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)P0sinωct, (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 𝑃 and ω are the amplitude and the angular frequency of the carrier, and 𝐸(𝑡) is the 2 envelope function, then Berktay’s farfield solution predicts a self-demodulated wave 𝑝 where P0 and ωc 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 square𝑝 of(𝑡) the∝𝑃 modulation ∂ 𝐸 (𝑡)/∂𝑡 envelope:, (2) 4 2 2 2 2 5 This dependence implies that the self-demodulatedp (t) P ∂ E (wavet)/∂t (𝑝, ) is not linear to 𝐸(𝑡) 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 𝐸(𝑡). 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 to the to input the input of the of sound the sound card. Appl. Sci. 2020, 10, 2070 3 of 11 Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 11
1 card.The Themeasurements measurements were were taken taken in inthe the listening listening ro roomom of anan acousticsacoustics laboratorylaboratory with with di ffdifferenterent 2 absorbentabsorbent materials: materials: foam, foam, melamine melamine foam foam and and regenerated regenerated cotton cotton bonded bonded with with thermosetting thermosetting resin. resin. 3 TheThe reverberation reverberation times times were were less less than than 0.25 0.25 s from s from the the third third octave octave band band of 320of 320 Hz. Hz.
4 2.2.2.2. Measurement Measurement Procedure Procedure 5 TheThe frequency frequency response response of of a loudspeakera loudspeaker describes describes the the range range of of audible audible frequencies frequencies that that it canit can 6 reproduce.reproduce. For For conventional conventional devices, devices, it it is is usually usually measured measured in in an an anechoic anechoic chamber chamber where where the the 7 loudspeakerloudspeaker under under test test is is excited excited by by a sweepa sweep signal signalx( t𝑥)(.𝑡 This). This sweep sweep typically typically ranges ranges from from 20 20 Hz Hz to to 8 2020 kHz. kHz. The The signal signal emitted emitted by the by speakerthe speaker was thenwas recordedthen recorded with a with flat response a flat response microphone microphone to obtain to 9 theobtain signal they( tsignal). By means𝑦(𝑡). By of means FFT techniques, of FFT techniques, the impulse the responseimpulse responseh(t) and itsℎ( corresponding𝑡) and its corresponding transfer 10 functiontransfer were function obtained: were obtained: ! ( ( ))f f t(y(t)) ℎ(𝑡)h(t) = = 𝑖𝑓𝑓𝑡i f f t . . (3)(3) ( ( ))f f t(x(t)) 11 For parametric loudspeakers, the process encompasses more stages. First, an upsampling of 12 For parametric loudspeakers, the process encompasses more stages. First, an upsampling of the the excitation signal was performed to avoid aliasing when moving to the ultrasonic range. Then, 13 excitation signal was performed to avoid aliasing when moving to the ultrasonic range. Then, the the chosen predistortion technique was applied to the signal and emitted through the speaker. 14 chosen predistortion technique was applied to the signal and emitted through the speaker. Afterwards, a microphone recorded the signal and a bandpass filter was applied. Subsequent 15 Afterwards, a microphone recorded the signal and a bandpass filter was applied. Subsequent downsampling was used to obtain the signal in the audible range. This signal was compared with the 16 downsampling was used to obtain the signal in the audible range. This signal was compared with original excitation signal. This process is summarized in Figure2. The spectral representation of the 17 the original excitation signal. This process is summarized in Figure 2. The spectral representation of signal at each step of the process can be found in Supplementary Figure S2. 18 the signal at each step of the process can be found in Supplementary Figure 2.
19 20 FigureFigure 2. Block2. Block diagram diagram of the of transferthe transfer function function measurement measurement method method in an ultrasonic in an ultrasonic parametric parametric array. 21 array. The International Standard IEC 60268-21 [11] was approved in 2018 and specifies measurement methods to evaluate the transfer behavior of a device under test (DUT). It can be applied to 22 The International Standard IEC 60268-21 [11] was approved in 2018 and specifies measurement electroacoustic transducers, active and passive sound systems, amplified speakers, televisions, portable 23 methods to evaluate the transfer behavior of a device under test (DUT). It can be applied to audio devices, car sound systems or professional equipment. Therefore, the DUT can contain 24 electroacoustic transducers, active and passive sound systems, amplified speakers, televisions, components that perform signal processing before the transduction of the electrical signal into an 25 portable audio devices, car sound systems or professional equipment. Therefore, the DUT can contain acoustical output signal radiated by the passive actuators. This capability makes this standard suitable 26 components that perform signal processing before the transduction of the electrical signal into an for evaluating parametric loudspeakers. 27 acoustical output signal radiated by the passive actuators. This capability makes this standard All transfer functions and distortion measurements described in the paper have been performed 28 suitable for evaluating parametric loudspeakers. following this standard. Some of the measurements and post-processing has been carried out with the 29 All transfer functions and distortion measurements described in the paper have been performed help of the ITA-Toolbox, an open source toolbox for Matlab [12]. 30 following this standard. Some of the measurements and post-processing has been carried out with 31 2.3.the Audio help Measurementsof the ITA-Toolbox, in the Presence an open of source a High-Level toolbox Ultrasonic for Matlab Carrier [12].
