harmonics and a strong low-pass 7 Thisequalization. dependence implies that the self-demodulated wave (p2) is not linear to E(t) and that it will suffer 8 fromVarious high levels preprocessing of distortion techniques due to the generatedhave been harmonics developed and to areduce strong distortion low-pass equalization. using different 9 modulationsVarious preprocessingof the envelope techniques (). Existing have experimental been developed measuremen to reducets [8-10] distortion are mostly using dibasedfferent on 10 modulationsthe total harmonic of the distortion envelope Eor(t )at. Existingcertain repr experimentalesentative measurementsfrequencies, which [8–10 may] are not mostly completely based 11 oncapture the total the harmonicnon-linear distortion response orof atthe certain speakers. representative Here, we frequencies,present an extensive which may comparison not completely of the 12 capturedifferent the amplitude non-linear modulation response oftechniques the speakers. under Here, various we modulation present an extensiveindices in comparisonterms of frequency of the 13 diresponse,fferent amplitude harmonic modulation distortion techniques and intermodul under variousation modulationdistortion. indicesThis instudy terms analyzes of frequency the 14 response,intermodulation harmonic distortion distortion and and the intermodulation harmonics dist distortion.ortions of This the study different analyzes amplitude the intermodulation modulation 15 distortiontechniques and for the various harmonics modulation distortions indices. of the Furthermore, different amplitude the analysis modulation is split by techniques order. To for avoid various the 16 modulationpresence of indices.spurious Furthermore, signal in the the measurem analysis isents, split byour order. method To avoidpreviously the presence selects ofa spuriousdynamic 17 signalmicrophone in the with measurements, limited frequency our method response. previously selects a dynamic microphone with limited 18 frequencyIn the response. Material and Methods section we describe: the experimental setup, the measurement 19 procedure,In the Sectionthe method2 we describe: employed the to experimental measure audi setup,ble thesound measurement in the presence procedure, of high-levels the method of 20 employedultrasonic tocarrier measure and audiblethe evaluated sound amplitude in the presence modulation of high-levels techniques. of ultrasonicIn the results carrier section, and thewe 21 evaluatedreport and amplitude analyze the modulation response techniques.and distortion In the of Sectionthe different3, we reportmodulation and analyze techniques the response and indices. and 22 distortionWe conclude of the by di summarizingfferent modulation the results techniques and their and potential indices. Weimplications. conclude by summarizing the results and their potential implications. 23 2. Materials and Methods 2. Materials and Methods 24 2.1. Experimental Setup 2.1. Experimental Setup 25 A PC (Intel Xeon with 16Gb of RAM, Intel Corporation, Santa Clara, California, USA) was A PC (Intel Xeon with 16Gb of RAM, Intel Corporation, Santa Clara, California, USA) was connected 26 connected to the audio output card (Focusrite Scarlett 18i20, Focusrite plc. High Wycombe, to the audio output card (Focusrite Scarlett 18i20, Focusrite plc. High Wycombe, Buckinghamshire, 27 Buckinghamshire, England) for general audio input/output. For emitting audible sound, the card England) for general audio input/output. For emitting audible sound, the card output was connected 28 output was connected to an auto-amplified monitor (Neumann KH120A, Georg Neumann GmbH, to an auto-amplified monitor (Neumann KH120A, Georg Neumann GmbH, Berlin, Germany). For the 29 Berlin, Germany). For the ultrasonic output, the card was connected into an amplifier (Akozon DC12- ultrasonic output, the card was connected into an amplifier (Akozon DC12-24V 2 100 W power 30 24V 2 × 100 W power amplifier, 14-100 KHz, Akozon, Shenzhen, Guangdong, China)× and then into a amplifier, 14-100 KHz, Akozon, Shenzhen, Guangdong, China) and then into a parametric array shown 31 parametric array shown in Figure 1 (array SSCI-018425 made of 49 transducers, Switch Science Inc., in Figure1 (array SSCI-018425 made of 49 transducers, Switch Science Inc., Tokyo, Japan). The largest 32 Tokyo, Japan). The largest output voltage amplitude of the amplifier was 24 Vpp, which was output voltage amplitude of the amplifier was 24 Vpp, which was sufficient and within the normal 33 sufficient and within the normal operating voltage of the transducers forming the array. operating voltage of the transducers forming the array. 34 35 FigureFigure 1.1. UltrasonicUltrasonic arrayarray employedemployed forfor thethe parametricparametric speakerspeaker mademade ofof 4949 ultrasonicultrasonic transducerstransducers ofof 36 1616 mmmm diameter.diameter. 37 ForFor receivingreceiving audio,audio, aa microphonemicrophone (di(differentfferent modelsmodels werewere employed)employed) waswas placedplaced 22 metersmeters awayaway 38 fromfrom thethe sound source. source. Except Except for for the the GRAS GRAS microphone, microphone, which which needed needed the Norsonic the Norsonic type 335 type front- 335 39 front-endend for signal for signal conditioning, conditioning, the microphones the microphones were weredirectly directly connected connected