Fractional Zero-phase Filtering And 90? Phase Shift Detection Research

The result of digital signal denoising,enhancement and feature point detection has a direct impact on the accuracy of subsequent signal comprehension and recognition.To meet the demand of no phase distortion,how to make a balance between smooth and enhancement filtering as well as feature point detection accuracy and anti-noise property is therefore a difficult issue to be solved.Based on digital signal batching processing,non-casual signal processing is adopted,which provides greater freedom than casual signal processing.Meanwhile,the introduction of fractional calculus expands the scope of signal processing operator design and thus improves signal processing performance.Combining advantages of fractional calculus and non-casual signal processing,fractional non-casual signal processing has played an important role in modern nonlinear signal processing due to its further improvements in signal processing.Based on above questions,fractional zero-phase filtering and 90°phase shift detection are proposed in this paper.First of all,based on facts that amplitude-frequency and phase-frequency characteristics of fractional calculus are determined by fraction order as well as reverse phase frequency characteristics of reverse filtering,fractional cascade zero-phase filtering algorithm applied in signal denoising is then proposed,which embeds forward-backward filtering into fractional integration filter design.Simulation of electrocardiosignal denoising shows that the proposed algorithm can filter signal noise and retain the main characteristic waveforms of original signals simultaneously.That means it can avoid phase distortion and has advantages of good fidelity quality,high anti-noise performance and low computing complexity.Secondly,fractional center summation operators are defined as linear weighted sum of fractional casual calculus operators and non-casual ones,which are essentially a one-dimension fractional cascade zero-phase filter.A two-dimension fractional zero-phase mask operator is then constructed to ensure rotation invariance of fractional center summation operators used in two-dimension image filtering.Simulation of image structure protection denoising indicates that,under the basis of avoiding phase distortion,the above two-dimension fractional zero-phase integral mask operator can filter the noise of image smoothing region and reserve the image edge information and texture details;simulation of image structure protection enhancement shows that the designed differential mask operator is verified to enhance the details of image high-frequency edge and texture information and reserve the low-frequency contour information in smoothing region simultaneously.In addition,it can avoid phase distortion and singularity drift effectively.Thirdly,considering the fact that Hilbert transform provides a 90?phase shift without changing the magnitude,envelope detection technique based on fractional Hilbert transform is developed which extends Hilbert transform from traditional integral domain to fractional domain.It conducts a fractional envelope demodulation to vibrating signals using Hilbert transform and makes a measurement of rolling bearing faint vibration signal via fractional spectrum analysis of the modulated wave.Simulations and experiments show that,envelope detection technique based on fractional Hilbert transform is wellbalanced between detection accuracy and background noise filtering.In the end,given the definition of the fractional calculus and fractional difference,fractional central difference operator,that is essentially a one-dimension 90?phase shift filter,is defined.It has the same phase-frequency characteristics as traditional first-order derivative which turns out to be a 90?phase shift.In addition,due to the fractional power function derived based on its magnitude and frequency,tradeoff can be made between detection accuracy and anti-noise performance by regulating fraction orders.Simulation of electrocardiosignal QRS characteristic waveform detection shows that the proposed algorithm has relatively high detection accuracy and positioning precision.Meanwhile,simulation of improved two-dimension fractional center differential mask operator with rotation invariance indicates that the proposed algorithm has advantages of good stability quality,high detection accuracy and strong anti-noise performance.