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Design and Performance of a Sigma-Delta Digital Loudspeaker Array Prototype
Abstract and Figures
Digital loudspeaker arrays (DLAs) are electroacoustic transducers reconstructing acoustic signals out of binary audio streams, usually consisting of a digital signal processing module driving multiple actuators (small loudspeakers). In this work a DLA prototype was implemented using an all-digital audio chain driven by 1-bit sigma-delta signals. The prototype implementation is described and its performance measured and evaluated using frequencydomain and THD analysis. These results also compare the DLA performance when driven by either sigma-delta or PCM input signals.
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... A digital loudspeaker directly uses digital signals to drive the speaker without digital-to-analog converters (DAC). It primarily consists of three modules: signal-encoding, digital amplifier, and digital transducer modules [1]. The signal-encoding module encodes the input signal by a predetermined number of bits. ...
... Their experimental results showed that a 12-bit digital loudspeaker was capable of achieving an 84 dB dynamic range. Tatlas et al. [1,14] compared the performance of a 5-bit PCM-driven DTA with that of a 1-bit SDM-driven DTA through simulations and experiments. The results indicated that the level of the harmonic distortion of the 1-bit SDM-driven DTA was smaller than that of the 5-bit PCM-driven DTA. ...
... The module will set some components of x(n) = [x 1 (n), x 2 (n), · · · x 8 (n)] to 1, whose index corresponds to the index of the v(n) largest components of y s (n). For example, if v(n) is 4 and y s (n) is [9,5,6,4,3,7,8,1], the four largest components are 9, 8, 7, and 6, whose indexes are 1, 7, 6, and 3, respectively, so x 1 (n),x 7 (n),x 6 (n) and x 3 (n) will be set to 1, and the others of x(n) will be set to 0. The "-min" module selects the minimum of f s (n) = [ f s 1 (n), f s 2 (n), · · · f s 8 (n)] and sets its negative value as the output w s (n). ...
Digital transducer array (DTA) has the advantages of greater integration scale, smaller size, lower cost, and possibly improved electroacoustic efficiency over existing analog systems. The original DTA is realized using pulse code modulation (PCM) technique, where a large number of loudspeaker elements are needed to map PCM audio signals to the transducers. Recently, sigma-delta modulation (SDM) driven DTA was proposed, which can achieve a satisfactory performance with only a few transducer elements. In this report the quantization noise and harmonic distortion of multibit SDM-driven DTA in each channel are investigated. The spatial distribution of signals emitted by multibit SDM-driven DTA is then derived. To confirm the analysis, a four-bit SDM-driven DTA system is constructed based on field-programmable gate array.
... En 2009, Tatlas [73] présente un HPDM composé de 32 transducteurs électrodynamiques de 15 mm de diamètre qui sont disposés selon la figure 1.42 au sein d'une matrice en polymère. La fréquence propre des haut-parleurs est de 500 Hz. ...
... b) THD mesuré en pilotage Sigma-Delta et simulé en pilotage PCM. Image tirée de[73] ...
The Digital Loudspeaker Array (DLA) is an electroacoustic transducer which receives as input a digital signal and performs the analog conversion directly into the air. It consists of a plurality of radiating elements arranged in a matrix. These elements will be designated by the term “speaklet” when they are reduced in size. The acoustic radiation of a DLA is indeed very sensitive to the size of the matrix due to differences in path length, which makes it especially suitable for MEMS technology. This thesis is on the study of a piezoelectric MEMS DLA. After an introduction that is increasingly focused on the subject, the thesis addresses the multiphysics modeling of the DLA, dimensioning of the speaklets and experimental tests. Analytical formulas, numerical simulations and finite element models are developed and used to predict the mechanical behavior of the presented speaklets, the pressure radiated by the DLA and the electrical power consumption. The speaklet are then dimensioned from the technological stack (set in advance) in order to maximize the pressure level. Experimental tests involving the use of an anechoic chamber, an optical interferometer, a vibrometer and an impedancemeter validate most of the models. Otherwise, these tests are usefull for improving some of them or for showing their limitations. The results have shown the importance of the residual stresses, which cause an initial deformation of the speaklets and modify their resonance frequencies, thus rendering ineffective the use of large radii. In accordance with the models, the static deflection of the speaklets is nonlinear but their dynamic behavior is linear. This enables characterizations using transfer functions. Theory and sound recordings show that a DLA made of such speaklets can produce in the best case the same pressure to that generated by the same matrix driven in an analog way. In our case, more distortions were obtained in digital reconstructions because of non-uniform responses of the speaklets, due to different access resistances. However, the presented DLA has other advantages, the most important being the very low power consumption it is theoretically possible to achieve using the adiabatic charge principle. The piezoelectric MEMS DLA thus appears as a promising technology. The optimization of our first prototype using the developed tools should indeed lead to a DLA able to generate an equivalent presure to that obtained with analog control, but with a far greater electroacoustic efficiency. Future work should then focus on the design of nonlinear speaklets and on the shaping of the pulse of pressure they generate, in order to increase the total pressure level.
... The paper of Tatlas et al. (2009) describes design, construction and measurements of a digital transducer array prototype, driven directly by 1-bit sigmadelta modulated (SDM) audio stream. The prototype includes a DSP stage implemented via a FPGA, a digital amplification module, and a two-dimensional array consisting of miniature electrodynamic loudspeakers, positioned on a surface to form a DLA (Fig. 13). ...
