Filter Design of Wavelet Transform for 2-D Image

The filter design is the key to 2-D image wavelet transform. Based on the studying of image properties and 1-D wavelet theory,the authors describe a parasymmetry boundary extension method and realize 2-D discrete wavelet transform by means of 1-D wavelet transform according to correlation of adjacent pixels. Also,it is proved that the discrete wavelet transform of inverse data stream in row and the sign of discrete detail signal will be inversed,and that a filter of wavelet transform based on symmetry of bi_orthogonal filter is constructed. The test has proved the fine reconstruction and perfect SNR.     

Two Channel Filter Banks and Wavelet Transform of Discrete Sequences

Multirate filter banks and wavelet transform are closely related theoretically and practically. This paper researches the wavelet transform of discrete-time sequences basing on dendriform filer banks in the signal processing field, analyses the theory and design method of two channel conjugate quadrature mirror filter banks and fast implement of discrete orthogonal wavelet transform and generation of orthogonal wavelets, and points out the internal relationship between them.     

Filtering Construct of Adaptive Filter Grou Pwith Multi-scale Decomposition

The principle and method of the adaptive filter and the filtering with wavelet transform were analyzed, and the model and method of adaptive filtering with wavelet transforms for the transient signal was established. The separated noise of signal by the multi-scale decomposition of wavelet transforms, was the input signal of adaptive filter, and accordingly the optimal filtering method of signal-noise decomposition was realized. By the adaptive filter grou Pbased on the wavelet transform, the optimal filtering to the multi-noise of signal is achieved at the same time, and the method presented in this paper has the excellent filtering capability. Examples of application demonstrate that this method presented is excellent to realize the optimal estimate to the valuable signal and noise of the transient signal in the same frequency segment.     

Computation of the Wavelet and Scaling Functions Using Coefficients of Wavelet Filter

To associate the discrete wavelet transform with the continuous wavelet transform, an iterative convolution algorithm is given by analyzing the and scaling function using coefficients of wavelet filter. usually used methods of the computation The way of judging the convergence of improved algorithm on of the wavelet function iterative convolution is given. The advantages of improved algorithm is analyzed. The experimental result shows that the modified algorithm is effective.     

EEG Signal Denoising Based on Wavelet Transform

The article focuses on the method of noise cancellation for EEG signal. The method of notch filter is discussed. According to the frequency of noise and the principle of notch filter, the design result of the notch filter and the denoised signal are presented. Then, the analysis of EEG signal are proposed based on wavelet transform (WT) and noise cancellation using WT. Wavelet transform is a multi-resolution time-frequency analysis method. It can decompose mixed signal into signals at different frequency bands. The EEG signal is analyzed and denoised using WT, then the results are presented respectively. Comparing the experiment results shows that WT can detect and process noise in the EEG signal effectively.     

Application of Wavelet Transform to De-noising Method

The wavelet transform is a new subject developed quickly in the past ten years. Compared with the Fourier transform, the wavelet transform is a part of time-frequency transform. The most important character is that it can be used to transform a signal into basic units at different scales and location, each unit represents a component of original signal difference from others. The wavelet transform has been proven to be a powerful and efficient tool for processing signal due to this character. This paper introduces the de-noising principles of the wavelet transform. It is proved to be an effective method by the simulating analysis.     

A Virtual Wavelet Transform Analyzer for the Signal Analysis Based on the Direct Algorithm

A virtual wavelet transform analyzer for the signal analysis based on the direct algorithm is introduced so that the discrete wavelet transform and continuous wavelet transform is maken to signal in the direct algorithm. The authors first introduce the direct algorithm of the WT, which is numerical algorithm obtained from the original formula of the wavelet transform by directly numericalizing. Then some conclusions are drawn on the direct algorithm. The examples are the sampling principle and technology for the wavelets, the limitation of the scale range of the wavelets and the measures to solve the edge phenomenal in the direct algorithm of the discrete wavelet transform, and some conclusions in the direct algorithm of the continuous wavelet transform. The virtual wavelet transform analyzer for the signal analysis based on the direct algorithm explored based on these studies and combined with virtual instrument technique can make the discrete wavelet transform and continuous wavelet transform to signal with any basic wavelet. It can be applied in studying the property of any basic wavelet and learning the theory on the wavelet transform, and also in making some engineering signal analysis. In the end, the authors give some typical examples for the application of the virtual analyzer. These examples show that the analyzer can be applied in many situations.     

