BINAURAL REPRODUCTION OVER LOUDSPEAKERS USING A MODIFIED TARGET RESPONSE. Ismael Nawfal and Joshua Atkins

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1 The 2 th International Conferene on Auditory isplay (ICA 214) June 22 25, 214, New York, USA BINAURAL REPROUCTION OVER LOUSPEAKERS USING A MOIFIE TARGET RESPONSE Ismael Nawfal and Joshua Atkins Beats Eletronis, LLC 161 Cloverfield Blvd Ste 5N Santa Monia, CA 944, USA {ismael.nawfal, josh.atkins}@beatsbydre.om ABSTRACT Crosstalk anellation (XTC) is a tehnique that an be used to play binaural ontent, typially meant for headphone playbak, over two or more loudspeakers. Though effetive at reating a binaural spatial sound field at the listening position, many XTC algorithms introdue spetral oloration, suffer from spatial robustness issues and reate filters that are unrealizable in pratie. Past approahes to dealing with this issue rely heavily on regularization. In this work we propose a new topology for loudspeaker binaural rendering (LBR) that performs better than onventional tehniques without the need for regularization ommonly assoiated with rosstalk anellation based binaural renderers (XTC-BR). We then explore the use of a proposed LBR in the ontext of multiple output hannels. A method is investigated to further optimize the filter design proess by seleting an appropriate modeling delay and filter length using methods pratied in XTC filter design. 1. INTROUCTION In order to obtain a binaural effet with the use of two or more loudspeakers, it is neessary to ontrol the amount of rosstalk from eah speaker that arrives at an individual s ears. For this to our, a set of filters an be designed to redue or eliminate the rosstalk at the listening position. This onept of using aousti rosstalk anellation (XTC) to ahieve a binaural or spatial effet has been extensively explored sine the original system was proposed by Atal and Shroeder in 1966 [1]. The onepts related to XTC an be extended to reate virtual audio soures in spae. The effetiveness of this type of rosstalk anellation based binaural renderer (XTC-BR) is dependent on the filter design method employed, suh as hoie of regularization, ost funtion, as well as the physial onstraints determined by the number of loudspeakers used and their geometry in spae. Loudspeaker span influenes the effetiveness and robustness of a XTC or XTC-BR and has a large effet on the feasibility of different XTC filter design methods reported in the past [2, 3, 4, 5, 6]. Aoustially, losely angled loudspeakers tend to provide more robustness to head movement, but ompromise the ahievability of XTC at lower frequenies [5, 6] and typially require a onsider- This work is liensed under Creative Commons Attribution Non Commerial (unported, v3.) Liense. The full terms of the Liense are available at θ max θ min d s d h Figure 1: An example of a typial listening position with an M speaker uniform linear speaker array onsisting of a minimum span θ min, maximum span θ max, listener distane d h, and speaker spaing d s. able amount of regularization. By ontrast, widely angled loudspeakers tend to reprodue lower frequenies at the expense of spatial robustness. Using more than two drivers allows for multiple spans whih improves the effetiveness and robustness of a rosstalk aneler aross a wider frequeny range [7]. Similarly, the distane between drivers in a XTC system plays a role in determining the upper frequeny limit at whih XTC is ahievable [4]. To address this, a linear array was suggested in [4] using either a multi-band approah proessing band-passed ontent to appropriately spaed loudspeakers or utilizing a onstant speaker spaing, d s in Figure 1, orresponding to the highest frequeny of interest. A similar relationship between speaker distane and reproduible frequeny was examined further in [8], where a oneptual transduer is proposed whose position varies with frequeny. In [9], a uniformly spaed linear array was introdued that implemented XTC utilizing a sub-band regularization sheme. A uniformly spaed linear array is illustrated in Figure 1. Past approahes to XTC filter design inlude the use of Tikhonov regularization [1], using plane-wave approximations of the HRTF [11], jointly optimizing for a set of measurement positions [12], using sub-band approahes to ahieve anellation only in a ertain frequeny range [9], and adjustment of the error-norm to better math pereption [13]. The signal proessing assoiated with a multihannel XTC

