Design Of Near Perfect Reconstruction DFT Modulated Filter Banks

Modulated filter banks have gained more and more attention in recent years. As compared with cosine modulated filter banks, DFT modulated filter banks own an unique advantage that it can split positive and negative frequency components into different subbands for independent processing and thereby are suited to analyze and process complex-valued signals. DFT modulated filter banks are widely applied into many areas such as data compression, feature extraction, adaptive filtering, image processing, etc. This paper presents a new method for the design of modulated nearly perfect reconstruction DFT modulated filter banks with different analysis and synthesis prototype filters. This paper mainly consists of two parts:The first aspect is contributed to a novel design method for the prototype filters of a nearly perfect reconstruction (NPR) discrete Fourier transform (DFT) modulated filter bank. The objective is derived from the output distortion induced by the filter bank, the aliased components that appear in the output, and the stopband energy of the prototype filters. Compared with the current methods of DFT modulated filter bank, the design method proposed in this paper can generate filter banks with equivalent, even better performances, at the same time, owns a simple optimization formulation and considerable design flexibility (the stopband level of the filters, output aliasing of the filter bank and output distortion can be compromised by adjusting the weight coefficients in terms of different application requirement).The simulation results verify the effectiveness of the method.In the second aspect, we propose a formulation for the design of near perfect reconstruction (NPR) DFT modulated filter bank, which minimizing the output distortion, the output aliasing, and stopband energy for the filter bank. A new iterative algorithm is proposed to optimize simultaneously over both the analysis and the synthesis filter banks. This algorithm is shown to have an optimal solution for each iteration. The advantage of this problem formulation is that the output distortion, output aliasing, and stopband energy of the prototype filters can be flexible compromised depending on the particular practical application. For a fixed stopband level, the proposed algorithem yields a significant reduction in both output aliasing and output distortion of the prototype filters compared to existing methods applied to the numerical examples.