Design Of Frequency Response Masking Filter Based On Analytical Coefficient Configuration Of All-phase Filters

The frequency response masking technique has been widely used in a lot of fields such as multi-carrier communication,software radio and so on,since it can obtain a sharp transition band only consuming a few resources.Once the structure of FRM is selected,the subfilter's coefficients configuration will become the key problem.Therefore,it is an urgent task to develop an efficient coefficient configurating method that can ensure an excellent transfer characteristic of the FRM filter.This paper will introduce the all-phase filter design method to implement the FRM configuration.The main work focues on enhancing both filter's transfer characteristics and design efficiency.The analytic coefficients' formula of the all-phase filter provides a straightforward and effective way of fast FRM configuration.Based on the absorption of the existing literatures,this paper proposes two new theoretical properties of the all-phase filter.First,the frequency response of any frequency point can be approximated by interpolating the four adjacent frequency sampling points centered around it with the Fourier spectrum of the convolution window.Second,as long as the frequency vector possesses a symmetry,the transfer curve nearby the transition band of all-phase filter also exhibit an approximate symmetry centered with the 6-dB point at the transition band.Based on the above two properties,in combination with the single-convolution-window mode and a frequency vector in which only a single transition point variable parameter is involved,this paper deduces the corresponding improved filter coefficient analytic formula.In order to quickly find the appropriate transition point,2 optimization methods were proposed: the trasnsition point optimization method based on differential evolution algorithm and the analytical method based on Lichtenberg ratio.In addition,in order to realize the arbitrary control of the cutoff frequency point,this paper also proposes an amplitude-frequency compensation method based on genetic algorithm.Through the simulations,it can be find that the Lichtenberg ratio method possesses a higher efficiency,in that only 3 simple steps lead to the FRM filter's coefficients.As a result,the computation complexity is largely reduced.Finally,in order to apply the above all-phase design methods to the classical FRM filtering,this paper also deduces the matching relationship between prototype filters and masking filters.Thus,a high-performance all-phase FIR design of wide suitabiblity is derived.Numerical results show that,the proposed design can efficiently realize an FRM filter with sharp transition band and excellent transfer performance.