2 The 2 th International Conferene on Auditory isplay (ICA 214) June 22 25, 214, New York, USA x1[n] xs[n] b1,r[n] b1,l[n] bs,r[n] bs,l[n] Binaural Synthesis xr[n] xl[n] h 1,R[n] h M,R[n] h 1,L[n] h M,L[n] Crosstalk Caneller g1,r[n] gm,r[n] g1,l[n] gm,l[n] yr[n] Figure 2: A typial XTC-BR system for simulating binaural soures over loudspeakers with S soures and M loudspeakers. The filters h [n] represent XTC filters while filters b[n] represent the HRTFs of the desired angle to be rendered. yl[n] x 1 [n] x S [n] h b 1,1[n] h b 1,M [n] h b S,1[n] h b S,M [n] Loudspeaker Binaural Renderer g 1,R [n] g M,R [n] g 1,L [n] g M,L [n] y R [n] y L [n] is illustrated in Figure 2. Many alternative methods to XTC have been proposed in the literature for sound field synthesis over two or more loudspeakers with most approahes fousing on large loudspeaker arrays. The most widely used methods are Higher-Order Ambisionis (HOA), Vetor Based Amplitude Panning (VBAP), and Wave Field Synthesis (WFS) [14, 15, 16]. HOA and WFS are often referred to as analytial methods sine they formulate and solve the synthesis problem exatly using approahes from physial aoustis. Of these three, only WFS has been studied extensively for reprodution over linear loudspeaker arrays [17, 18] (HOA and VBAP fous on irular and spherial arrays). More general methods that treat sound field reprodution as a numerial inverse problem have also been studied extensively in reent work [19, 2, 21]. The approah presented in this paper shares more ommonality with the numerial approahes than the analytial methods like HOA and WFS, but draws inspiration from the XTC literature where the goal is foused on binaural reprodution. Here we study the effetiveness of a proposed loudspeaker binaural renderer (LBR), using a novel method illustrated in Figure 3, to simulate virtual soures at arbitrary angles. In the onventional approah, the filters for a XTC-BR are designed with a target flat frequeny response at the ipsilateral ear and a fully attenuated response at the ontralateral ear and then onvolved with HRTFs assoiated with a desired angle. While this works well at playing bak an unknown binaural reording, it is suboptimal for the binaural simulation ase, espeially when regularization methods are employed. To address this, we propose a modified target response for the filter design whereby a set of LBR filters is designed diretly. This approah has two motivations. Firstly, it leads to ahievable binaural reprodution filters without the need for regularization at low-frequenies. Seondly, the neessary amount of rosstalk attenuation is over-estimated in the traditional sheme, as the binaural effet is typially ahievable with 15-2 db of hannel separation depending on the soure ontent used [22]. Through simulations we will show how this approah leads to better timbral reprodution without the need for traditional forms of regularization. We will also expand our work to the multihannel ase shown in Figure 1. Additionally we will propose an optimization sheme for filter generation that ensures the faithful spatial reprodution of multihannel ontent while also reduing proessing requirements. We will fous on the effet of modeling delay and filter length, parameters ommonly explored in rosstalk filter design, on the filter design of our proposed LBR. Figure 3: The proposed LBR system for simulating binaural soures over loudspeakers with S soures and M loudspeakers. The filter h b [n] represents the binaural rendering filter used to simulate a virtual soure. 2. BACKGROUN AN THEORY A onventional XTC system is shown in Figure 2. We define x s[n] as a monaural soure signal, x L[n] and x R[n] as inputs to the rosstalk aneler, h m as the rosstalk anellation filter for loudspeaker m, g m,l and g m,r as the aousti transfer funtions between eah loudspeaker and eah ear, and y L[n] and y R[n] as the reprodued signals at eah ear. From this, we an write the reprodued sound field at the listening position as y L[n] = y R[n] = M g m,l (h m,l x L[n] h m,r x R[n]) m=1 M g m,r (h m,l x L[n] h m,r x R[n]). m=1 where represents the onvolution operator. The aousti path models, g m,l and g m,r, are typially hosen using the measured HRTFs for eah path, but in some methods a plane-wave approximation is used as a simplifiation [11]. In this ase, the ipsilateral propagation is simulated as δ[] and the ontralateral as αδ[n τ ], where δ[ ] is the delta funtion, α is a modeled attenuation fator, and τ is a modeled propagation delay. The desired sound field at the listening position will be d L[n] = t L