Separation of the Structure Signal by the Maximal Overlap Discrete Wavelet Transform and Fast Fourier Transform

Abstract

Power spectral density (PSD) is used for evaluating a structure’s vibration process. Moreover, PSD not only shows a discrete form of vibration but also presents various components in a vibration structure. The superposition of multiple vibration patterns on the same spectrum poses difficulty in analyzing the spectral information in the way needed to find the structure’s discrete vibration. This paper proposes a method for separating the synthetic vibration signal into a structure’s discrete vibration and other extraneous vibrations using the maximal overlap discrete wavelet transform (MODWT) method combined with the method of fast Fourier transform (FFT). With the combination of these two algorithms, MODWT and FFT, the signals of the synthesized vibration have been separated into component signals with different frequency ranges. This means that PSD will be formed, which is based on the combination of the single power spectra of the component signals. Thus, the single spectrum of each of these constructed components can be used to evaluate the types of discrete vibrations coexisting in a structure’s vibration process. The survey results in this paper show the sensitivity and suitability of select types of discrete vibrations to be separated out during the assessment of the structural change, so as to achieve the best possible plan for eliminating the unwanted and unexpected noise and vibration components.

Through the wall human heart beat detection using single channel CW radar

“…The radar-reflected echoes (t) can be divided into two components using the MODWT method ( Nguyen, , 2021 ; Shrifan et al, 2021 ). One is the detailed component and another is the approximation method shown below in the equation: …”

“…The radar-reflected echoes y(t) B 2 (t) can be divided into two components using the MODWT method (Nguyen, , 2021; Shrifan Frontiers in Physiology frontiersin.org The decomposed signal and its associated relative energy are shown here. The higher relative energy has been selected as the desired heartbeat signal from the Radar.…”