32 2.3.The Audio high measurements level of the ultrasonicin the presence primary of a high-level wave encumbers ultrasonic thecarrier measurement of the demodulated audible secondary signal. Carrier levels above 120 dB are common even at distances of 2 meters and 33 generateThe spurious high level signals of the in theultrasonic receiving primary system wave [13]. encumbers These spurious the measurement signals are not of perceived the demodulated by the 34 humanaudible ear secondary and thus itsignal. is desirable Carrier to levels filter themabove out. 120 dB are common even at distances of 2 meters and 35 generateSome methodsspurious proposedsignals in to the avoid receiving the appearance system [13]. of theThese spurious spurious signal signals are basedare not on perceived the use of by 36 acousticthe human filters ear [14 and–21 ]thus made it is of desirable a thin plastic to filter film them or phononic out. crystals with a bandgap at the carrier 37 Some methods proposed to avoid the appearance of the spurious signal are based on the use of frequency. These filters are mounted in front of the receiving transducer and reduce the amplitude of 38 acoustic filters [14-21] made of a thin plastic film or phononic crystals with a bandgap at the carrier the primary wave. However, the audible frequencies may also be affected by this method, especially 39 frequency. These filters are mounted in front of the receiving transducer and reduce the amplitude the high ones. The response in the audible range can be estimated without using filters by measuring in 40 of the primary wave. However, the audible frequencies may also be affected by this method, the secondary lobes, but the position of the lobes varies with the frequency. Recent methods to reduce 41 especially the high ones. The response in the audible range can be estimated without using filters by the spurious signal based on phase-cancellation [22,23] are only suitable for axial measurements. 42 measuring in the secondary lobes, but the position of the lobes varies with the frequency. Recent Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 11 Appl. Sci. 2020, 10, 2070 4 of 11 1 methods to reduce the spurious signal based on phase-cancellation [22,23] are only suitable for axial 2 measurements. 3 OtherOther techniques techniques use use a a condenser condenser microphone microphone orthogonalorthogonal toto the the incident incident wave wave where where its its 4 ultrasonicultrasonic sensitivity sensitivity isis lower lower [24[2].4]. Thereby, Thereby, the the amplitude amplitude of of the the recorded recorded ultrasonic ultrasonic waves waves is is 5 reducedreduced while while preserving preserving the soundthe sound level inlevel the audiblein the audible range. This range effectively. This effectively prevents the prevents generation the 6 ofgeneration spurious signals.of spurious signals. 7 BasedBased on on the the previous previous principle, principle, we we explored explored the the use use of of a a microphone microphone with with reduced reduced ultrasonic ultrasonic 8 sensitivitysensitivity but but good good audio audio performance. performance. Two Two condenser condenser (GRAS (GRAS AC40 AC40 –– GRO,GRO, G.R.A.S. G.R.A.S. SoundSound & & 9 Vibration,Vibration, Holte, Holte, Denmark, Denmark, Behringer Behringer ECM8000 ECM8000 -- BHO,BHO, Behringer Behringer International International GmbH, GmbH, Willich, Willich, 10 Germany)Germany) and and three three dynamic dynamic (Shure (Shure SM57 SM57 - - SH7, SH7, Shure Shure Inc. Inc. Niles, Niles, Illinois, Illinois, USA, USA, Behringer Behringer XM8500 XM8500 11 -- BHX BHX and and BCT BCT MD1 MD1 – – BCT, BCT Behringer, Behringer International International GmbH, GmbH, Willich, Willich, Germany) Germany) microphones microphones were were 12 selectedselected for for the the study. study Detailed. Detailed specification specification can can be be found found in in Supplementary Supplementary Table Table SI. I. TheThe frequency frequency 13 responseresponse of of the the microphones microphones in in the the audible audible range range was was measured measured by by emitting emitting sweeps sweeps with with a a monitor monitor (Neumann KH120A, Georg Neumann GmbH, Berlin, Germany) with flat response ( 2 dB between 14 (Neumann KH120A, Georg Neumann GmbH, Berlin, Germany) with flat response (+±-2 dB between 15 5454 Hz Hz and and 20 20 kHz) kHz) and and is is shown shown in in Figure Figure3a. 3.a.