x[n] and d R[n] = t R x[n]. Conventionally, the target reprodution filters, t L and t R, are hosen as the filters and δ[n ], where is a modeling delay. This hoie of filters aims at ahieving zero signal at the ontralateral ear and a delayed version of the signal at the ipsilateral ear, a senario muh like the headphone listening ase. The modeling delay is important to ensure ausality of the designed filters in the onventional design framework [12]. The filter design then aims to find the filters h m suh that a suitable hoie of error funtion, e(y L[n], d L[n], y R[n], d R[n]), is minimized. Typially the l 2-norm ost funtion is hosen. We fous the analysis in this work on the speifi senario where the rosstalk aneler is used with a binaural renderer (XTC-BR) to simulate a sound soure from a given diretion. (1)

3 The 2 th International Conferene on Auditory isplay (ICA 214) June 22 25, 214, New York, USA 2 Response at Speaker 1 2 Response at Ipsilateral Ear Conv β = Conv β = Response at Speaker 2 2 Response at Contralateral Ear Figure 4: A omparison of XTC filter responses at the speaker generated using a onventional time domain method with regularization parameter β =,.1 and.1 for stereo reprodution using loudspeakers at a 5 angular span. Figure 5: A omparison of XTC filter responses at the ear generated using a onventional time domain method with regularization parameter β =,.1 and.1 for stereo reprodution using loudspeakers at a 5 angular span Traditional Filter Generation Methodology XTC filters are ommonly alulated in the time domain by solving the following minimization, whih solves for the filters h I,1 h I,M and h C,1 h C,M, minimize G h t 2 β h 2 (2) h t I = [,,, 1,,, ] N h 1 t C = [,,,,,, ] N h 1 t = [t I, t C gm,i = [gm,i[],, gm,i[n g 1],,, gm,c = [gm,c[],, gm,c[n g 1],,, G = [ ] onvmtx(g 1,I ) onvmtx(gm,i) onvmtx(g1,c) onvmtx(gm,c) h m = [h m[],, h m[n h 1]] h = [ h 1 h M where t I and t C are the desired responses at the ipsilateral and ontralateral ears respetively. Similarly g m,i and g m,c are the atual HRTF responses at the ipsilateral and ontralateral ears respetively. The notation 2 is the l 2-norm and onvmtx( ) reates the ayli onvolution matrix of size N g N h 1 by N h for a given vetor. Variables N g, N h, and N t orrespond to the lengths of the aousti path, filter, and desired response, respetively, and represents the modeling delay that is used to ensure ausality. The variable M refers to the number of loudspeakers. The vetor t onsists of the perfet rosstalk anelled response at the listener s ears. Tikhonov regularization is often used to avoid issues with matrix inversion where the parameter β on- trols the amount of regularization [11, 23] and is ommonly used in a frequeny dependent fashion [9, 24, 25]. Modifiations to this form an be seen in [26], where a non-onstant regularization parameter is alulated. The designed filters, h, an be onvolved with HRTF measurements from a partiular soure angle to simulate a binaural sound from a desired diretion as done in XTC-BR and shown in Figure 2. Alternatively, XTC filters an be designed in the frequeny domain to allow for onstraints that better math pereption. Note that due to Parseval s theorem, the ost funtion is the same in time and frequeny when using the l 2-norm. These methods along with the typial regularization approahes have been explored in [9, 11, 27]. The problem in the frequeny domain an be written as minimize G F Bh t 2 β F Bh 2. (3) h F B = blkdiag(f, M) t = [(Ft I) T, (Ft C) T [ ] G diag(fg = 1,I ) diag(fgm,i) diag(fg1,c) diag(fgm,c) where F represents the disrete Fourier transform matrix of size max(n g N h 1, N t) by N h, diag( ) is the diagonal matrix formed from a vetor, and blkdiag(, M) is the blok diagonal matrix formed by repeating a matrix along its diagonal M times. The underline notation represents a quantity in the frequeny domain Proposed Filter Generation Method We propose altering the onventional XTC-BR approah to use a modified target response for the filter design so that LBR filters are designed diretly. This proposed method will generate wellbehaved filters that do not require any onstraints for regularization. Our design paradigm is illustrated further in Figure 3. Our proposed method, whih solves for the filters h b L,1 h b L,M and h b R,1 h b R,M, an be desribed as minimize G b h b t b 2 (4) h b

