Application of fast wavelet transformation in signal processing of MEMS gyroscope

Decomposition and reconstruction of Mallat fast wavelet transformation （WT） is described. A fast algorithm, which can greatly decrease the processing burden and can be very easy for hardware implementation in real-time, is analyzed. The algorithm will no longer have the processing of decimation and interpolation of usual WT. The formulae of the decomposition and the reconstruction are given. Simulation results of the MEMS （micro-electro mechanical systems） gyroscope drift signal show that the algorithm spends much less processing time to finish the de-noising process than the usual WT. And the de-noising effect is the same. The fast algorithm has been implemented in a TMS320C6713 digital signal processor. The standard variance of the gyroscope static drift signal decreases from 78. 435 5 （°）/h to 36. 763 5 （°）/h. It takes 0. 014 ms to process all input data and can meet the real-time analysis of signal.

Properties of an improved Gabor wavelet transform and its applications to seismic signal processing and interpretation

This paper presents an analytical study of the complete transform of improved Gabor wavelets （IGWs）, and discusses its application to the processing and interpretation of seismic signals. The complete Gabor wavelet transform has the following properties. First, unlike the conventional transform, the improved Gabor wavelet transform （IGWT） maps time domain signals to the time-frequency domain instead of the time-scale domain. Second, the IGW＇s dominant frequency is fixed, so the transform can perform signal frequency division, where the dominant frequency components of the extracted sub-band signal carry essentially the same information as the corresponding components of the original signal, and the sub- band signal bandwidth can be regulated effectively by the transform＇s resolution factor. Third, a time-frequency filter consisting of an IGWT and its inverse transform can accurately locate target areas in the time-frequency field and perform filtering in a given time-frequency range. The complete IGW transform＇s properties are investigated using simulation experiments and test cases, showing positive results for seismic signal processing and interpretation, such as enhancing seismic signal resolution, permitting signal frequency division, and allowing small faults to be identified.

Variational Mode Decomposition-Informed Empirical Wavelet Transform for Electric Vibrator Noise Analysis

Electric vibrators find wide applications in reliability testing, waveform generation, and vibration simulation, making their noise characteristics a topic of significant interest. While Variational Mode Decomposition (VMD) and Empirical Wavelet Transform (EWT) offer valuable support for studying signal components, they also present certain limitations. This article integrates the strengths of both methods and proposes an enhanced approach that integrates VMD into the frequency band division principle of EWT. Initially, the method decomposes the signal using VMD, determining the mode count based on residuals, and subsequently employs EWT decomposition based on this information. This addresses mode aliasing issues in the original method while capitalizing on VMD’s adaptability. Feasibility was confirmed through simulation signals and ultimately applied to noise signals from vibrators. Experimental results demonstrate that the improved method not only resolves EWT frequency band division challenges but also effectively decomposes signal components compared to the VMD method.

Implementation of VLSI on Signal Processing-Based Digital Architecture Using AES Algorithm

Continuous improvements in very-large-scale integration(VLSI)technology and design software have significantly broadened the scope of digital signal processing(DSP)applications.The use of application-specific integrated circuits(ASICs)and programmable digital signal processors for many DSP applications have changed,even though new system implementations based on reconfigurable computing are becoming more complex.Adaptable platforms that combine hardware and software programmability efficiency are rapidly maturing with discrete wavelet transformation(DWT)and sophisticated computerized design techniques,which are much needed in today’s modern world.New research and commercial efforts to sustain power optimization,cost savings,and improved runtime effectiveness have been initiated as initial reconfigurable technologies have emerged.Hence,in this paper,it is proposed that theDWTmethod can be implemented on a fieldprogrammable gate array in a digital architecture(FPGA-DA).We examined the effects of quantization on DWTperformance in classification problems to demonstrate its reliability concerning fixed-point math implementations.The Advanced Encryption Standard(AES)algorithm for DWT learning used in this architecture is less responsive to resampling errors than the previously proposed solution in the literature using the artificial neural networks(ANN)method.By reducing hardware area by 57%,the proposed system has a higher throughput rate of 88.72%,reliability analysis of 95.5%compared to the other standard methods.

Empirical Wavelet Transform;Stationary and Nonstationary Signals

Signal decomposition into the frequency components is one of the oldest challenges in the digital signal processing.In early nineteenth century,Fourier transform(FT)showed that any applicable signal can be decomposed by unlimited sinusoids.However,the relationship between time and frequency is lost under using FT.According to many researches for appropriate time-frequency representation,in early twentieth century,wavelet transform(WT)was proposed.WT is a well-known method which developed in order to decompose a signal into frequency components.In contrast with original WT which is not adaptive according to the input signal,empirical wavelet transform(EWT)was proposed.In this paper,the performance of discrete WT(DWT)and EWT in terms of signal decomposing into basic components are compared.For this purpose,a stationary signal including five sinusoids and ECG as biomedical and nonstationary signal are used.Due to being non-adaptive,DWT may remove signal components but EWT because of being adaptive is appropriate.EWT can also extract the baseline of ECG signal easier than DWT.