(a) (b)
16 FigureFigure 3. 3.Relative Relative frequency frequency response response of of the the di differentfferent microphones. microphones. ( a(a)) Response Response in in the the audible audible range range 17 withwith a a calibrated calibrated monitor monitor as as an an emitter. emitter. ( b(b)) Response Response in in the the ultrasonic ultrasonic range range with with the the ultrasonic ultrasonic array array 18 usedused as as the the emitter. emitter. Response Response normalized normalized at at carrier carrier level level measured measured by by a a GRO GRO microphone. microphone.
19 TheThe same same procedure procedure was was repeated repeated in in the the ultrasonic ultrasonic range range using using the the parametric parametric speakerspeaker asas anan 20 emitter.emitter. TheThe responsesresponses areare shownshown inin FigureFigure3 b.3b. The The response response of of the the GRO GRO microphone microphone (i.e., (i.e. upper, upper 21 curve)curve) can can be be used used as an as approximation an approximation of the of normalized the normalized frequency frequency response response of the ultrasonic of the ultrasonic emitter 22 measuredemitter measured at 2 m since at 2 m this since microphone this microphone had the ha flattestd the flattest ultrasonic ultrasonic response. response. The responseThe response of the of 23 parametricthe parametric speaker speaker peaked peak ated 40.9 at 40.9 kHz, kHz, with with a 3 a dB-3 dB bandwidth bandwidth of of 1.5 1.5 kHz kHz and and a a6 -6 dB dB bandwidth bandwidth − − 24 ofof 3.9 3.9 kHz. kHz. ThisThis reducedreduced bandwidth bandwidth isis the the cause cause of of a a spurious spurious signal signal being being typically typically smaller smaller at at high high 25 frequencies.frequencies. TheThe progressiveprogressive reductionreduction ofof thethe levelslevels atat thethe sidebands,sidebands, whichwhich areare usedused toto emitemit thethe 26 modulatedmodulated audio, audio, leads leads to to a a partial partial reduction reduction of of the the non-linearity non-linearity acquired acquired by by the the microphones. microphones. 27 TheThe dynamic dynamic microphones microphones (i.e., (i.e., SH7, SH7, BHX BHX and and BCT) BCT) registeredregistered a a carriercarrier levellevel reductionreduction ofof 3030 dB.dB. 28 ThisThis means means that that the the recorded recorded audio audio is is less less likely likely to to be be a affectedffected by by distortion distortion artifacts artifacts generated generated from from 29 thethe high high levels levels of of pressure. pressure. This This eeffectffect is is illustrated illustrated in in Figure Figure4 ,4 which, which shows shows the the frequency frequency responses responses 30 obtainedobtained with with di differentfferent microphones microphones when when the the ultrasonic ultrasonic array array is is emitting emitting with with a a conventional conventional AM AM 31 modulationmodulation (i.e., (i.e. DSBAM,, DSBAM, described described in furtherin further sections). section Fors). For the the two two condenser condenser microphones, microphones, GRO GRO and 32 BHO,and BHO, the spurious the spurious signal signal was aff wasecting affecting the recordings the recordings along most along of themost frequency of the frequency range. This range. was This not 33 thewas case not when the usingcase when the dynamic using the microphones. dynamic microphones Their experimental. Their curves experimental show good curves agreement show with good 34 theagreement theoretical with curves the theoretical of a parametric curves loudspeaker. of a parametric These loudspeaker curves were. proportional These curves to weref n, where proportionalf is the 35 frequencyto 푓푛, where and n푓 isis the the ratio frequency between and di ff푛raction is the lengthratio between and absorption diffraction length length [16 ].and Di ffabsorptionraction length length is 36 the[16 area]. Diffraction of the transmitter length is divided the area by the of wavelengththe transmitter at the divided primary by frequencies the wavelength and absorption at the primary length 37 isfrequencies the inverse and of the absorption nominal length absorption is the coe inversefficient of atthe the nominal primary absorption frequencies. coefficientn = 2 corresponds at the primary to Appl. Sci. 2020, 10, 2070 5 of 11 Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 11
1 thefrequencies. Westervelt 푛 solution = 2 corresponds [6] for a large to the ratio, Westerveltn = 1 is a solution good approximation [6] for a large to the ratio, solution 푛 = 1 obtained is a good 2 byapproximation Berktay and Leahy to the [ 25solution] for a smallobtained ratio. by In Berktay practice, and the Leahy curves [2 lie5] for somewhere a small ratio. between In practice,n = 1 and the 3 n curves= 2 [26 ].lie In somewhere our experiments, between the 푛 response = 1 and of푛 the= 2 [ dynamic26]. In our microphones experiments, was the in response good agreement of the dynamic with 4 themicrophones curve f 1.6 from was approximatelyin good agreement 500 Hz–4 with kHz.the curve 푓1.6 from approximately 500 Hz–4 kHz.