4 The 2 th International Conferene on Auditory isplay (ICA 214) June 22 25, 214, New York, USA Proposed Conv β = Response at Speaker Conv β = Proposed Target Response at Ipsilateral Ear Response at Speaker 2 2 Response at Contralateral Ear Figure 6: A omparison of the speaker responses of the LBR and XTC-BR methods with regularization parameter β=,.1 and.1, attempting to use loudspeakers at a 5 angular span to simulate a soure at /- 3. t b L = [,,, t b L[],, t b L[N t 1],,, ] N h 1 t b R = [,,, t b R[],, t b R[N t 1],,, ] N h 1 t b = [t b L, t b R gm,l b = [gm,l[], b, gm,l[n b g 1],,, gm,r b = [gm,r[], b, gm,r[n b g 1],,, G b = [ onvmtx(g b 1,L ) ] onvmtx(gm,l) b onvmtx(g1,r) b onvmtx(gm,r) b h b m = [h m[],, h m[n h 1]] h b = [ h b 1 h b M where t b L and t b R are the desired responses at the left and right ears respetively. Similarly g b m,l and g b m,r are the atual HRTF responses at the left and right ears respetively. The elements in h b are the desired LBR filters that simulate a virtual soure at a speifi angle and t b onsists of the desired responses at the listener s ears. Note here we do not solve for XTC filters, but rather filters that best render a binaural soure at a given angle. By solving diretly, the filter design proess is simplified and there is no need to apply both XTC and binaural rendering filters as is done in XTC- BR. Filters generated using this method were found to perform well when designed with a filter length orrelating to the length of the soure HRTF used. The generated LBR filters an be used to render virtual soures in spae by alulating filter oeffiients in advane with a desired spatial resolution and using interpolation tehniques ommonly used in XTC and XTC-BR [2]. 3. SIMULATIONS In this setion we ompare the XTC-BR method against the proposed LBR method. We study the appliation of Tikhonov reg- Figure 7: A omparison of the ear responses of the LBR and XTC- BR methods with regularization parameter β=,.1 and.1, attempting to use loudspeakers at a 5 angular span to simulate a soure at /- 3. ularization to the XTC and XTC-BR filter design problems and evaluate the simulated reprodution at eah ear and the resulting filters in eah ase. In this experiment we generate filters for loudspeakers measured with a span of 5 to simulate idential loudspeakers with a span of 6 using the onventional and proposed filter design methods. A loudspeaker span of 6 is onsidered standard for stereo reprodution of musi. To test the effiay of eah method in widening a stereo image from 5 to 6 we study the ability of the designed filters to simulate virtual loudspeakers at /- 3. All filters were designed to be 124 taps inorporating a modeling delay of 256 samples and were generated using time-domain design methods shown in Equation 2 and Equation 4. The HRTFs used were measured in an anehoi hamber known to have a utoff of 4 Hz using a KEMAR manikin plaed 2 m from a studio monitor with a near flat frequeny response from 5 Hz to 2 khz. Firstly we examine the effet of the regularization parameter, β, on onventional XTC filter design. Figure 4 shows the onventional XTC filter generation utilizing different β values. As an be seen in the graph, the use of regularization an influene the frequeny response of the designed filter. This an lead to a ompromise in the robustness of the designed filter espeially at low frequenies. Comparing the simulated response at the ear in Figure 5, it is lear that the use of a regularizer has an effet on pereived ross-path attenuation. An inrease in β simultaneously redues the power required by a speaker for playbak and the level of ross-path attenuation. The onventional XTC-BR method shown in Figure 2 utilizing different β values was ompared against our proposed LBR method shown in Figure 3. Both methods attempt to simulate a soure at /- 3 utilizing loudspeakers with a 5 span. The simulated speaker and ear responses for both methods an be seen in Figure 6 and Figure 7 respetively. Both figures show that eah method tends to math the desired target response well at mid and high frequenies. However, the proposed LBR method tends to math better below 2 Hz. Informal listening onfirmed that the LBR method performed better than the onventional XTC-BR approah by better simulating a target angle with limited timbral arti-

