## 1 Introduction  
The prediction of the acoustic response associated with squeal noise is often overlooked because it requires one to solve first the nonlinear dynamic problem. However this problem is of increasing interest to researchers by carrying out numerical simulations and experimental studies [1; 2; 3; 4; 5; 6; 7; 8] because noise pollution due to friction-induced vibrations has become a major problem in the automotive industry. A review on the subject of acoustic friction phenomena can be found in [9] and comprehensive review on mechanisms of the brake squeal phenomena and friction-induced vibration are also available in [10; 11; 12; 13; 14; 15].  
Even if the prediction of squeal noise is essential and of primary interest for designing brake systems, the estimation of the acoustic noise, based on numerical tools for nonlinear models with many degrees of freedom, can be rather expensive and requires considerable resources both in termsof computation time and data storage. So, one of the most important limitations and drawbacks of such a simulation is the problem size to be considered. Thereby simplifications and reductions in the mathematical modeling are usually required. This model reduction step can imply an approximation of the original system leading to a bad representation of the vibration behavior. In the case of mechanical systems subjected to friction-induced vibration, the performance of model reduction techniques [16; 17; 18; 19] for the stability prediction as well as the transient and stationary evolutions of the nonlinear responses of the brake system can be affected by such reductions.  
Nowadays, one of the main scientific challenges is not only to investigate the potential of reduced basis for the prediction of squeal noise but also to be able to provide criteria to quantify the relevance of different choices of reduction bases for such acoustic problem. One of the objectives of this study is to answer this question by proposing a complete approach, allowing for the development of numerical techniques based on the Double Modal Synthesis method for the prediction of squeal noise and the the use of the multiresolution signal decomposition of acoustic radiation and wavelet representation in order to analyze in detail the relevance of the reduction bases. It should be noted that this work is in the continuity of the previous works [20; 21; 22] that address the efficiency of the Double Modal Synthesis method for the stability analysis and the prediction of self-excited vibrations.  
The present paper is organized as follows. Firstly, the modeling of the Finite Element Model of the brake system under study is presented. Results for the stability analysis and the transient nonlinear dynamics, as well as the prediction of squeal noise based on acoustic radiation are briefly investigated. Secondly, the use of the multiresolution signal decomposition of acoustic radiation and wavelet representation is discussed. More precisely two criteria are proposed in order to quantify the efficiency of reduced models to accurately represent the acoustic fields for different scales of representation. Finally, the proposed methodology acoustic is applied and validated on the brake system under study.