5 6 FigureFigure 4. Frequency4. Frequency responses responses of the di offf erence-frequency the difference-frequency signal obtained signal with obtaine the testedd with microphones. the tested 7 Themicrophones. ultrasonic array The ultrasonic was used asarray an emitterwas used with as aan conventional emitter with DSBAM a conventional modulation. DSBAM modulation.
8 TheThe BHX BHX microphone microphone is consideredis considered suitable suitable for evaluatingfor evaluating predistortion predistortion techniques techniques in view in view of the of 9 resultsthe results shown shown in Figures in Figure3 ands4 as3 and well 4 as as the well usable as th rangee usable of frequencies range of frequencies of the ultrasonic of the speaker. ultrasonic 10 Thespeaker. rest of The the measurementsrest of the measurements detailed in detailed this article in arethis performedarticle are performed with this microphone. with this microphone.
11 2.4.2.4. Preprocessing Preprocessing Techniques techniques 12 AmplitudeAmplitude modulation modulation (AM) (AM) is is the the most most common common preprocessing preprocessing technique technique in in parametric parametric 13 loudspeakers.loudspeakers. It It consists consists of of changing changing the the amplitude amplitude of of a a relatively relatively high-frequency high-frequency carrier carrier of of angular angular frequency ωc according to the amplitude of a modulating signal. The envelope of the carrier wave is 14 frequency ω푐 according to the amplitude of a modulating signal. The envelope of the carrier wave is 15 weightedweighted with with the the desired desired audible audible sound sound signal signals( t푠).(푡). 16 DoubleDouble side side band band amplitude amplitude modulation modulation (DSBAM) (DSBAM) was was the originalthe original method method used used by Yoneyama by Yoneyama [27] 17 to[2 produce7] to produce wideband wideband audio audio with with parametric parametric loudspeakers. loudspeakers. The The modulated modulated ultrasonic ultrasonic wave wavep(t )푝is(푡) 18 expressedis expressed as as pDSBAM(t) = [1 + m s(t)]sin(ωct), (4) 푝퐷푆퐵퐴푀(푡) = [1 + 푚 푠(푡)] sin( ω푐 푡), (4) 19 where m is the modulation index and has values ranging from 0 to 1. DSBAM is simple to implement 20 andwhere requires 푚 is low the modulation computational index resources. and has values In addition, ranging it generatesfrom 0 to 1. a DSBAM louder audible is simple signal to implement since it 21 usesand both requires sidebands. low computational However, due resources. to the tone In diaddition,fference betweenit generates the a upper louder (USB) audible and signal lower since band it 22 (LSB),uses theboth second sidebands. harmonic However, is also due louder. to the tone difference between the upper (USB) and lower band 23 (LSB),A simple the second solution harmonic to reduce is also the louder second. harmonic is to transfer the energy to a single band as in 24 the singleA simple side band solution amplitude to reduce modulations the second (SSBAM) harmonic [28 is], to which transfer are namedthe energy LSBAM to a forsingle the band lower as or in 25 USBAMthe single for theside upper band sideband.amplitude Thismodulations modulation (SSBAM) can be obtained[28], which by a usingre named high-pass, LSBAM low-pass for the filterlower 26 oror adding USBAM a quadrature for the upper term sideband. to the conventional This modulation AM. For can the be latter, obtained a Hilbert by filterusing is high needed-pass, to convertlow-pass 27 thefilter modulating or adding signal a quadratures(t) into term its orthogonal to the conventional counterpart AM.sˆ(t) For. The the modulations latter, a Hilbert are expressedfilter is needed as: to 28 convert the modulating signal 푠(푡) into its orthogonal counterpart 푠̂(푡) . The modulations are
29 expressed as: p (t) = [1 + ms(t)]sin(ωct) msˆ(t)cos(ωct), (5) LSBAM − 푝퐿푆퐵퐴푀(푡) = [1 + 푚푠(푡)] sin(ω푐 푡) − 푚푠̂(푡) cos(ω푐 푡), (5) 푝푈푆퐵퐴푀(푡) = [1 + 푚푠(푡)] sin(ω푐 푡) + 푚푠̂(푡) cos(ω푐 푡). (6) Appl. Sci. 2020, 10, 2070 6 of 11
pUSBAM(t) = [1 + ms(t)]sin(ωct) + msˆ(t)cos(ωct). (6) Inspired by Berktay’s solution, a square root operation was added to the AM modulation, leading to the so-called square root amplitude modulation (SRAM): q pSRAM(t) = [1 + ms(t)]sin(ωct). (7)