5 The 2 th International Conferene on Auditory isplay (ICA 214) June 22 25, 214, New York, USA tap filter Optimization elay (samples) tap filter Optimization elay (samples) tap filter Optimization elay (samples) tap filter Optimization elay (samples) Figure 8: A omparison of the residual l 2 errors for LBR filters at the left ear for 128, 256, 512 and 124 taps rendering at, 3, 9 and 135 at different modeling delays. All filter lengths and target HRTF ombinations suggest similar optimal modeling delays. fats, speifially in the lower frequeny range. This better performane was ahieved without the use of any type of regularization. 4. APPLICATION In the previous setion, a omparison of the proposed LBR and onventional XTC-BR method of binaural reprodution of a single soure was evaluated via simulation and informal listening. It was found that although both methods tended to math the binaural target well, the LBR method performed better partiularly at lower frequenies. Having ompared LBR and XTC-BR methods, in this setion we ontinue our evaluation of our proposed LBR method by applying it to the ontext of an eight speaker uniform linear speaker array simulating multiple soures. Two parameters play a signifiant role in the filter optimization of the proposed LBR: modeling delay,, and modeled filter length, N h, as seen in Equation 4. The HRTF measurements used in this setion were taken using a KEMAR mannequin plaed 2 m in front of an 8 speaker linear array in an anehoi hamber. Eah speaker in the linear array onsisted of a 1 m woofer paired with a 2.5 m tweeter rossing over at 2 khz. The distane between drivers, d s, was 1 m, whih orresponds to θ min = 3 and θ max = 2. Impulse responses were aquired using the logarithmi sine sweep method [28]. The target HRTFs were measured with the same studio monitor desribed in Setion 3 at angles orresponding to those ommonly assoiated with 7.1 surround sound playbak:, 3, 9 and 135. Measured responses were trunated to 2 samples, removing minor refletions that were observed within measurements and ontent residing near the noise floor elay Optimization A modeling delay is important to ensure ausality of the designed filters in the XTC filter design [12]. It is stated in [12] that any ausal modeling delay is usually onsidered aeptable and that a delay that falls in the middle of the ausal region would be reason Filter Optimization Filter Length Figure 9: Residual l 2 error for LBR filters at the left ear as a funtion of filter length using a modeling delay of 55 samples determined in Setion 4.1. able. An optimal modeling delay will minimize the least squares ost funtion while ensuring ausality and robustness of the final filter design. The modeling delay is desribed as and is appended to the beginning of the target HRTF response, t s, in Equation 4. In order to determine an optimal delay, the residual l 2 error was alulated for various modeling delays for filter lengths of 128, 256, 512 and 124 samples. As an be seen in Figure 8, the modeling delay remains relatively onsistent for all filter lengths. It would be reasonable to assume, as in [12], that any modeling delay in the ausal region would be aeptable, thus we hoose the smallest modeling delay in the ausal region in our study of filter length optimization whih is 55 samples. Note that the modeling delay used is only relevant during the filter design proess and does not impat the omputational omplexity of the resulting filters Filter Length Optimization Sine the filter length used diretly influenes the omputational omplexity of real-time appliations, shorter filter lengths are preferred. Using the onlusions in Setion 4.1, a modeling delay of 55 samples is used in order to establish an optimal filter length. We will define the optimal filter length to be the filter length at whih a signifiant redution in residual l 2 error ours. Residual l 2 errors assoiated with filter lengths were iteratively alulated and are shown in Figure 9. As expeted, shorter filters tended to generate more residual l 2 error, however there is a point at whih the filter length no longer beomes a limiting fator. In the figure we an see the optimal filter length for our example is 86 taps, whih orresponds to the point at whih the residual l 2 error reahes a level below -12 db Joint Optimization Figure 1 shows a three-dimensional representation of the optimization sheme desribed in Setion 4. From Setion 4.1 and Setion 4.2 we suggest a modeling delay of 55 samples and a filter length of 86 taps for this partiular problem. The assumption is that all areas that are shown as dark blue in Figure 1 would be appropriate seletions for modeling delay and filter length ombinations in order to generate binaural rendering filters due to their very low residual l 2 errors

