Implementation of a new algorithm using the STFT with variable frequency resolution for the time-frequency auditory model

Abstract

A signal processing technique is proposed for the time-frequency analysis of unsteady sound signals considering the auditory perception model and is called VFR-STFT (short-time Fourier transform with variable frequency resolution). 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 frequency. The frequency resolution of the VFR-STFT can be adjusted to a number of analyzed frequency ranges by introducing the downsampling technique. With the VFR-STFT, calculation schemes are presented for minimizing undesirable effects, such as the distortion of the overall sound level due to nonoverlapping of the analysis windows and the impairment of partial spectra due to the finite order of antialiasing filters. In addition a procedure for equalizing time grids at all frequency ranges is included in order to describe the two-dimensional time-frequency map (TFM) 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 to those from other time-frequency analysis methods such as STFT, VFR-FFT (fast Fourier transform with variable frequency resolution), and the wavelet packet method.