This procedure theoretically removes distortion but introduces infinite harmonics of the original signal s(t). Therefore, the resulting reduction in the distortion is limited by the bandwidth of the ultrasonic emitters [29]. A set of preprocessing techniques based on quadrature amplitude modulation has been proposed to deal with the bandwidth limitation of the emitters [30]. This class of preprocessing techniques referred to as modified amplitude modulation (MAM) can be adapted to the available bandwidth using different orders of the Taylor expansion for the distortion term modulated by the orthogonal carrier. The modulated ultrasonic waves for the first two orders are described as: 1 2 2 p (t) = [1 + ms(t)]sin(ωct) + 1 m s (t) cos(ωct), (8) MAM1 − 2 1 2 2 1 4 4 p (t) = [1 + ms(t)]sin(ωct) + 1 m s (t) m s (t) cos(ωct). (9) MAM2 − 2 − 8 Due to the low-cost of its implementation, FM-based methods have also been analyzed empirically [31]. However, demodulating FM waves causes higher harmonic distortions at conventional sound pressure levels. There are combined methods that achieve higher sound pressure levels at lower frequencies [32]. We kept the scope of the paper to amplitude modulation techniques, but frequency modulation is a promising technique that could be included in future studies. Double side band amplitude modulation (DSBAM), lower side band amplitude modulation (LSBAM), upper side band amplitude modulation (USBAM), square root amplitude modulation (SRAM), modified amplitude modulation 1 (MAM1) and 2 (MAM2) can be found as block implementations in Supplementary Figure S1. These preprocessing techniques were implemented in Matlab.
3. Results
3.1. Frequency Response We used an 11-second logarithmic sweep from 18 Hz to 22 kHz as excitation signal for each of the six modulations (using a modulation index of m = 1). Magnitude curves of the transfer functions are shown in Figure5. The curves were smoothed by applying 1 /12th bandwidth spectral averaging. The parametric speaker barely reproduced low frequencies and the response increased by about 12 dB/octave between 300 and 1500 Hz. After 1500 Hz, the transfer functions varied slightly for each modulation. LSBAM showed the largest difference with a marked decrease at 6.5 kHz. This is due to the asymmetric response of the loudspeaker array that also had a marked decrease at approximately 33.5 kHz (which is 6.5 kHz below the carrier frequency of 40 kHz; Figure2b). This minimum was not present in the USBAM since this modulation only uses the upper sideband. Beyond 10 kHz, all responses dropped abruptly due to the limited frequency response of the recording microphone. Similar curves, with a lower relative level, were obtained for each modulation if the modulation index was reduced. Appl.Appl. Sci. Sci.2020 20,2010, ,10 2070, x FOR PEER REVIEW 7 of7 11of 11
1 2 FigureFigure 5. Transfer 5. Transfer functions functions measured measured with with different different preprocessing preprocessing techniques techniques (modulation (modulation index index m = 1). m 3 = 1). 3.2. Harmonic Distortion
4 3.2.In Harmonic the audio distortion range, there are different parameters and methods to evaluate the non-linear response of a speaker. The most widespread measure for characterizing the non-linear response of a speaker is 5 In the audio range, there are different parameters and methods to evaluate the non-linear the total harmonic distortion (THD) obtained by sinusoidal signals of increasing frequency. Using 6 response of a speaker. The most widespread measure for characterizing the non-linear response of a consecutive increments of stationary tones (step-by-step method) is the most common procedure 7 speaker is the total harmonic distortion (THD) obtained by sinusoidal signals of increasing frequency. employed to measure distortion of parametric loudspeakers that can be found in the literature [33]. 8 Using consecutive increments of stationary tones (step-by-step method) is the most common However, in the audio range it is preferable to use the technique based on sweeps proposed by 9 procedure employed to measure distortion of parametric loudspeakers that can be found in the Farina [34] that offers benefits in terms of ease of use, signal-to-noise ratio and immunity against the 10 literature [33]. However, in the audio range it is preferable to use the technique based on sweeps temporal variation of the DUT. We will use this method. 11 proposed by Farina [34] that offers benefits in terms of ease of use, signal-to-noise ratio and immunity The advantage of measuring impulse responses using sweeps is that the artifacts generated by 12 against the temporal variation of the DUT. We will use this method. the harmonic distortion can be eliminated, since these appear at negative times in relation to direct 13 The advantage of measuring impulse responses using sweeps is that the artifacts generated by sound, and can be separated from the desired h(t) [35]. In addition, when using a logarithmic sweep as 14 the harmonic distortion can be eliminated, since these appear at negative times in relation to direct excitation signal, the harmonics will have a constant group delay independent of the frequency when it 15 sound, and can be separated from the desired ℎ(푡) [35]. In addition, when using a logarithmic sweep is deconvoluted with the reference spectrum. They will therefore appear in predictable positions of h(t) 16 as excitation signal, the harmonics will have a constant group delay independent of the frequency and can be separated by windowing if the sweep is sufficiently slow. Hence, with a single excitation 17 when it is deconvoluted with the reference spectrum. They will therefore appear in predictable signal, both the linear transfer function of the system and the harmonic distortion decomposed into 18 positions of ℎ(푡) and can be separated by windowing if the sweep is sufficiently slow. Hence, with several orders can be obtained, eliminating the influence of non-linearities. We measured harmonics 19 a single excitation signal, both the linear transfer function of the system and the harmonic distortion up to the 5th order. 