Research On Reconstruction Algorithm Of Non-uniform Filter Banks

The theory of multirate signal processing is often used in radar,voice,image and other signal processing fields.The use of this technology effectively reduces the rate of data processing,data storage space and data processing complexity etc.The core of multirate signal processing theory is the filter banks theory.In a filter bank system,the input signal is decomposed into a plurality of sub-band signals by multiple filters which have different characteristics at the front end of the system.After extraction and deceleration,the different sub-band signals are processed according to the actual needs.Then,the sub-band signal are reconstructed into the original signal as much as possible by interpolation and the corresponding synthesis filter bank at the back end of the system.So the reconstruction performance of the entire filter bank is the key point of the filter bank theory.Filter banks can be divided into two groups: uniform filter bank(UFB)which uniformly divide input signal and non-uniform filter bank(NUFB)which divide the input signal into sub signal with different bandwidth according to the actual needs.So the non-uniform filter bank has better flexibility.In recent years,the design of non-uniform filter bank has attracted the attention of many scholars.So far,the complete reconstruction of non-uniform filter bank is still a difficult problem.The realization of fully reconstruction needs very complex design method,which hardly to be achieved.Thus,the method of approximate reconstruction which is flexible and simple is used to design NUFB in the practical application.There are three kinds of distortion in approximate reconstruction project,including amplitude,phase and aliasing distortion.The appropriate analysis and synthesis filter bank can avoid aliasing distortion,and the linear phase filter can avoid phase distortion.At the same time,the amplitude distortion can be reduced to the minimum value with the optimization algorithm.At present,It is difficult to design non-uniform filter bank with perfect reconstruction,because of the amplitude,phase and aliasing errors.In this paper,the elimination of these errors is studied in order to further improve the reconstruction performance of the non-uniform filtering system.Firstly,the first design idea of non-uniform filter bank is introduced,which is direct design method.The reconstruction conditions of non-uniform filter bank are derived directly from the frequency domain,and they are expressed as the form of matrix equations.In the actual design process,the filter coefficients in the analysis filter bankare designed simultaneously according to the given frequency band characteristics.Then,the coefficients of the corresponding synthesis filter bank can be obtained by seeking the optimal solution of the reconstruction matrix equation with the iterative optimization idea.This method can design different types of filter bank,which has great flexibility.Subsequently,the design idea of non-uniform filter bank with tree structure is detailedly analyzed and simulated.The design of non-uniform filter bank with tree structure is based on the two channel filter bank.In this paper,the different two channel filter bank were analysed comparatively,and then the dual channel FIR standard quadrature mirror filter with linear phase characteristics was selected as the basic module,combining with the tree structure to design non-uniform filter bank.The reconstruction condition of the non-uniform filter bank constructed by tree structure is deduced to design a specific prototype filter.The entire non-uniform filter bank constructed by tree structure can be completely reconstructed with low complexity,as long as the designed prototype filter satisfies the derived reconstruction condition.The prototype filter is designed by iterative optimization in order to satisfy the derived reconstruction condition.In the specific design process,the prototype filter is designed by discrete weighted squared error criterion.Compared with other filter design methods,the prototype filter designed by this method has better passband flatness and stopband attenuation characteristics with the same design parameters.So that the filter can effectively suppress the out-band signals.Finally,the tree structure with discrete weighted squared error criterion is simulated.Compared with the existing algorithm,this design method which eliminates aliasing distortion and ensures the linear phase of each channel filter can effectively reduce the stopband attenuation of the filter and better reduce the amplitude distortion so that the reconstruction performance of non-uniform filter bank is further improved.