# Calculation of 1/f Fluctuation from Sound Signal and Comfort Evaluation
## 1 Introduction
We propose that it is possible to regularly select sound signals and create a feeling of comfort by establishing a method to analyze the relevant factors. Furthermore, this paper found that a sound signal including \(1/f\) fluctuation also made the experiment's participants comfortable. In this study, we focused on the \(1/f\) fluctuation included in sound signals to analyze factors that give people a feeling of more comfort. In the \(1/f\) fluctuation, the power spectral density is inversely proportional to frequency f. The \(1/f\) fluctuation included in music has a relaxing effect on humans [19]. In various research fields, the psychological influence of sound signals, including the \(1/f\) fluctuation, has been recently investigated [20; 21; 22; 23; 24; 25; 26; 27; 28; 29]. [PERSON] et al. [30] reported that music has strong \(1/f\) fluctuation characteristics. Additionally, music was exhibited by electroencephalographic \(\alpha\) and \(\beta\) waves via the measurement of participants' brain waves while they listened to the music, and the \(1/f\) fluctuation was visualized by the frequency analysis of the music. Moreover, [PERSON] et al. [31] calculated the change in the fluctuation coefficient for the time history of the instantaneous frequency of the sound signal. Thus, there is extensive research on the \(1/f\) fluctuation in various fields. However, there is no existing description of the calculation method used for the \(1/f\) fluctuation in a sound signal, and there is insufficient sound signal information in studies on sound signals that include the \(1/f\) fluctuation. Moreover, the method to detect \(1/f\) fluctuations in sound signals has not been established. According to [PERSON] [32], there is a \(1/f\) fluctuation in the change of acoustic power and instantaneous frequency. However, the calculation method used to obtain these two changes from the sound signal was not clarified. Although there is extensive research on the \(1/f\) fluctuation, such as the calculation method and the evaluation of its relaxation effect on humans, as described above, there are no studies on the most suitable calculation method for the fluctuation. This study investigated fundamental considerations of the established calculation methods used to determine the frequency and amplitude fluctuation coefficient via a discrete Fourier transform using time changes to clarify the \(1/f\) fluctuation in sound signals. In this paper, \"fluctuation\" indicates the fluctuation from a physical quantity's average value or increase/decrease from the average value. Additionally, the fluctuation of the sound signal means the fluctuation of \"pitch of sound = frequency\" and \"volume of sound = amplitude\", which are elements of sound. We considered a subjective evaluation of comfort when a human listened to a sound signal including two different \(1/f\) fluctuation coefficients to determine the comfort of the human according to the difference in the calculated fluctuation coefficient. We also conducted experiments to improve human comfort on the basis of the fluctuation coefficient.