20 decomposed into several orders can be obtained, eliminating the influence of non-linearities. We In Supplementary Figure S3, we present the decomposed harmonic distortion for the different 21 measured harmonics up to the 5th order. preprocessing techniques. It can be seen that beyond the 2nd order harmonic, the distortion was 22 In Supplementary Figure 3, we present the decomposed harmonic distortion for the different negligible. Most of the distortion resides in the second harmonic (see Supplementary Figure S3). It is 23 preprocessing techniques. It can be seen that beyond the 2nd order harmonic, the distortion was worth noting that some techniques (e.g., MAM1) reduced the 2nd harmonic considerably at some 24 negligible. Most of the distortion resides in the second harmonic (see Supplementary Figure 3). It is frequencies, almost to the levels of the 3rd harmonic. 25 worth noting that some techniques (e.g., MAM1) reduced the 2nd harmonic considerably at some The level of total harmonic distortion (L ) in decibels was determined by the formula: 26 frequencies, almost to the levels of the 3rd harmoniTHD c. q 27 The level of total harmonic distortion (퐿푇퐻퐷) Pin5 decibels was determined by the formula: ep2 ( f ) 5 n=21 n f (10) √∑푛=1 푝̃푛푓(푓) LTHD( f ) = 20lg dB. (10) 퐿푇퐻퐷(푓) = 20 lg ( p ( f ) ) 푑퐵. 푝̃푓e(푓f )
28 where 푝̃푛푓(푓) is the RMS value of the nth-order harmonic component and 푝̃푓(푓) is the RMS value where epn f ( f ) is the RMS value of the nth-order harmonic component and ep f ( f ) is the RMS value of 29 of the first harmonic of the fundamental component. the first harmonic of the fundamental component. 30 Figure 6 shows the 퐿푇퐻퐷 obtained for all modulations with m = 1. 퐿푇퐻퐷 smaller than 5% (i.e., Figure6 shows the LTHD obtained for all modulations with m = 1. LTHD smaller than 5% 31 – 26 dB) were generally acceptable levels for domestic audio equipment. MAM techniques provided (i.e., 26 dB) were generally acceptable levels for domestic audio equipment. MAM techniques 32 the− best results up to 2.6 kHz, and single sidebands (i.e., LSBAM and USBAM) provided the best Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 11
1 overall result, staying below the distortion threshold throughout the working frequency of the
2 speaker. For DSBAM, the high level of the second harmonic caused 퐿푇퐻퐷 greater than – 20 dB in 3 virtually the entire frequency range. MAM and SRAM modulations obtained good results up to 2 4 Appl.kHz Sci. but2020 ,for10, 2070higher frequencies. Its behavior was similar to the conventional DSBAM modulation.8 of 11 5 The smallest values for harmonic distortion were obtained with single sideband modulations. This is 6 because these modulations used only one band, thus there was only one difference-signal. The other 7 providedtechniques the use bestd resultsa double up band to 2.6 and kHz, thus and produce singled sidebands two difference (i.e.,-signals LSBAM generating and USBAM) more provided harmonics 8 theand best increasing overall result, the harmonic staying belowdistortion. the distortion threshold throughout the working frequency of the speaker. For DSBAM, the high level of the second harmonic caused LTHD greater than 20 dB 9 In Supplementary Figure 4, we show the 퐿푇퐻퐷 for each predistortion technique and modulation− 10 inindex virtually ranging the entire from frequency 0.1 to 1 at range. 0.1 steps. MAM In and general, SRAM the modulations larger theobtained modulation good index, results the up more to 11 2 kHzdistortion but for appear highered frequencies.. However, Its this behavior increment was similar was more to the conventionalpronounced forDSBAM DSBAM modulation. along all 12 Thefrequencies, smallest values for SRAM for harmonic from 1 to distortion 6 kHz, for were MAM1 obtained beyond with 1 single kHz, sidebandand for MAM2 modulations. beyond This1.5 kHz. is 13 becauseBoth LSBAM these modulations and USBAM used were only less one affected band, thus by there an increase was only of onetotal di ff harmonicerence-signal. distortion The other as the 14 techniquesmodulation used index a double increase bandd. and thus produced two difference-signals generating more harmonics and increasing the harmonic distortion.
