For the noise control of commercial products, the most important fact is the subjective feeling of the human being on noise and the countermeasure plans should be properly prepared for reducing the annoyance due to the noise source. It is recently known that sound quality metrics are more useful for describing the subjective preference of product sounds than the strength related metrics. Example metrics of the former include loudness, sharpness, roughness and fluctuation strength and the latter includes the overall sound pressure level expressed in the A-weighted decibels. As a result of psychoacoustic research, models of sound quality metrics have been developed that allow for prediction and evaluation of attributes of hearing events. However, signal-processing techniques for the analysis of unsteady sounds in these models have been not clearly given yet.
In this study, models of sound quality metrics for unsteady sounds are generated and the signal-processing techniques appropriate for this purpose are introduced such as digital filtering and time-frequency analysis. Based on Zwicker's loudness model for steady sounds, the loudness model for unsteady sounds is suggested. For dealing with nonstationary acoustic signals, the suggested loudness model contain the signal processing technique such as bandpass filtering and envelope extraction and simulation algorithms of psychoacoustic facts such as post-masking and temporal integration. In the proposed roughness model, the analysis method based on the Fourier transform for overlapped 47 critical bands is used and details of each step such as calculation of excitation and correlation coefficient are discussed. The proposed roughness model is in turn used for modeling the fluctuation strength. In modeling the fluctuation strength, several weighting functions complying with the psychoacoustic experimental results are employed. The usefulness of suggested models is confirmed by comparing the calculation results of present model with psychoacoustic facts. Additionally, previous models are revised to improve the calculation accuracy of the present models and to make easy for searching the mainly contributing frequency components to the sound quality of a product. For example, in the revised loudness model, overlapped 47 critical bandpass filters instead of conventional 24 filters are used especially for minimizing the loudness error of frequency-varying pure tones within the same critical band.
In addition, a signal processing technique is proposed for the time-frequency analysis of the unsteady sound signals considering the auditory perception model, which is called the VFR-STFT (Short Time Fourier Transform with Variable Frequency Resolution). The conventional STFT, which is commonly used for the spectral analysis of unsteady sounds, is not suitable for the auditory model because the frequency resolution of the spectral analysis within the hearing system is not constant but varies with frequencies. In this study, the frequency resolution of the VFR-STFT can be adjusted to the variation of analyzed frequency ranges by introducing the downsampling technique. In the implementation of the VFR-STFT, calculation schemes are included for minimizing the undesirable effects: the distortion of overall level due to non-overlapping of the analysis windows and the impairment of partial spectra due to the finite order of anti-aliasing filters. Additionally, a procedure for equalizing time grids at all frequency ranges is included in order to describe the two-dimensional time-frequency map having different time grids. The proposed VFR-STFT is applied to the spectral analysis of the extraction of tonal components in an unsteady sound. The results are compared with those from other time-frequency analysis methods such as STFT, VFR-FFT (Fast Fourier Transform with Variable Frequency Resolution) and wavelet packet method. It is found that the proposed VFR-STFT algorithm describes the auditory sensation of time-varying and intermittent tones very excellently as well as steady sounds.
