This paper presents a time-frequency distribution which is suitable for a signal analysis. It is difficult to obtain a high resolution in both time and frequency domains in the time-frequency analysis of the signal. However, the multiple short-time Fourier transform (NISTFT) is proposed as a means which obtains high resolution in both time and frequency domains. Further, it is extended to achieve higher resolution signal analysis using multiple expression of the MSTFT. The diagnosis of rotating condition of the pumps is attempted with driving sound using several expressions of time-frequency distributions based on the MSTFT.