15
16 FigureFigure 6. Comparison6. Comparison of ofLTHD 퐿푇퐻퐷levels levels for for each each modulation modulation technique technique (modulation (modulation index index m = m1). = 1).
17 3.3.In Intermodulation Supplementary Figuredistortion S4, we show the LTHD for each predistortion technique and modulation index ranging from 0.1 to 1 at 0.1 steps. In general, the larger the modulation index, the more distortion 18 When a system is excited by a two-tone stimulus, intermodulation distortion may appear at the appeared. However, this increment was more pronounced for DSBAM along all frequencies, for SRAM 19 sum and difference of the two tones and their harmonics. If one of the tones (푓 ) is significantly lower from 1 to 6 kHz, for MAM1 beyond 1 kHz, and for MAM2 beyond 1.5 kHz. Both1 LSBAM and USBAM 20 than the other tone (푓 ), the intermodulation components are concentrated around the highest were less affected by an increase2 of total harmonic distortion as the modulation index increased. 21 frequency, at frequencies 푓2 ± 푛푓1 (where 푛 is a natural number). According to the IEC Standard 22 3.3.60268 Intermodulation-21 [26], the Distortion total intermodulation distortion (퐼푀퐷푇 ), in percentage and considering only 23 intermodulation components up to 3rd order, can be expressed as: When a system is excited by a two-tone2 stimulus, intermodulation distortion may appear at the sum ∑ 푝̃(푓2 − 푘푓1) + 푝̃(푓2 + 푘푓1) (11) ( ) 푘=1 and difference of the two퐼푀 tones퐷푇 푓1, and푓2 = their harmonics. If one of the tones100%( f1), is significantly lower than 푝̃(푓2) 24 the other tone ( f2), the intermodulation components are concentrated around the highest frequency, at frequencies f2 n f1 (where n is a natural number). According to the IEC Standard 60268-21 [26], 25 where 푝̃(푓2 ± (±푛 − 1)푓1) is the RMS value of the nth-order intermodulation component at the sum the total intermodulation distortion (IMDT), in percentage and considering only intermodulation 26 and difference of the two tones, and 푝̃(푓2) is the RMS value of the fundamental component at the components up to 3rd order, can be expressed as: 27 excitation frequency 푓2. 28 To analyze this parameter along Pthe2 entire frequency range, the calculation has been divided k=1 ep( f2 k f1) + ep( f2 + k f1) 29 into two parts: variationIMD ofT the( f1, lowf2) -=frequency tone− 푓1 from 20 Hz to100%, 1 kHz while keeping the (11) high- p( f2) 30 frequency tone 푓2 at a constant frequency of 7 kHze, and variation of the high-frequency tone 푓2 from 31 500 Hz to 20 kHz while keeping the high-frequency tone 푓1 at a constant frequency of 60 Hz. where ep( f2 (n 1) f1) is the RMS value of the nth-order intermodulation component at the sum and ± − difference of the two tones, and ep( f2) is the RMS value of the fundamental component at the excitation frequency f2. To analyze this parameter along the entire frequency range, the calculation has been divided into two parts: variation of the low-frequency tone f1 from 20 Hz to 1 kHz while keeping the high-frequency Appl. Sci. 2020, 10, 2070 9 of 11
Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 11 tone f2 at a constant frequency of 7 kHz, and variation of the high-frequency tone f2 from 500 Hz to 20 kHz while keeping the high-frequency tone f1 at a constant frequency of 60 Hz. 1 The intermodulationThe intermodulation distortion distortion is shown is shown in Figure in Figure7. The 7. graph The graph shows shows that the that lowest the lowest values values of of 2the intermodulationthe intermodulation distortions distortions were were obtained obtained with with SRAM SRAM and MAMand MAM modulations. modulations. Single Single sideband sideband 3 modulations obtained the worst results. It is also observed how the 퐼푀퐷푇 measured with the lower modulations obtained the worst results. It is also observed how the IMDT measured with the lower 4single single lateral lateral band band (LSBAM) (LSBAM) had aha peakd a peak around around 6.5 kHz 6.5 kHzcaused caused again again by the by minimum the minimum that thethat the 5parametric parametric array array had inha thed in ultrasonic the ultrasonic response. response.
