## 2 Perceptually Informed Friction Sound Synthesis
### Source Modeling
#### 2.1.2 Empirical Observations on Recorded Sounds  
In this section, empirical observations of various nonlinear friction sounds are presented. Five situations are analyzed: a creaky door, a squeaking and singing wet wineglass, a squeaking wet plate, and a bowed cello string. These five situations were chosen as they are the consequence of a human movement and are therefore good candidates to be used in gesture guidance device. Except for the door creak and the cello, the recordings were made in an anechoic room using a cardioid Neumann-KM84i microphone positioned about 30 cm above the rubbed object. The recorded sounds are available online [21] from [22]. An inharmonicity analysis was performed for each sound. A partial tracking routine developed by [PERSON] [23] was used to detect the set of peaks of the spectrum in each frame of the excerpt. A linear regression was applied to the inharmonicity value, \(\gamma_{n}=\frac{f_{n}}{nf_{0}}-1\), where \(f_{n}\) is the n-th peak detected, and \(f_{0}\) the fundamental. If the spectrum is harmonic the inharmonicity \(\gamma_{n}\) is 0. The analysis of the three recordings revealed that they all had harmonic spectra. * _Creaky Door._ The time-frequency representation of the sound is presented in Figure 3. The sound has a harmonic spectrum whose fundamental frequency varies over time. The fundamental frequency is related to the rotation speed and the pressure at the rotation axis of the door. The large range of variations of the fundamental frequency is also a noticeable characteristic of this signal morphology that varies from a very noisy like sound when \(f_{0}\) is low, to a \"singing\" harmonic one for higher values. Figure 2: The conveyer-belt model and a typical stick-slip motion. * _Squeaking Wet Plate._ The spectrograms of the squeaking sound and the impulse response of the plate are shown in Figure 4. This sound is also harmonic but provides less variations of the fundamental frequency than the creaky door. In addition, the fundamental frequency \(f_{0}\) slowly varies around a central value. The vibrating modes of the plate are clearly visible on the impulse response and are excited when \(f_{0}\) gets close to the excitation frequency. This observation consolidates the stance to use the perceptual action/object paradigm based on a separate control of the exciter and the resonator. * _Squeaking and Singing Glass._ When a glass is rubbed, the associated sound may reveal several behaviors qualified as squeaking and singing, see Figure 5. The squeaking phase provides a similar behavior as the squeaking wet plate: \(f_{0}\) varies chaotically around a central value. The singing phase appears when \(f_{0}\) falls on a wineglass mode. The transitions between the squeaking and singing situations are almost instantaneous and hardly predictable. Figure 4: Short Term Fourier Transform of a sound produced by a squeaky wet plate and its impulse response. Figure 3: Short Term Fourier Transform of a creaky door sound. * _Bowed Cello String._ The sound of a bowed string shows behaviors similar to those of the singing wineglass, see Figure 6. The fundamental frequency is locked to a vibrating mode of the string according to the bow velocity and force. The main difference resides in the attack which is smoother than in the singing wineglass sound. These empirical observations lead us to hypothesize that the acoustical morphology that mainly characterizes such auditory events relies on the temporal evolution of the fundamental \(f_{0}\) frequency of a harmonic spectrum. As it is well known for sustained musical instruments most of these acoustical behaviors can indeed be modeled by a harmonic spectrum whose fundamental frequency varies over time. The analyses of the previously recorded sounds confirmed that these assumptions also hold for other friction cases. Nevertheless, even if each spectrum locally is perfectly harmonic, each individual harmonic is not perfectly localized in frequency and should be considered as a band-pass filtered noise with a very thin bandwidth.