Wavelet analysis and its application to signal processing

The construction of basic wavelet was discussed and many basic analyzing wavelets was compared. Acomplex analyzing wavelet which is continuous, smoothing, orthogonal and exponential decreasing was presented, andit was used to decompose two blasting seismic signals with the continuous wavelet transforms (CWT). The resultshows that wavelet analysis is the better method to help us determine the essential factors which create damage effectsthan Fourier analysis.

Investigation on the automatic parameters extraction of pulse signals based on wavelet transform

This paper analyses a key problem in the quantification of pulse diagnosis. Due to the subjectivity and fuzziness of pulse diagnosis,quantitative methods are needed. To extract the parameters of pulse signals,the prerequisite is to detect the corners of pulse signals correctly. Up to now,the pulse parameters are mostly acquired by marking the pulse corners manually,which is an obstacle to modernize pulse diagnosis. Therefore,a new automatic parameters extraction approach for pulse signals using wavelet transform is presented. The results testified that the method we proposed is feasible and effective and can detect corners of pulse signals accurately,which can be expected to facilitate the modernization of pulse diagnosis.

Kravchenko atomic transforms in digital signal processing

The modified atomic transformations are constructed and proved. On their basis the new complex analytic wavelets are obtained. The proof of the Fourier transforms existence in L~ and L2 on the basis of the theory of atomic functions （AF） are presented. The numerical experiments of digital time series processing and physical analysis of the results confirm the efficiency of the proposed transforms.

Singularity detection of the thin bed seismic signals with wavelet transform

The location of singularities may be detected by local maxima of the wavelet transform modulus. The digital modeling and focusing process to wavelet transform of the reflecting seismic signals have been done. It has been found that the locations of singularities after wavelet transform are only affected by two factors, their original locations and the seismic wavelet length, which says it does not matter with what shape the wavelet will be. The wavelet length can be determined according to the wavelet transform results and be eliminated thereafter so that we are able to detect thin bed seismic signal with resolution of l/32 wavelength. The singularities have been recovered with improved resolution of the seismic section by real data processing.

RESEARCH OF WAVELET TRANSFORM INSTRUMENT SYSTEM FOR SIGNAL ANALYSIS

After brief describing the Principle of wavelet transform (WT) of signals, a new signals analysis system based on wavelet transform is introduced. The design and development of the instryment of wavelet transform are described. A number of practical uses of this system demonstrate that wavelet transform system is specially functional in identifying and processing impulse, singular and non-smooth signals, so that it should be evaluated the most advanced signal analyzing system.

Analysis of penetration acceleration signal based on wavelet transformation

In order to analyze the composition and frequency distribution of acceleration signal in the process of projectile penetrating,this paper uses wavelet transform to decompose penetration acceleration signal to get the distribution of penetration acceleration signal in different frequency bands.Compared with the ideal acceleration signal curve and its characteristics,it can be concluded that the frequency range of the acceleration signal in the axis of the projectile and the vibration frequency range of the projectile are 31.25-62.5kHz and 62.5-125 kHz,respectively.Finally,the penetration acceleration signal curve is obtained by Simulink.

Application of Mellin Transform in Wideband Underwater Acoustic Signal Processing

According to the features of the wideband underwater acoustic signals,an algorithm for the wideband ambiguity function is put forward based on Mellin transform.The wideband acoustic signal processing using the fast Mellin transform is also explored.The theoretical analysis and simulation results show that the algorithm has not only high computation efficiency but also good concentration in wideband ambiguity domain.It suits for the wideband underwater acoustic signal processing.

Study on Singularity of Chaotic Signal Based on Wavelet Transform

Based on the variations of wavelet transform modulus maxima at multi-scales, the singularity of chaotic signals are studied, and the singularity of these signals are measured by the Lipschitz exponent.In the meantime, a nonlinear method is proposed based on the higher order statistics, on the other aspect, which characterizes the higher order singular spectrum (HOSS) of chaotic signals. All computations are done with Lorenz attractor, Rossler attractor and EEG(electroencephalogram) time series and the comparisions among these results are made. The experimental results show that the Lipschitz exponents and the higher order singular spectra of these signals are significantly different from each other, which indicates these methods are effective for studing the singularity of chaotic signals.