6
Figure 7. Comparison of IMDT values for each modulation (m = 1). 7 Figure 7. Comparison of 퐼푀퐷푇 values for each modulation (m = 1) All measurements were repeated systematically for different modulation indices varying from 8 All measurements were repeated systematically for different modulation indices varying from 0.1 to 1 at steps of 0.1. The results are shown in Supplementary Figure S5. In this case, the MAM 9 0.1 to 1 at steps of 0.1. The results are shown in Supplementary Figure 5. In this case, the MAM and and SRAM techniques provide the lowest distortion even at large modulation indices. The rest of 10 SRAM techniques provide the lowest distortion even at large modulation indices. The rest of techniques are more sensitive to changes in the modulation index. 11 techniques are more sensitive to changes in the modulation index. 4. Conclusions 12 4. Conclusions Parametric arrays have multiple applications in targeted audio delivery. However, the 13self-demodulation Parametric of arrays the highly have directive multiple ultrasonic applications carrier in targeted is a non-linear audio delivery. process that However, introduces the self- 14distortion demodulation of the audio of signal. the highly Multiple directive techniques ultrasonic have been carrier proposed is a based non-linear on amplitude process modulation. that introduces 15We havedistortion experimentally of the evaluated audio signal. six di ff Multipleerent amplitude techniques modulation have been techniques proposed in terms based of a frequency on amplitude 16response modulation. as well as We harmonic have experim and intermodulationentally evaluated distortion. six different We analyzed amplitude the harmonicmodulation distortion techniques at in 17di fferentterms frequencies of a frequency and decomposed response as well by orders. as harmonic Additionally, and intermodulation the distortion ofdistortion. different We modulation analyzed the 18indices harmonic is evaluated distortion for all at the different modulations frequencies techniques. and decomposed by orders. Additionally, the distortion 19 Whenof different selecting modulation a modulation indices technique is evaluated and for modulation all the modulations index there techniques. must be a balance between 20sound qualityWhen and selecting audio level.a modulation A large modulationtechnique and index modulation will lead index to louder there audible must be sound a balance but with between 21more sound distortion. quality In general,and audio we level. recommend A large MAM1 modulation with aindex modulation will lead index to louder of 0.6. audible This configuration sound but with 22produces more the distortion. lowest levels In general, of harmonic we andrecommend intermodulation MAM1 distortion with a modulation while only indexdecreasing of 0.6 the. This 23audible configuration signal by 2 dB. produces MAM1 the technique lowestmakes levels a of good harmonic use of the and limited intermodulation bandwidth of distortion the transducers. while only 24We acknowledgedecreasing the that audible for transducers signal by 2 withdB. MAM1 wider bandtechnique (e.g., makes electrostatic a good speakers),use of the limited MAM2 bandwidth could 25provide of betterthe transducers. results. In any We case, acknowledge the ultrasonic that transducers for transducers that we evaluated with wider are bandthe most (e.g. commonly, electrostatic 26used speakers), in this type MAM2 of devices. could provide better results. In any case, the ultrasonic transducers that we 27 Weevaluated hope thatare the this most study com promotesmonly used more in experimentalthis type of devices. measurements with parametric arrays 28that analyzeWe hope the distortion that this study of the promotes speakers. more The experimental measurement measurements technique that with we parametric used to avoidarrays that 29the appearanceanalyze the of distortion spurious signal of the is speakers. based on The selecting measurement a microphone technique with an that adequate we used frequency to avoid the 30 appearance of spurious signal is based on selecting a microphone with an adequate frequency 31 response, so it can be employed by most researchers. As future work, it would be desirable to measure 32 psychoacoustical parameters and user-subjective measurements. Appl. Sci. 2020, 10, 2070 10 of 11 response, so it can be employed by most researchers. As future work, it would be desirable to measure psychoacoustical parameters and user-subjective measurements.
Supplementary Materials: The following are available online at http://www.mdpi.com/2076-3417/10/6/2070/s1, Table SI: Main characteristics of the evaluated microphones, Figure S1: Block diagrams of preprocessing amplitude modulation techniques, Figure S2: Spectrogram of the signals corresponding to each stage of the measurement procedure, Figure S3: Harmonics up to the 5th order measured with the predistortion techniques (m = 1), Figure S4: Level of total harmonic distortion (LTHD) for the predistortion techniques at different modulation indices, and Figure S5: Intermodulation distortion (IMDT) for the predistortion techniques applied with different levels of modulation index (m). Author Contributions: Conceptualization, R.S.M. and A.M.; methodology, R.S.M. and A.V.; software, R.S.M.; validation, R.S.M., P.T. and A.V.; data curation, P.T. and R.S.M.; writing—original draft preparation, R.S.M.; writing—review and editing, R.S.M. and A.M. All authors have read and agreed to the published version of the manuscript. Funding: This work has been funded by the Spanish Ministry of Economy and Competitiveness through the R+D+I research project with reference BIA2016-76957-C3-2-R, and by the Government of Navarre through the Technology Transfer project 0011-1365-2019-000086. Conflicts of Interest: The authors declare no conflict of interest.
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