Research On Wavelet Transform Processors And Wavelet Inverse-transform Processors For Multiple Scales Using Surface Acoustic Wave Devices

Wavelet transform is a local time and frequency transformation.Wavelet theory has the the excellent time frequency location characteristic.It is especially suitable for analysis and processing of non-stationary signals.Wavelet transform is widely used in many fields,for example,mathematics,signal analysis,image processing,quantum mechanics,electronic countermeasure,computer recognition,data compression,seismic exploration,atmospheric and ocean analysis,mechanical fault diagnosis.The algorithm of wavelet transform needs a larger number of mathematical operations and complicated programs,it is very complicated and difficult to implement in engineering fields.In order to avoid complicated mathematics operations,scientists have developed surface acoustic wave?SAW?wavelet transform devices.The realization of wavelet transform with SAW devices inherited localization properties of wavelet transform.The SAW wavelet transform devices have many advantages,such as high processing speed,simple design,small size,good temperature stability,low cost and low power.If the electrodes envelopes of input interdigital transducer?IDT?for SAW wavelet transform device are designed according to the envelopes of the wavelet function,the wavelet transform can be implemented.The electrode-envelope-weighted?EEW?wavelet transform processors using SAW devices can be fabricated.However,there is a serious diffraction problem of the EEW wavelet transform processors.Diffraction problem can cause the diffraction loss and the wavefront aberration.In order to solve this problem,three novel wavelet transform processors and waveletinverse-transform processors using SAW devices for multiple scales are developed in this paper,that is,electrode-area-weighted wavelet transform processors and wavelet inverse-transform processors using SAW devices,electrode-width-weighted wavelet transform processors and wavelet inverse-transform processors using SAW devices,electrode-mixed-weighted wavelet transform processors and wavelet inverse-transform processors using SAW devices.The content and innovation of this paper are listed as follow:?1?Morlet wavelet function is used for three novel wavelet transform processors and wavelet inverse-transform processors using SAW devices for multiple scales,implementation scheme is as follow:?1?The electrode areas of IDTs for the electrode-area-weighted wavelet transform processor and wavelet inverse-transform processor using SAW device are equal to the envelope areas of the wavelet function.The acoustic apertures meet condition H²/??D.?2?The electrode widths of IDTs for the electrode-width-weighted wavelet transform processor and wavelet inverse-transform processor using SAW device are equal to the envelope amplitudes of the wavelet function.The acoustic apertures meet condition H²/??D.?3?The electrode lengths in the larger aperture district of IDTs for the electrode-mixed-weighted wavelet transform processor and wavelet inverse-transform processor using SAW device are equal to the envelope amplitudes of the wavelet function,that is,the electrode lengths are proportional to the envelope amplitudes of the wavelet function.The envelope widths are equal.The electrode widths in the smaller aperture district of IDTs for the electrode-mixed-weighted wavelet transform processor and wavelet inverse-transform processor using SAW device are equal to the envelope amplitudes of the wavelet function,that is,the electrode widths are proportional to the envelope amplitudes of the wavelet function.The aperture legnths are equal.?2?According to above scheme,the relationships between physical parameters?material parameters,structural parameters?and their performance for three novel wavelet transform processors and wavelet inverse-transform processors using SAW devices for multiple scales are derived.The optimal structures for these processors are determined.?3?Key problems of three novel wavelet transform processors and wavelet inverse-transform processors using SAW devices for multiple scales are investigated and solved,such as diffraction problem,effect of piezoelectric substrates on frequency characteristics of wavelet transform processors using SAW devices,effect of output IDT number on bandwidths of wavelet transform processors using SAW devices,effect of electrode widths precision on frequency characteristics of wavelet transform processors using SAW devices and phase shift.?4?Three novel wavelet transform processors and wavelet inverse-transform processors using SAW devices for multiple scales are fabricated on X-112°Y LiTaO₃ substrate material.The experimental results are consistent with the theoretical derivation.It is proved that there are no diffraction with three novel wavelet transform processors and wavelet inverse-transform processors using SAW devices for multiple scales.