O-Solution 時間周波数解析機能 OS-0527
Users can perform Fourier transforms at arbitrary points (frame lengths and intervals). Therefore, since users can set arbitrary extraction time lengths, it is an effective method for observing very short-term spectral changes.
This is an analytical method that enables the simultaneous analysis of the temporal variations and spatial transitions of complex waveforms, such as sudden or non-stationary acoustic or vibrational signals. This method varies the analysis duration according to frequency. It is effective in capturing the overall results due to its good balance between time and frequency.
This is a case study analyzing the impact sound of a golf club, where the frequency changes in a short time.
Due to the short duration of the target signal, the spectral changes in the time direction become blurred in FFT analysis (see the figure below).
By using STFT, even with the same frame length, the user can arbitrarily set the frame interval and window function length, allowing for a clear display of the time variation of frequency components that change in a short time while maintaining frequency resolution (see the figure on the right).
This is a case study analyzing very short abnormal sounds included in machine working noises.
Since the frequency components of the abnormal sounds span a wide range, to obtain resolution for the low frequency components in FFT analysis, it is necessary to take a sufficiently large frame length.
However, since the duration of the abnormal sounds is very short, it is also necessary to keep the frame length as short as possible,
which means that sufficient frequency resolution and time resolution cannot be obtained (left figure).
In this example, the components surrounded by the red circle, which are low frequency components that would be overlooked in FFT analysis, become visible (right figure).
In this way, wavelet transform reduces frequency resolution and increases time resolution for higher frequencies (where frequency resolution is sufficient),
and increases frequency resolution while reducing time resolution for lower frequencies (where time variation is gradual).
In other words, this analysis method is similar to the constant ratio filter bank analysis used in acoustic analysis, such as 1/N octave band analysis.
