Research On The Design Of ?R Digital Filter Based On Least Squares Method

Our life has already entered the digital age.Digital filtering technology has become an indispensable subject and an irreplaceable technology.It has been applied in many fields,such as voice and image processing,communication and so on.Compared with continuous-time systems,discrete-time systems have many advantages,such as low sensitivity,high accuracy and large-scale integration.Because of these advantages,discrete time systems have advantages not only in volume but also in weight.With the passage of time,the research on digital filters has become more and more intensive,and the traditional analog filters have been gradually diluted in practical applications.Therefore,how to design a filter with high-performance has become a focus of research.In the image with continuous gray value changes,if there is a point and the gray values of adjacent pixels are very different,the human eye can easily perceive the existence of this point,which is considered to be a kind of noise.Gray level mutation represents high-frequency components in the frequency domain,while low-pass filter is to filter high-frequency components and reduce image noise.Similarly,the high-pass filter is to reduce the gray level changes in the smoothing area and highlight the details of the edge gray level.Image filtering is an indispensable processing technology in image processing.The image has strict linear phase requirements on the filter,and the performance of the filter directly determines the validity and reliability of subsequent image processing and analysis.FIR and ?R digital filters play an important role in the field of signal processing.Because of no closed form to design formula,it is hard for FIR digital filter to control the accuracy of the pass-band,stop-band and marginal frequency and it requires repeated calculation in design processing.Besides,if FIR filter has the same filter characteristics as ?R digital,it needs high order and increase the time delay when signals pass the system because of no controllable pole.?R digital filter uses rationalfraction of the ratio of two polynomials to approximate the frequency characteristic and it needs less order to get desirable properties.In addition,?R digital filter has linear phase.Therefore,the design of ?R digital filter with linear phase is significant for image filtering.The main contributions of this paper are as follows:(1)Aiming at the non-linear optimization problem caused by denominator of ?R filter transformation function,a new approximation method is proposed,which can be transformed into a linear optimization problem and greatly reduces the difficulty of optimization.(2)Based on the above ideas,a new design method of ?R digital filter based on least squares is designed.The filter designed by this method not only meets the given amplitude-frequency response,but also guarantees the linear phase.(3)A practical image filter is designed by using the method proposed in this paper,it is concluded that the ?R digital filter designed by this method has better filtering effect than the typical design method by calculating and analyzing the objective evaluation index of the filtered image.