Multipoint Equalization of Digital Car Audio Systems

Since car is nowadays the most used audio listening environment, au- tomotive equalization has ... sis of a measurement of the car impulse response in a single location. ..... [2] R. Shivley, “Automotive Audio Design (A Tutorial),”. Presented at ...
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Multipoint Equalization of Digital Car Audio Systems S. Cecchi, L. Palestini, P. Peretti and F. Piazza Universit´a Politecnica delle Marche DIBET - A3Lab Via Brecce Bianche, 1 60131 Ancona Italy [email protected] Abstract In this paper a novel approach for automotive sound system enhancement based on multipoint equalization is presented. Beginning from well known techniques applied to room equalization issues, a frequency domain algorithm that combines fractional octave smoothing of measured impulse responses (IRs) in multiple locations is developed. The IRs are calculated using well positioned microphones inside a car taking into account the properties of the environment. Several results are presented considering different methods to combine the IRs and confirming the validity of the approach in comparison with single point equalization.

1. Introduction The automobile is a well-known small noisy environment with several negative influences on the spectral, spatial and temporal attributes of the reproduced sound field [1]. Specifically, depending on the absorbing or reflecting interior materials, on the position of the loudspeakers and on the shape of the car cabin, the reflected sounds can attenuate or amplify the direct sound from the loudspeakers [2]. In this context, audio equalization is strongly required to enhance tone quality and modify frequency response to approximately obtain desired results in terms of audio quality. Equalizers are used to compensate for speaker placement, environment characteristics and to enhance the listening experience in relation to the user requirements. This compensation is accomplished by cutting or boosting, i. e. attenuating or amplifying a range of frequencies. Since car is nowadays the most used audio listening environment, automotive equalization has been attracting a great deal of attention in recent years. Moreover, the availability of lowcost consumer DSP allows for mass production of sound enhancement systems. Regarding car equalization, many works that can be found in literature cope with fixed equalization. Fixed equalization algorithms based on different inversion approaches, such as frequency deconvolution, have been presented in [3] together with a surround processor to re-

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A. Carini Universita’ di Urbino STI Piazza della Repubblica, 13 61029 Urbino Italy [email protected] move and to add unwanted/wanted reverberation components. The application of warped and spectral smoothed filters to static automotive equalization has also been investigated [4, 5]. All these approach are based on single point equalization i.e. the equalization filter is designed on the basis of a measurement of the car impulse response in a single location. On the other hand, a variety of approaches on multipoint room equalization are documented [6, 7, 8, 9, 10, 11]: these approaches enlarge the equalized zone by measuring the room impulse response in multiple locations. An exact equalization technique for multiple positions based on MINT (multiple-input/multiple-output inverse theorem) was proposed in [7]. With this technique, exact equalization can be obtained considering a number of equalization points lower than the number of sound sources (loudspeakers) and provided that the room responses have uncommon zeros among them. A multiple channel adaptive equalization system was proposed in [8]. This system adaptively minimizes the sum of the squared errors between the equalized responses and a delayed version of the reproduced signal. In [9] a multipoint equalization filter using the common acoustical poles of room transfer functions was proposed. A multiple position room response equalization technique based on fuzzy c-means clustering and frequency warping was introduced in [6, 10]. Specifically, given a set of room impulse responses measured at different positions, the technique in [6] applies a fuzzy c-means algorithm for clustering these room responses on the basis of their similarity. A prototype impulse response, obtained by combining the centroids of clusters, is then used for designing the low order equalization filter by means of Linear Predictive Coding (LPC) analysis. In order to obtain a better fit of the LPC model to the room response in the low frequency region, the measured room responses are frequency warped using a psychoacoustically motivated Bark scale [11]. In [12] the method of [6] was further developed by introducing a weighted fuzzy c-means clustering algorithm that allows to introduce different weights on the room impulse response samples. Although the technique in [6] is able to obtain only a magnitude equalization of the room response, it is effective and robust against displacement effects. In [11] the technique of [6] has been improved by perform-

Proceedings of the 6th International Symposium on Image and Signal Processing and Analysis (2009)

Figure 1. Overall scheme of the proposed approach.

