Resolution conversion of a local time-frequency region by convolution of a Gaussian and Gabor spectrum

The main purpose of music signal analysis is to extract the two types of information as follows. One is the time information such as onset, and the other is the frequency information such as pitch. Therefore, the required time-frequency resolution varies according to each time-frequency region. How­ever, the time-frequency resolution in the Short Time Fourier Transform (STFT) is constant in any time-frequency region. Thus, the analysis requirements cannot be satisfied by analyzing the music using STFT only once. Therefore, we must perform reanalysis employing different resolutions. In addition, the problem with reanalysis is that the computational cost increases. In this paper, we propose a method of converting to any resolution spectra in any local time-frequency region without performing reanalysis. We focused on the mathematical characteristics of the Gaussian that the convolution of two Gaussians become a Gaussian with different standard deviation. The proposed method can reduce the computational cost to about 1/10 compared with reanalysis using STFT.