Design Of Fractional Calculus Digital Filter And Its Application On Image Processing

Fractional order calculus as a linear problem of the tool, has shown great superiority and cut a striking figure in many direction of practice. But at the same time the engineering’s study time is not long, the application is still in the stage of development, far from mature, there are still many problems to be solved, so this paper and Realization of fractional calculus theory to make a preliminary attempt and exploration.At present a lot of signals given in the form of fractional calculus results are not with the explicit expression, but with the popularity of digital computer using, many computational problems can be transformed into discrete form. For fractional calculus of discrete signal processing operations, is equivalent to convolution the filtering operation on the discrete signal, so the design of fractional order calculus digital filter has important significance. At the same time, the application of fractional order digital filter in image processing also has far-reaching significance. The main work is as follows:The first chapter is the introduction, briefly described the development of fractional calculus, the significance of the research of fractional order digital filter and its significance in image processing.The second chapter discusses the basic theory and mathematical background of fractional calculus, which lays a theoretical foundation for the following chapters.The third chapter mainly based on fractional order calculus theory introduces the traditional digital filter’s advantages and disadvantages, and realizes the design and simulation of fractional calculus digital filter.The fourth and the fifth chapter introduces some applications of fractional order digital filter in image processing by MATLAB software, such as copper flat wire image processing and digital watermarking technology’s application.Finally, it summarizes the full text, and researches some problems encountered during the analysis.Fractional calculus as a new research direction, this paper only makes some elementary research on the application of fractional calculus, although there has been some progress, the fractional calculus has a broad application prospect for other scholars to study.