ing most of its operations in the frequency domain reducing the computational complexity. Differently from [6], the fuzzy c-means clustering is applied to the room amplitude frequency responses at different positions. In this paper, we present a multipoint fixed equalization scheme applied in the frequency domain. The equalizer is designed to compensate for the magnitude spectrum irregularities of the car environment. Specifically, given a set of car impulse responses (CIRs) related to different channels of the audio system and measured in different locations, this technique produces an equalization function based on the fractional octave smoothed version of the magnitude spectrum of CIRs. The paper is organized as follows. Section 2 provides a description of the proposed approach. The experimental results are presented in Section 3. More in details, the car environment with the hardware set-up is described in Section 3.1 while Section 3.2 reports the simulation results, in terms of spectral deviation, obtained by exploring different alternatives within the proposed approach and comparing it with the single point equalization technique. Finally, conclusions are drawn in Section 4.

2. Proposed Algorithm Fig. 1 shows the overall structure of the proposed approach. The operations performed by the proposed equalizer are the following: Step 1: M = N · P car impulse responses of length L

samples are measured at different positions in the zone to be equalized, where N is the number of channels considered (loudspeakers) and P the number of microphones. Step 2: After the estimation of the frequency responses by means of FFT of length K, fractional octave smoothing is performed on the frequency responses using the methodology of [13]. This technique is able to perform magnitude as well as phase spectrum smoothing simultaneously. However, since we are concerned with magnitude equalization, only the magnitude spectrum is smoothed considering nth-octave bands. The basic equation for performing non uniform frequency magnitude spectrum smoothing of an impulse response h(n) with a frequency response H(k) is given by, Hcs (k) = Hcs (m (k) , k) =

K−1 X

Wsm (m (k) , i) |H ((k − i) mod K)|

i=0

where Wsm (m (k) , k) is a zero-phase window function and m (k) is the half-window length which is a monotonically increasing function of the frequency index k. This method simulates a well-known property of the auditory system which presents a poorer frequency resolution at higher frequencies. In this way it is possible to consider a non-uniform resolution which decreases with increasing frequency to obtain a less precise equalization at higher frequency resulting in a broader equalized zone [14]). Step 3: In this step a representative response of the car cabin environment is derived taking into account all the smoothed CIRs considering the left and right channels separately. The prototype frequency response has been obtained using different approaches: • Mean: the prototype is realized computing the arithmetic mean of the smoothed frequency responses as follows Hp (k) =

Figure 2. Loudspeakers and microphones position inside the car.

M 1 X Hi (k) M i=1

k = 0, · · · , K − 1

• Fuzzy c-means: the fuzzy c-means algorithm is used to extract the common patterns of the room amplitude responses. The prototype is obtained from the weighted

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mean of the cluster centroids as follows:  Pc PM 2 ∗ j=1 l=1 µj (Hl ) Hj  P Hp = P c M 2 j=1 l=1 µj (Hl ) where H = [H (0) , · · · , H (K − 1)], µ (·) are the cluster membership functions, with j = 1, · · · , c, and c is the number of centroids. • Median: the prototype is computed sorting each bin of the smoothed frequency responses and calculating the mean of the two central values (K even). In formulas, Sk = sorti [Hi (k)] k

Hp (k) =

(1)

k

S M −1 + S M b 2 c b2c 2

k = 0, · · · , K − 1

where S is a length-M vector of sorted values. • Root Mean Square: the prototype is the root mean square of the smoothed frequency responses: v u M u 1 X 2 Hi (k) k = 0, · · · , K − 1 Hp (k) = t M i=1 • MinMax: the prototype is derived minimizing the maximum error between the computed response and the car frequency responses, as follows i 1h min (Hi (k)) + max (Hi (k)) i 2 i k = 0, · · · , K − 1

Hp (k) =

In Section 3.2 experimental results will be reported for each of the above methods. Step 4: The inverse model of the prototype function (Hinv ) is obtained. The equalization filter has been computed in two alternative ways: 1. Frequency deconvolution with regularization [15] to avoid excessive gains especially at high frequencies is applied to the prototype to obtain the frequency domain inverse filter: Hinv (k) =

Hp∗ (k) 2

|Hp (k)| + β (k)

k = 0, · · · , K − 1

where β is the frequency dependent regularization factor. The corresponding time domain filter is truncated by an appropriate window function to have a more compact representation: its length is usually limited due to the beneficial effect of the smoothing and to the fact that CIRs are also well bounded in time (i.e. 4096 samples at 48 kHz).

