DS-2000 Frequently Asked Questions

The DS-0230 Time-Frequency Analysis Software is designed to perform calculations such as Short-Time Fourier Transform, Wavelet Transform, and Wigner Distribution Analysis on time-domain data (file extensions: .dat/.prn) recorded with various software in the DS-2000 series or our FFT analyzers (CF-6400/CF-5000/CF-4200 series, etc.).

■Wigner distribution

The Wigner distribution is an analytical method that enables the simultaneous analysis of the temporal variation and spatial transition of complex waveforms such as sudden or transient sounds and vibrations. Proposed in 1932 by E. Wigner in the field of quantum mechanics, the Wigner distribution was later applied to acoustic analysis by T. Classen and W. Mecklenbraker, and has since gained attention as a means of analyzing transient signals. Because the Wigner distribution has the energy dimension, it offers the highest resolution in both time and frequency, allowing it to better capture the characteristics of transient signals compared to conventional methods. However, negative energy and cross terms often appear, requiring specialized interpretation. By utilizing the time-frequency distribution of transient signals inherent in the Wigner distribution function, it is expected to become an effective tool for analyzing impact sounds, abnormal sounds, and the transient characteristics of acoustic equipment.

■ Wavelet Transform

The wavelet transform is a new analytical technique that continues to develop, enabling the simultaneous analysis of the temporal variation and spatial transition of complex waveforms such as sudden or transient acoustic and vibrational waves. Initially introduced by petroleum exploration engineers as a tool for analyzing artificial seismic waves, wavelet transform analysis has since been explored by physicists, mathematicians, and engineers, who have attempted to establish its mathematical foundations and apply it to various fields. As its name suggests, the wavelet transform uses a single function that is (practically) localized both in time and frequency, and then applies scale and shift transforms to it to obtain a set of functions which are used as basis functions. Because it is a natural analytical method that uses long time data for low frequencies (slow fluctuations) and short time data for high frequencies (fast fluctuations), it is attracting attention as a means of analyzing various transient phenomena. The distribution of absolute squared values in the wavelet transform results is called a scalogram. The wavelet transform in the DS-0230 time-frequency analysis software can display the signal spectrum on the time-frequency plane as either a two-dimensional or three-dimensional color image.

STFT