Sentence examples for detail functions from inspiring English sources

They are referred to as the detail functions.

2. Once the wavelet coefficients C s,p) are calculated, the detail functions are constructed using Equation 3.   3.

It computes the wavelet decomposition, Equation 1, and constructs the detail functions, Equation 3, using a fast convolution implementation by means of the fast Fourier transform (FFT).

This algorithm decomposes the original record into detail functions (functions with a very dominant frequency and modulated amplitude) and reconstruct the signal through an iterative procedure that independently scale these detail functions to obtain an average match with the target spectrum [17].

Damage detection using the FWT is relatively simple; in this work we used the FWT implementation available in the Matlab to decompose the signal in its approximation and detail functions.

Figure 3 (top) shows the detail functions obtained at the first level of decomposition using the Bior6.8 wavelet (notice that the Complex Morlet Wavelet used for the CWT cannot be used to implement the FWT).

Open image in new window Fig. 3 Detail function for the first level of decomposition for the clean signal (top), detail function for the first level of decomposition for the signal with SNR = 100 along with its Fourier spectrum (middle) and detail function for the seventh level of decomposition for the signal with SNR = 100 along with its Fourier spectrum (bottom).

Multiply each detail function D(s j,t) by the corresponding spectral ratio R(f j ) and reconstruct the signal with Equation 2.

It seen that a spike appears in the detail function that can be clearly related to the discontinuity caused in the signal.

Additional decompositions were performed to check if the discontinuity could be detected from a different detail function with narrower frequency content but the results were no successful, Fig. 3 (bottom) shows for example the results for the level 7 of decomposition (detail function with frequency content between 504 and 508 Hz).

Detail function of detector probe is presented in Appendix 1. Limit dead volume of 0.14 ml from endcap to probe is small enough to cause a precise determination of breakthrough time.