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Therefore, the FrFT has excellent localization performance for LFM signals.
However, only weak coherency strain energy is the effective driving force for LFM in the case of melting of one-phase alloys.
For LFM imaging, we have employed various AFM cantilever tips (i.e., SNL-10, ScanAsyst Air, ScanAsyst Fluid, Bruker) with their stiffness in the range of 0.1 to 1 N/m.
The chirp rates for LFM are 40 MHz/ μs,80 MHz/ μs,100 MHz/ μs,1200 MHz/ μs.And the length of rectangular window is set to be 400 and the SNR values from -5 to 5 dB.
For LFM imaging, we have utilized a triangular-shaped microcantilever whose normal spring constant knorm is in the range of 0.16 to 1 N/m, suitable for contact mode AFM imaging.
Figure 5 plots the comparison results among the common detectors for LFM signal in Equation (42) with T = 40 s, w 0 = w 1 = 0.1 rad / s, m 0 = 0.2 rad / s 2, m 1 = 0.4 rad / s 2. Figure 5 The comparison among the common detectors for LFMf signals.
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In recent years, several time-frequency-based methods for LFM-signal detection have been proposed.
Therefore, the generalized detector can be regarded as an effective detector for LFM-signal.
It can be seen that, for LFM-signal, the generalized detector will reach its maximum corresponding to the chirp rate.
For LFM-signal, the first- and second-order differential in time domain is expressed as follows, respectively, (21).
Then a new detector for LFM-signal is obtained, which is the integration of the 4th-power modulus of the fractional Fourier transform, (12).
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