Error measure of filter used in optical wavelet transform for image data compression

This paper analyzs the error measure of filter used in optical wavelet transform for image data compression, designs a measure system for filter's error and implements it by using matlab platform, meanwhile, it indicat and overcom the shortage of Photoshop in image statistical characteristic analysis. The batch operation and the precision of histogram information. Experiment results have proven its correctness.     

Binary phase only filter based watermarking combined with discrete wavelet transform

The binary phase only filter (BPOF) based digital image watermarking combined with a discrete wavelet transform (DWT) was proposed. Firstly, the DWT transform was applied to an image. Then, the discrete Fourier transform (DFT) was applied to the low frequency subband of the DWT transform. Next, the phase information of the DFT was binarized to obtain the BPOF, which would be taken as the watermark and embedded into the corresponding magnitude. Compared to applying the DFT transform to the whole image and embedding the BPOF watermark in the entire frequency range, or in the low frequency range, the watermark robustness in JPEG compression is improved significantly while maintaining the watermark imperceptibility and detection efficiency. This method may be used to demonstrate the authenticity and integrity of an image. The simulation experiments demonstrate the efficiency of this method.     

Audio blind watermarking scheme combined DWT DCT QR

In order to protect the copyright of digital audio and video in Internet, we propose a novel audio blind watermarking scheme combined discrete wavelets transform, discrete cosine transform, QR decomposition and audio characteristics. In this algorithm, the audio are split into blocks, and each block are decomposed on two dimensional discrete wavelet transform (DWT), then the approximate sub band coefficients are decomposed on discrete cosine transform (DCT), and the first quarter of the DCT coefficients are decomposed on QR decomposition and get a triangle matrix. At last, the watermarking information is embedded into the triangle matrix. The experiments show that the algorithm can get better balance between transparency and robustness of watermark, and it has strong robustness against the common audio signal processing such as additive white Gaussian noise, re sampling, re quantization, low pass filter, MP3 compression and cutting replacement.     

Wavelet-Based Multiresolution Analysis to Noise Elimination

The wavelet transform is a new subject developed quickly in the past ten years Compared with Fourier transform and Gabor transform, the wavelet transform is a part of time-frequency transform, so the message can be obtained from the signals effectively. By means of the fractionized multiresolution analysis to the signals, many problems unalbe to be solved by Fourier tranform have been solved in this way.Based on the fact that the maxima of the noise wavelet transform reduces dramatically with the increase of the scale, we obtain the result that this way is more advanced than the Fourier transform multiresolution analysis to the noise elimination.     

The Extended Kalman Filter Data Fusion Algorithm Based on Discrete Stationary Wavelet Transformation

It is difficult to establish precise mathematical model in extended Kalman filter data fusion algorithm for GPS/ DR integrated vehicle navigation system, an improved extended Kalman filter data fusion algorithm is put forward based on Discrete stationary wavelet transformation. The simulation results show that the algorithm is better than the extended Kalman filter data fusion algorithm, and is available for GPS/DR integrated vehicle navigation system.     

Speedy Recognition of Noise in Real Time Signal Based on Wavelet Transform

It's necessary to process position and gesture of rocket on real time within the flight of rocket. This work should base exact data. But much noise has been found in the data and the noise recognize is regarded as a focus. A speedy online arithmetic recognizing noise is proposed based on wavelet transform. The computing complexity measured by time of this arithmetic is a constant which is greatly reduces the works of calculation of wavelet transform. It can recognize the noise fast when the signal is gathered. The applications in these problems show that the effective arithmetic satisfies the needs of real time and can handle the real time data measured in other yields.     

Based on Wavelet Transform to Extract and Analyze Rabbit Somatosensory Evoked Potential

To extract rabbit somatosensory evoked potential(SEP),the authors locate waveform of rabbit SEP and analyze it.The rabbit was narcotized and stimulated by 0.5 Hz electric pulse.Potential of scalp was sampled at 3 764 Hz.Rabbit somatosensory evoked potential was extracted by one-dimension multi-resolution analysis,and continuous wavelet transform(CWT) was employed to locate and analyze the wave of SEP.The results show that Single-trail SEP can be extracted by Daubechies wavelet,when compared wavelet transform result of single-trail with result of averaged SEP.Wave component of SEP can be located precisely through the method of continuous wavelet transform.Frequency feature of SEP can also be analyzed by CWT.The technique of continuous wavelet transform,which can project a one-dimension signal into a two-dimension time-frequency space,will become a useful method to process medical electronic signal.     