AN ALGORITHM FOR CODING VIDEO SIGNAL BASED ON 3-D WAVELET TRANSFORMATION

This paper presents an algorithm for coding video signal based on 3-D wavelet transformation. When the frame order t of a video signal is replaced by order 2, the video signal can be looked as a block in 3-D space. After splitting the block into smaller sub-blocks, imitate the method of 2-D wavelet transformation for images, we can transform the sub-blocks with 3-D wavelet. Most of video signal energy is in the decomposed low-frequency sub-bands. These sub-bands affect the visual quality of the video signal most. Quantizing different sub-bands with different precision and then entropy encoding each sub-band, we can eliminate inter- and intra-frame redundancy of the video signal and compress data. Our simulation experiments show that this algorithm can achieve very good result.

Biomedical Image Processing Using FCM Algorithm Based on the Wavelet Transform

An effective processing method for biomedical images and the Fuzzy C-mean (FCM) algorithm based on the wavelet transform are investigated.By using hierarchical wavelet decomposition, an original image could be decomposed into one lower image and several detail images. The segmentation started at the lowest resolution with the FCM clustering algorithm and the texture feature extracted from various sub-bands. With the improvement of the FCM algorithm, FCM alternation frequency was decreased and the accuracy of segmentation was advanced.

Extraction of Partial Discharge Acoustic Signal by Wavelet Transform with Teager′s Energy Operator

To develop a measurement system for monitoring partial discharge （PD） without the effect of external interferences,an algorithm of PD signal extraction based on wavelet transform with Teager＇s energy operators was presented. Acoustic signal generated by PD was selected to remove excessive interfering signals and electromagnetic interferences. Acoustic signals were collected and decomposed into I0 levels by wavelet transform into approximation and detail components. “Daubechies 25” was proved to be the most suitable mother wavelet for the extraction of PD acoustic signals. Compared with conventional wavelet denoising method, Teager＇s energy operators were adopted to the PD signal reconstruction and the signal to noise ratio was in creased by 20%-25% inthe experiment,without lost in energy and pulse amplitude.

DETECTION OF TRANSIENT SIGNAL USING THE DISCRETE WAVELET TRANSFORM

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The Signal Extraction of Fetal Heart Rate Based on Wavelet Transform and BP Neural Network

This paper briefly introduces the collection and recognition of bio-medical sig nals, designs the method to collect FM signals. A detailed discussion on the sys tem hardware, structure and functions is also given. Under LabWindows/CVI,the ha rdware and the driver do compatible, the hardware equipment work properly active ly. The paper adopts multi threading technology for real-time analysis and make s use of latency time of CPU effectively, expedites program reflect speed, impro ve s the program to perform efficiency. One threading is collecting data; the other threading is analyzing data. Using the method, it is broaden to analyze the sig nal in real-time. Wavelet transform to remove the main interference in the FM a nd by adding time-window to recognize with BP network; Finally the results of c ollecting signals and BP networks are discussed.8 pregnant women’s signals of F M were collected successfully by using the sensor. The correct of BP network rec ognition is about 83.3% by using the above measure.

Realization of Wavelet Transform Using SAW Devices

Based on the characteristics of surface acoustic wave(SAW) devices, the theory for realizing wavelet transform (WT) by SAW is deduced. Simulated experiment shows that the method of implementing WT using SAW devices has virtues of high speed and utility and is compatible with digital technique. It is important to implement wavelet transform.

A secure image steganography algorithm based on least significant bit and integer wavelet transform

The rapid development of data communication in modern era demands secure exchange of information. Steganography is an established method for hiding secret data from an unauthorized access into a cover object in such a way that it is invisible to human eyes. The cover object can be image, text, audio,or video. This paper proposes a secure steganography algorithm that hides a bitstream of the secret text into the least significant bits（LSBs） of the approximation coefficients of the integer wavelet transform（IWT） of grayscale images as well as each component of color images to form stego-images. The embedding and extracting phases of the proposed steganography algorithms are performed using the MATLAB software. Invisibility, payload capacity, and security in terms of peak signal to noise ratio（PSNR） and robustness are the key challenges to steganography. The statistical distortion between the cover images and the stego-images is measured by using the mean square error（MSE） and the PSNR, while the degree of closeness between them is evaluated using the normalized cross correlation（NCC）. The experimental results show that, the proposed algorithms can hide the secret text with a large payload capacity with a high level of security and a higher invisibility. Furthermore, the proposed technique is computationally efficient and better results for both PSNR and NCC are achieved compared with the previous algorithms.