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Wavelet Analysis of electronic information science

Abstract: Wavelet analysis is the current rapid development of mathematics in a new area, is currently applied mathematics and engineering disciplines in a rapidly growing new field, it also has a deep and is widely used theoretical double meaning of the article describes the theory of wavelet analysis source, and introduced the wavelet analysis in the computer, electronics and information in the field of application, analysis, wavelet transform analysis of several forms of the advantages and disadvantages of these transformations forms, and these transformations form of voice and image processing in specific applications.

Keywords: electronic information, wavelet analysis, Fourier analysis, image processing

Foreword

Wavelet analysis theory are scientists, engineers, and mathematicians created, reflecting the large integrated interdisciplinary scientific era, the trend of penetration of wavelet theory from the Fourier analysis [1], thinking also comes from Fourier analysis, but it can not replace Fourier analysis, it is a new development of Fourier analysis, wavelet theory and Fourier analysis of the complementary strengths and complementary research and practice good results have been confirmed by wavelet analysis and wavelet analysis is the application of theory to study closely together now It has been in the field of information technology has made remarkable achievements the six high-tech electronic and information technology is an important area, it is an important aspect of image and signal processing today, and signal processing has become a work of contemporary science and technology an important part of the purpose of signal processing: an accurate analysis, diagnosis, and quantification of encoding, transmission or storage quickly and accurately reconstruct (or restore from the mathematical point of view of ground, signal and image processing can be integrated as signal processing (image can be seen as two-dimensional signal, wavelet analysis to many analysts in many applications, can be attributed to the signal processing problem now with the practice for its stable and unchanging nature of the signal processing is still the ideal tool is the Fourier analysis, but in practice the vast majority of non-stable signals, and especially for non-stable signal is wavelet analysis tools.

First, wavelet and time-frequency analysis, signal processing, signal processing, the main purpose is to extract the useful signal information, and remove useless information. The main purpose of signal analysis is to find a simple and effective method of signal transformation in order to highlight the signal The important features to simplify the complexity of computing for example, discrete-time Fourier transform sequence DFT FFT algorithm using a simplified example. Fourier transform is a function space characterization [2], solution of differential equations, numerical calculations the main methods and


effective mathematical tool. It can put a lot of common differential, integral, and the simplification of the convolution algebra, computer applications, DSP processing tools from the physical sense, understanding, a periodic vibration signal can be seen as a simple harmonic vibration frequency between overlay, because the Fourier transform is also a clear physical meaning, that is amplitude-frequency, phase-frequency characteristics is limited, so that Fourier transform can not be further in-depth analysis of the signal, in this regard, than the Fourier transform of the wavelet superior.

Gabor transform is a windowed Fourier transform, it is non-stationary signal analysis can play a good role, is an effective signal processing method, but the Gabor transform of time - frequency window is fixed, the window not adaptive, multi-scale signal analysis does not apply and the mutation process, and its discrete form useless orthogonal expansion, difficult to achieve efficient algorithm, which is a major flaw Gabor transform, and therefore also limits the engineering of the Gabor transform applications.

In the signal analysis and processing in order to improve the efficiency of the algorithm, the signal conversion processing points should belong to the orthogonal basis, Fourier transform with orthogonal space-based, but a clear physical meaning and is restricted, you can get the wavelet The room was of. Second, the wavelet analysis and image analysis of analog image signal during transmission vulnerable to a variety of noise interference, and interference by the analog image signal when it is difficult to completely recover. In addition, in the analog domain, the need for man and machine, machine-machine exchange of information and images such as compression, enhancement, restoration, feature extraction and identification of a series of processing and comparison is difficult. Therefore, from the completion of graphic communications and data communications network integration perspective, or from a variety of image signal processing point of view, the digital image signal is the most pressing issues. digitized image signal is the key to image coding. Coding is the analog signal into a digital signal technology, not only is the application of image coding techniques linear pulse code modulation techniques, and important is the use of the statistical properties of the image signal and visual physiology and psychology of the image characteristics of the image for source coding.

Wavelet image coding is a new image coding method, which is based on wavelet transform theory in recent years studies have shown that the wavelet transform as a widely applicable tool, also can be applied to the study of fractal geometry must be noted that a images after wavelet transform decomposition, there are two similarities for use. One is the sub-image itself, self-similarity, that is encoded as a sub-image when the image spatial domain can usually separate fractal image coding method for image compression, the other is in the same direction between the different resolutions of sub-images of each other like sex because of low-resolution wavelet decomposition range of sub-image high-resolution sub-image than double the range of small, so the


code more general method of fractal coding method greatly reduces the encoding time coding effect is concerned, this method is also more satisfactory. Links to free download http://www.hi138.com

Third, the wavelet analysis in the field of electronic information application of

wavelet analysis of a wide range of applications, including: the many disciplines of mathematics, signal analysis, image processing, quantum mechanics, theoretical physics, electronic warfare and weapons of military intelligence; computer classification and recognition, synthetic music and language, medical imaging and diagnostics, seismic data processing, large machinery fault diagnosis, etc., for example, in mathematics, numerical analysis it has been used to construct fast numerical methods, curve and surface structure, solving differential equations, control theory, etc. In signal analysis filtering to noise, compression, transmission, etc. In the image processing image compression, classification, identification and diagnosis, decontamination, etc. In the medical imaging to reduce B- CT, magnetic resonance imaging time and improve resolution, etc. are reproduced in the Fan China Network http://.

1. Wavelet analysis for signal and image compression wavelet analysis is an important aspect of the application which is characterized by high compression ratio, compression speed, compressed to maintain unchanged the characteristics of signals and images, and interference in the transmission can be based on Wavelet compression in many ways, the more successful have the best wavelet packet-based method, wavelet domain texture modeling approach, zero-tree wavelet compression, wavelet transform vector compression.

2. Wavelet applications in signal analysis is also very wide and it can be used for border processing and filtering, time-frequency analysis, signal to noise separation and extraction of weak signals, seeking fractal index, signal identification and diagnosis as well as multi-scale edge detection.

3. In engineering and other applications, including computer vision, computer graphics, surface design, turbulence, remote study of the universe and biological medicine. References

[1] Tande Kun, Sun Hui, Fu Xuefeng. Plane based on wavelet finite element method of problem solving, Hebei Engineering University (Natural Science Edition), 2008.

[2] Yang Shaohua. Based on wavelet transform and the PCA face recognition improvement methods, Jilin Engineering and Technical Teachers College, 2008. Links to free download http://www.hi138.com

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