6 The 2 th International Conferene on Auditory isplay (ICA 214) June 22 25, 214, New York, USA 5 of providing a pereptually aeptable 128 tap filter. ue to these onlusions, we propose that residual l 2 error should be used as baseline in onjuntion with pereptual evaluation in order to ensure that all spatial rendering is intat after optimization Modeling elay (samples) Filter Length (taps) Figure 1: A waterfall plot showing the relationship between modeling delay, filter length and residual l 2 error for generated LBR filters. 5. ISCUSSION In order to onfirm the seletion of our optimal values of = 55 samples and N h = 86 taps, informal listening was onduted with the derived optimal modeling delay and filter length values. Though numerially shown to have minimum residual l 2 error, pereptually these values did not provide the expeted spatial rendering. A listening test was set up in order to determine the minimum modeling delay required in order to ahieve the expeted spatial rendering, ignoring residual l 2 error data and the optimal modeling delay that was alulated previously. It was found that a modeling delay of approximately 1 samples, whih fell well within the ausal region, was the minimum neessary to ahieve the orret spatial rendering of all angles (, 3, 9 and 135 ) with 124 tap binaural filters. The derived optimal filter length of 86 taps also failed to provide orret rendering, and thus the filter length was redued inrementally from 124 taps in order to determine a minimum length that would provide the expeted spatial rendering. A filter length of 2 samples was subjetively determined to provide the orret spatial rendering with no signifiant timbral artifats utilizing a modeling delay of 1 samples. Interestingly, this value orresponds to the lengths of the measured and target HRTF responses, N g and N t respetively (from Equation 4), whih were used during the filter design proess. This indiates that the length of the HRTF measurements used in the design proess may play a more dominant role in determining the optimal length of a binaural rendering filter than residual l 2 error. espite the residual l 2 error data that was derived, subjetive listening indiates that residual l 2 error is not a suffiient metri in determining the effetiveness of filters to be used for binaural rendering. Though values of modeling delay and filter length have low residual l 2 error and fall in the ausal region they did not neessarily generate pereptually valid filters. This is in ontrast to [12], whih suggested seleting a modeling delay in the middle of the ausal region or a modeling delay with the lowest residual l 2 error as a rule of thumb. These suggestions made in [12] were not validated with listening tests as done here. As an example, note the modeling delay versus residual l 2 error for a 128 tap filter in Figure 8 where we an see a lear ausal modeling delay region. espite this, we found that no ausal modeling delay was apable CONCLUSIONS In this paper we have shown a tehnique for reproduing a binaural sound soure with minimal artifats. In departure from previous methods with rosstalk anelers, the proposed LBR approah attempts to diretly design the optimal reprodution filter for a given soure angle. This redues the need for regularization and simplifies the overall filter design proess. A omparison of the proposed LBR and onventional XTC-BR reprodution of a single soure was evaluated via simulation and informal listening evaluation. It was found that although both methods tended to math the binaural target well, the LBR method performed better at lower frequenies. We have also applied the LBR method to the ontext of reproduing a binaural sound soure using multiple drivers with minimal artifats. The system was implemented and validated with an 8-hannel uniform linear array. We have shown that both the hoie of delay applied to the target response and desired filter length play a signifiant role in the optimization of the residual l 2 error funtion. espite determining a method for minimizing residual l 2 error while reduing modeling delay and filter length, informal listening evaluations have shown that residual l 2 error may not be the only fator that should be onsidered when attempting to optimize binaural rendering filters. Instead, modeling delay and filter length should be validated pereptually, taking filter design residual l 2 error as a tool for narrowing down the seletion proess. 7. REFERENCES [1] B.S. Atal and M.R. Shroeder, Apparent sound soure translator, US Patent 3,236,949, Feb [2] W.G. 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