## 1 Introduction  
Noise produced by cars is important not only inside but also outside [1]. Due to the development of automotive technology and the increased interest in environmental issues, many innovative noise reduction techniques for automotive engines have been studied, especially for the development of electric cars. As the number of electric vehicles increases, the reduction of tire noise becomes more important [2; 3]. Tire-road noise is the main source of noise produced by a car and is a remarkably complex phenomenon resulting from the combination of airborne and structure-borne phenomena, where the source is provided by the contact between tire and pavement [4]. In this context, it is however of paramount interest to improve the tires, but also the road pavements. Studies regarding optimal road texture and mixture design for noise abatement have been widely available in recent years [5; 6; 7; 8; 9; 10; 11]. For satisfying consumer demand on low tire noise, prediction systems for tire noise waveforms are necessary, and further elements for sound analysis and prediction steps of the process preceding the establishment of the design are also needed. The pattern noise prediction method is important because it is difficult to change the shape and arrangement of the tire after they are determined in the beginning of the tire development process. In addition, because the pattern shape is associated with various tire performances such as groove wander, hydroplaning, and brake performance, it is an important design element. Therefore, optimal design of pattern shape is required to satisfy not only the noise performance but also other performances. Generally, the major pneumatic tire noise is divided into two types. One is the interior noise due to structure-borne path and air-borne path [12]. Airborne noise is related to compression of the air trapped within the tread of the rolling tire [13]. The other is the exterior noise caused by only the air-borne path [14]. Generally, in acoustics, the difference between structure-borne and air-borne noise is the medium of transmission, but in terms of tire noise, the difference is sometimes focused on the noise generation mechanism, which is usually misused. Strictly speaking, the latter should be called the vibro-dynamic noise and aerodynamic noise or vibro-acoustic noise and aeroacoustics noise. Pattern noise is mainly associated with the shape of the tire tread pattern, is in the range of over 500 Hz, and is a phenomenon due to air. Road noise is mainly below 500 Hz and occurs with vibration of the vehicle structure through the transfer path. Especially, pattern noise is the interior transmission sound that air delivers to the medium and is defined as air-borne noise which is over 500 Hz. A large proportion of pattern noise is correlated to air-pumping noise, which is caused by the compression and expansion of air grooves and is generated because of the grounding of the tread, the shape of the road surface, and the groove depth. Therefore, accurate noise prediction is important in the design step. A common method of estimation of the tire pattern noise is to use the blocked pitch sequence [15]. This method uses a genetic algorithm to reduce the tire air-pumping noise that is generated by the repeated compression and expansion of the air cavity between the tire pitch and the road surface. Genetic algorithms have been used to determine the optimal tire pitch sequence with low levels of tire air-pumping noise using image-based air-pumping models. However, it is difficult to predict the actual waveform with this traditional method, and in most cases, the method has limitations because it does not consider the transfer function and precise mechanism of tire pattern noise. In this study, adaptive filter theory was applied to identify the transfer function between the grooves of patterns and measured acoustic data. To predict the waveform of an actual pattern noise in time domain, the impulse response of this transfer function was convolved by the scanned pattern input of tires.