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Figure 3. Audio equipment setup in the car trunk: the system is composed by five professional souncards connected by the amplifiers to the loudspeakers and directly to the microphones.

2. A low order all-pole LPC model is extracted from the prototype using the Levinson-Durbin algorithm [11]: the time domain equalizer is the FIR filter obtained from the inverse of the all-pole LPC model. The use of a low order equalizer allows to reduce the computational cost as well as improve the robustness toward displacement effects [11]. In both methods, the frequency range considered for the inversion is from 100 Hz to 16 kHz. In Section 3.2 the two methods will be compared in terms of spectral deviation.

3. Experimental results In the following, experimental results will be reported considering a real car environment as described in Section 3.1. Measured CIRs have been divided in two suitable subsets in order to handle separately the left and right channels. Starting from this point of view, the techniques presented above for the prototype definition will be evaluated in order to identify the more performing approach for the specific set of measured CIRs (Section 3.2.1). The performance of the multipoint equalization will be also compared with the single position approach in terms of inversion effectiveness (Section 3.2.2).

3.1. Hardware Set Up Real tests have been performed on a Mercedes R320 CDi V6 Sport car (Fig. 3): regarding I/O equipment fourteen loudspeakers with dedicated high quality automotive power amplifiers and four microphones (located on the roof) have been considered for the equalization task. The loudspakers and microphones are positioned as described in Fig. 2. As shown in Fig. 3 professional ASIO soundcards connected to a Personal Computer have been used to manage all the system I/Os [16, 17].

Prototype Mean Fuzzy C mean Median MinMax RMS

Inversion

SDi

SDf

∆SD

Fast Deconv

5.0713

3.0349

2.0364

LPC

5.0713

3.0446

2.0268

Fast Deconv

5.0713

3.2342

1.8372

LPC

5.0713

3.2370

1.8344

Fast Deconv

5.0713

3.0727

1.9986

LPC

5.0713

3.0733

1.9981

Fast Deconv

5.0713

3.2953

1.7760

LPC

5.0713

3.2899

1.7814

Fast Deconv

5.0713

3.1505

1.9209

LPC

5.0713

3.1545

1.9168 Figure 5. Magnitude frequency responses of a CIR between the R1R front and the first microphone (see Fig. 2) with its smoothed version and the resulting inverse filter obtained from the Mean prototype. The smoothed CIR is attenuated of 20dB for a better evaluation.

Table 1. Spectral deviations SD and their improvement ∆SD = SDf − SDi considering different ways to obtain the car prototype frequency response and the inverse filter.

3.2. Algorithm Validation As a term of comparison, the spectral deviation measure has been selected: it is the deviation of the magnitude responses away from a flat frequency response [6]. In formulas, v u Qh X u 1 2 SD = t (10 log10 |E (i)| − D) (2) Qh − Ql + 1 i=Ql

D=

1 Qh − Ql + 1

Qh X

(10 log10 |E (i)|)

(3)

i=Ql

calculated with E = H while after the equalization SDf is derived considering E = H · Hinv . 24 CIRs were firstly measured in the car with omnidirectional microphones positioned on the roof and considering Maximum Length Sequences (MLS) excitation with a sampling frequency of 48 kHz and length L = 4096 samples. The three-way systems composed by a tweeter, a midrange and a woofer were considered as single units for the purpose of CIRs measurements. Regarding the frequency smoothing, a factor of 32 was considered for the fractional octave resolution. Two validation sessions have been done: the

where Ql and Qh define the frequency region of interest to the equalization issue. The initial spectral deviation SDi is

Figure 4. Magnitude of prototypes obtained by all the methods.

Figure 6. Magnitude spectra of a CIR between the R1R front and the first microphone (see Fig. 2) without and with multipoint equalization.