Systems Analysis Based on Continuous Wavelet Transform

The linear time invariant vibration system is analyzed by Continuous Wavelet Transform(CWT),the relationship of wavelet transform of output signal with the pulse response of system and input signal is put forward.As an exapmle,the wavelet transform of the output signal of system with single degree of freedom is calculated and compared with the direct wavelet transform result of the actual output signal,it shows that the two results are in complete agreement.     

FTIR结合小波变换分析鉴别8种根茎类作物

为了区分鉴别8种根茎类作物,通过采用傅里叶变换红外光谱(FTIR)结合小波变换(WI)、主成分分析(PCA)和聚类分析(HCA)的方法,测试研究了8种根茎类作物40个样品的红外光谱。结果表明：8种样品红外图谱相似,但在1800~700 cm-1范围内,红外光谱的峰位、峰形及吸收强度差异明显。对此范围内的原始红外光谱进行连续小波和离散小波变换。提取连续小波变换的第15层系数和离散小波变换的第5尺度细节系数数据,进行主成分分析和聚类分析。连续小波和离散小波的前3个主成分的累计贡献率分别为93.12%、89.78%,主成分分析和聚类分析正确率为100%。最终结果显示：傅里叶变换红外光谱技术结合小波变换的方法可以区分鉴别不同种的根茎类作物。     

Multiresolution Wavelet Transform for Detection of EEG Abnormal Rhythms

The signal of brain activity is a non-stationary random signal including lots of physiology and disease information, which is of important action for doctors to judge pathological changes in brain. So the analysis and process of the EEG signals are always attended. In this paper, the authors take account of the time-frequency localization of wavelet transform and use multiresolution wavelet transform to detect EEG abnormal rhythms. The signals of different scales after EEG signals are transformed by multiresolution wavelet transform not only reflect the frequency information of the signals, namely the more great scale is the lower of the frequency of the signals,but also reflect the time information of the signals, namely EEG state at that time. The test results indicate that the abnormal rhythms of the EEG signals can be detected effectively if right wavelet basis is selected.     

A Research on the Characteristics of Mexican-hat Mother Wavelet Used in Optic Realization

The Mexican hat mother wavelet used in optic realization is analysed. Its characteristics on time frequency domain localization, accurate reconstruction condition, regularity order and orthonormality are discussed. The error concept for the Mexican hat wavelet that the non tensor product two dimensional form of mother wavelet is obtained from the turning of its one dimensional form is corrected. The reason is explained for that the Mexican hat mother wavelet can't be used in conventional discrete wavelet transform for image data compression,but when it is used in 2 D image wavelet transform realized by optic way, it features excellent energy localization.     

Application limitation of the Hilbert Huang transform to earthquake ground motion analysis

We presented herein detailed comparison between emulational and real earthquake signals. Intrinsic Mode Functions (IMF) were regarded as products of the empirical mode decomposition (EMD) during Hilbert Huang transform (HHT) processing. This could be ascribed primarily to the failure of separating the correct frequency from mixed and similar frequency components. It was difficult to remove IMF signal from the earthquake record and to obtain correct earthquake energy distribution in frequency. Furthermore, The Hilbert transform sometimes induced erroneous instantaneous frequencies. Thus, care must be taken in the application of HHT in earthquake engineering. The combination of the Hilbert transform with wavelet transform could produce better analysis of earthquake record.     

Suppression of Periodic Narrowband Interferences in Cable Partial Discharge Detections

There are background noises and interferences in the signal acquired,due to partial discharge(PD) detection system covers a broad frequency band.To suppress periodic narrowband signal which is a quite serious interference in PD measurement,the existing suppression method is introduced,the new method of wavelet packet transform is mainly studied to de-noise the periodic narrowband in XLPE cable PD detection system,which is based on the db4 basic wavelet using soft threshold.The results of the experiment show that wavelet packet transform is effective in restraining the periodic narrowband interferences to extract the PD pulses in XLPE cable PD monitoring system.