The development of digital microphones and loudspeakers adds new and interesting possibilities of their applications in different fields, extended from industrial, medical to consumer audio markets. One of the rapidly growing field of applications is mobile multimedia, such as mobile phones, digital cameras, laptop and desktop PCs, etc. The advances have also been made in digital audio, particularly in direct digital transduction, so it is now possible to create the all-digital audio recording and reproduction chains potentially having several advantages over existing analog systems.
This work presents a novel laser-based optoacoustic transducer capable of reproducing controlled and continuous sound of arbitrary complexity in the air or on solid targets. Light-to-sound transduction is achieved via laser-induced breakdown, leading to the formation of plasma acoustic sources in any desired spatial location. The acoustic signal is encoded into pulse streams via a discrete-time audio modulation and is reproduced by fast consecutive excitation of the target medium with appropriately modulated laser pulses. This results in the signal being directly reconstructed at the desired location of the target medium without the need for a receiver or demodulation device. In this work, the principles and evaluation results of such a novel laser-sound prototype system are presented. The performance of the prototype is evaluated by systematic experimental measurements of audio test signals, from which the basic acoustical response is derived. Moreover, a generic computational model is presented that allows for the simulation of laser-sound reproduction of 1-bit or multibit audio streams. The model evaluations are validated by comparison with the acoustic measurements, whereby a good agreement is found. Finally, the computational model is used to simulate an ideal optoacoustic transducer based on the specifications of state-of-the-art commercially available lasers.
Direct digital-to-acoustic converting systems do not make use of any kind of standard digitalto-analog converter throughout the electronic chain. Several systems were already reported and high values of THD and THD+N were found in the resulting wave fields together with a small minimum THD area or sweet-spot. However, the effects of transducer transfer characteristics, sampling rates, and bit-to-transducer assignments on the resulting acoustic fields have not yet been fully described. Results are shown on THD, THD+N, and directivities describing the audio fields produced by different direct digital-to-acoustic converting array systems. Each array was conceived with a different transducer type from experimental transducer responses. A significant reduction in the overall THD and THD+N in the listening space was achieved after using a randomized bit-to-transducer assignment. Practical advantages and limitations are reported that can be used in future implementations of digital-to-acoustic audio array systems.
A theory of smart loudspeaker arrays is described where a modified Fourier technique yields complex filter coefficients to determine the broad-band radiation characteristics of a uniform array of micro drive units. Beamwidth and direction are individually programmable over a 180arc, where multiple agile and steerable beams carrying dissimilar signals can be accommodated. A novel method of stochastic filter design is also presented, which endows the directional array with diffuse radiation properties.
A 7-bit digital multiple-voice-coil loudspeaker and a constant-current driver have been constructed and evaluated. Two's complement coding offers the best compromise between complexity, excessive power consumption, and distortion due to baseline drift. The effect of motion impedance and mutual coupling in a multiple-coil system is found to magnify the effective impedance of an individual coil by its weighting in the binary representation. This effect places an unreasonable demand on the output impedance of the driver unless damping is controlled, which can be achieved most effectively by a short-circuited voice coil. Optimum damping occurs when the damping resistance is equal to the negative resistance of an individual coil.
We propose a new digital to analogue (DA) conversion technique for acoustical transducer arrays. This technique utilizes the multidimensional band-limited property of array signals. Using the technique, a large dynamic-range wavefront is converted to multiple 1-bit waveforms which are over-sampled temporally and spatially. The I-bit waveforms are fed into a dense array of transducers. The acoustical wavefront transmitted from the array is approximately equal to the original wavefront, because the spatial high frequency components are eliminated by band-limitation due to wave propagation. This paper describes an over-sampling technique using two dimensional (2-D) Delta Sigma modulation for 1-D and 2-D arrays. Results of simulations are presented for evaluation and demonstration of the applicability of the proposed method.
The radiation pattern and the position-dependent distortion in a digital transducer array loudspeaker have been investigated and simulated by computer. Harmonic distortion in the sound field is significant and varies with different transducer arrangements. The directivity increases with increasing frequency and varies with the transducer selection procedure. Randomizing the selection of transducers at each sample interval improves the directivity but introduces high-frequency noise into the radiated sound field.
Using CMOS-MEMS micromachining techniques we have constructed a
prototype earphone that is audible from 1 to 15 kHz. The fabrication of
the acoustic membrane consists of only two steps in addition to the
prior post-CMOS micromachining steps developed at CMU. The ability to
build a membrane directly on a standard CMOS chip, integrating
mechanical structures with signal processing electronics will enable a
variety of applications including economical earphones, microphones,
hearing aids, high-fidelity earphones, cellular phones and noise
cancellation. The large compliance of the CMOS-MEMS membrane also
promises application as a sensitive microphone and pressure sensor
Digital Loudspeaker Arrays driven by 1-bit signals, " presented at the 116th Convention of the Audio Engineering Society
- N A Tatlas
- J Mourjopoulos
N. A. Tatlas and J. Mourjopoulos, " Digital Loudspeaker Arrays driven by 1-bit signals, " presented at the
116th Convention of the Audio Engineering Society, J.