Time frequency analysis function OS-0527

This function can evaluate transient phenomena that were difficult to capture by FFT analysis, and display clearly time change of the frequency component while maintaining its frequency resolution . The OS-0527 is equipped with STFT (Short Time Fourier Transform) and Wavelet transform.

Item	STFT	Wavelet Transform
Time resolution	constant	High frequency ：finer Low frequency：coarse
Frequency resolution	constant	High frequency ：coarse Low frequency：finer
Advantages	Stable results can be obtained by extending the FFT.	The time resolution and the frequency resolution are good balance.
Disadvantages	If the time resolution and frequency resolution are increased, the calculation time and the data amount will increase.	Only approximate frequency is obtained.

Case study 1　Burst signal analysis

By using the short-time Fourier transform, the frequency resolution and the time resolution are improved. Thus, transient vibration waveforms can be analyzed, and detailed analysis that cannot be performed with normal FFT analysis due to coarse time resolution is available.

Case study 2　Analysis of impact sound of a golf club

It is an example of analyzing the impact sound of a golf club as an example of the frequency changing in a short time. Since the time length of the target signal is short, the change in the spectrum becomes unclear with respect to the time change in the FFT analysis (left figure). While, by using STFT, even if the frame length is the same, the frame interval and window length can be set at any points and the time change of the frequency component that changes in a short time is clearly displayed while maintaining the frequency resolution. (right figure).

Time waveform for impact sound of a golf club

Case study 3　Analysis of mechanical operating sound

This is an example of analyzing transient noise generated from a machine tool. The time length of abnormal sounds is very short and their frequency components are seen over a wide range. In the FFT analysis, the frame length cannot take long enough to obtain the resolution of low frequency components. While, by using the wavelet transform, it is possible to comprehensively capture time and frequency information. In this example, the components (low frequency components) in the red circles that are not seen in the FFT analysis can be seen in the right figure. In this way, the wavelet transform raises the time resolution for high frequency components with sufficiently high frequency resolution, and raises the frequency resolution for low frequency components with gradual time change. This is an analysis method using a constant ratio filter bank similar to 1/N octave band analysis that is often used for acoustic analysis.