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Method Single point Multi point

Inversion

SDi

SDf

∆SD

Fast Deconv

4.7803

3.8059

0.9744

LPC

4.7803

3.6033

1.1771

Fast Deconv

5.0713

3.1575

1.9138

LPC

5.0713

3.1599

1.9115

Table 2. Spectral deviations SD and their improvement ∆SD for single point and multipoint equalization (mean values over the considered methods used to obtain the prototype).

former to identify the best approach for the prototype computation considering the car environment and a suitable selection of the impulse responses, the latter to highlight the superiority of the approach in comparison with the single point equalization. They will be both reported in the following. 3.2.1

Prototypes Comparison

Regarding the first simulations session, as already mentioned, measured CIRs have been divided in two subsets for the right and left channels, and from them two prototypes and their corresponding equalizers have been derived. Table 1 reports the spectral deviation values calculated with the different type of prototypes, averaged over more sets of CIRs measured in the same positions, while Fig. 4 depicts their magnitude spectra. Fig. 5 reports the right channel equalizer frequency response for the Mean prototype along with the magnitude of a particular CIR, and Fig. 6 shows the equalizer capability, on one of the considered CIRs, to

Figure 7. Magnitude spectra of single point and right channel multipoint equalizer derived by the Mean approach considering Fast Deconvolution inversion.

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Figure 8. Magnitude spectra of the same CIR equalized with multipoint and single point inverse filter.

compensate for the car cabin response achieving a flatter spectrum. As it can be seen, in the specific case the preferable approach to extract a prototype seems to be the Mean technique although comparable performances can be also achieved with the other methods. The proposed approach was also compared with the one reported in [11]. Performed simulations underlined that using fractional octave smoothing and frequency deconvolution with regularization instead of frequency warping and LPC modeling results in decreased SDf i.e. better performance. 3.2.2 Comparison with Single Point Approach In the second validation session, single point equalization was considered, in order to assess its inferiority with respect to the multipoint approach based on Mean prototype. In single point equalization, the inverse filter was derived from the smoothed frequency response of the overall system relative to the microphone located near the driver seat considering both inversion methods. The derived function was then applied to both left and right channels since for each microphone just one CIR has been considered representing the whole loudspeakers system; the single point equalizer is depicted in Fig. 7 together with the right channel equalizer for the multipoint case considering the Fast deconvolution approach. As expected, the single point approach results in poorer performance in terms of spectral deviation improvements (Table 2). Moreover, CIRs equalized with the multipoint equalizer exhibit flatter frequency responses compared to those obtained with single point approach, as Fig. 8 shows.

4. Conclusions In this paper, a multipoint fixed equalization approach for automotive sound system was presented. The equalizer

is designed in the frequency domain to achieve magnitude spectrum equalization of the car environment. From the set of frequency smoothed car cockpit impulse responses, two suitable prototypes for left and right channels respectively are extracted considering different approaches (Fuzzy cmean, Mean, Median, MinMax, Root Mean Square); therefore the inverse filter is obtained through frequency deconvolution with regularization or LPC modeling. In the analyzed case of study, the Mean technique for prototype definition allows to obtain better results. Regarding the method used for the inverse filter calculation, the LPC model permits to reduce the computational complexity to the detriment of slightly inferior performance. Moreover, considering single point equalization, the proposed method proves to be superior in terms of achieved spectral deviation as known for room equalization issue. Future works will be oriented toward the evaluation of the equalization performance in positions other than the microphones used to measure the impulse responses, to assess its robustness to displacement. Moreover, subjective listening tests to psychoacoustically evaluate the different strategies for prototype and inverse filter design techniques will be useful to determine the best approach to be selected for a specific environment.

5. Acknowledgments This work was supported by the European Commission as sponsor of the hArtes Project number 035143.

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[6] S. Bharitkar and C. Kyriakakis, Immersive Audio Signal Processing. New York: Springer, 2006. [7] M. Miyoshi and Y. Kaneda, “Inverse filtering of room acoustics,” Acoustics, Speech and Signal Processing, IEEE Transactions on, vol. 36, no. 2, pp. 145–152, Feb. 1988.

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