978-1-4244-7493-6/10/$26.00 ©2010 IEEE ICME 2010 PERFORMANCE ANALYSIS ON RECURSIVE SINGLE-SIDEBAND AMPLITUDE MODULATION FOR PARAMETRIC LOUDSPEAKERS Peifeng Ji 1 , Woon-Seng Gan 1 , Ee-Leng Tan 1 and Jun Yang 2 1 Digital Signal Processing Lab, Nanyang Technological University, Singapore 2 Institute of Acoustics, Chinese Academy of Sciences, Beijing, China Email: {pfji, ewsgan, etanel}@ntu.edu.sg, jyang@mail.ioa.ac.cn ABSTRACT A highly directional speech signal can be generated using parametric loudspeaker. The generation of highly directional sound beam is due to the nonlinear interaction of amplitude-modulated ultrasound waves in air. However, severe distortion is also generated during the reproduction of directional speech and several preprocessing techniques based on the Berktay’s farfield model have been proposed by researchers to reduce the distortion. In this paper, we carried out a thorough investigation on the analytical performance of the recursive single-sideband amplitude modulation (RSSB-AM) technique, which has been found to perform well for directional speech reproduction. Several important characteristics of the performance of the RSSB- AM are observed and optimal parameters of the RSSB-AM are also presented. Keywords—Directional Sound, Distortion Reduction, Nonlinear System, System Approximation 1. INTRODUCTION Highly directional sound beams are widely applied in the areas of medical ultrasound, acoustic microscopy, non- destructive testing, and underwater acoustics [1]. Unlike conventional loudspeaker that requires a large speaker array to deliver high directional sound wave, parametric loudspeaker [2-8] with a small aperture has a unique feature in delivering high-directivity low-frequency speech signal to a desired location by utilizing the nonlinear acoustic behavior in air. Berktay [9] has given an accurate and complete explanation of the parametric loudspeaker and also a farfield solution of 2 2 2 2 () ( )/ p t E t t ∝∂ ∂ , assuming the primary wave has the waveform of 1 () ( )sin c p t Et t ω = , where () Et is the modulation envelope function, c ω is the This work is supported by the Singapore National Research Foundation Interactive Digital Media R&D Program, under research grant NRF2007IDM-IDM002-086. angular carrier frequency and 2 () p t is the demodulated signal. Figure 1 shows a simple block diagram on how speech signal can be preprocessed in a system () g t before passing to the air modeled by an acoustic model (modeled by the Berktay’s model) ( ). ht To recover the speech signal ( ), x t the system () g t must approximate the inverse of the acoustic model, i.e., 1 () () g t h t − ≈ . There are many approaches [3, 10-15] in estimating the inverse of the acoustic model to achieve an output signal ˆ( ) x t as close as to ( ). x t However, due to the nonlinear acoustic property in air, nonlinear distortion () a d t consisting of harmonics and sum frequencies are generated together with the desired signal ( ). x t Therefore, we have ˆ( ) () ( ). a x t xt d t = + A preprocessing technique is used to minimize the distortion () a d t and results in a demodulated output signal 2 ˆ( ) () x t p t = which approximates the original desired signal ( ). x t Hence, the desired signal is heavily distorted if no preprocessing method is applied [15]. To improve the quality of the desired signal, many research works [3, 10- 15] have been carried out to determine a preprocessing method that reduces as much distortion as possible. The conventional double-sideband amplitude modulation (DSB- AM) [3] is one of the simplest preprocessing methods. However, this method suffers from high distortion as it does not remove the nonlinear distortion. Several other methods, such as the square root AM (SRAM) [10, 11], the single- sideband AM (SSB-AM) [12] and modified AM (MAM) [13] significantly reduce distortion, but all these methods have their disadvantages, i.e., both the SRAM and MAM need infinite bandwidth and the SSB-AM has high inter- modulation distortion (IMD), which will be discussed in this paper. Fig. 1. Block diagram of the operation of a parametric loudspeaker. 748 978-1-4244-7492-9/10/$26.00 ©2010 IEEE ICME 2010