Structure Of 1-Dimensional DFT Modulated Filter Banks And Design Algorithms

The theory and design of multirate filter banks have attracted more and more attentions in recent years, owing to their wide applications in communication, subband coding of speech and images, adaptive filter, radar and many other fields. This paper mainly studies oversampled filter banks in the 1-dimensional DFT modulated filter banks. As compared with critically sampled filter banks, oversampled filter banks are more flexible in design. This paper mainly consists of two parts.The first part deals with a simpler method for the design of oversampled nearly perfect reconstruction (NPR) DFT modulated filter banks with different analysis and synthesis prototype filters. In terms of the requirements on the aliasing in the subband, residual aliasing, stopband attenuation and output transfer function distortion, the design method involves the minimization of the output transfer function distortion while constraining the stopband energy of the analysis and synthesis prototype filters. The simpler constraint about passband flatness is introduced at the same time. The proposed method can generate filters with significantly better performance than filters obtained using current design methods, which is also verified by the numerical examples.The other part presents a novel structure of complex modulated filter banks, namely, interleaved discrete Fourier transform (DFT) modulated filter banks. In the filter banks, the analysis filters are generated by interleaved exponential modulating two different low-pass analysis prototype filters and the synthesis filters are generated by two different synthesis prototype filters via the same manner. This novel structure inherits the advantages of the DFT modulated filter banks, such as efficiency in computation, great ease in design, and partition of positive and negative frequency components for signals. Based on the structure, a design method for the four prototype filters of an oversampled nearly perfect reconstruction (NPR) modulated filter banks is proposed. The optimization of the prototype filters can be transformed into a simple nonlinear optimization problem. Because of using of the multi-prototype filters, more degrees of freedom make it possible to obtain the significantly better performance of complex modulated filter banks, which also is proved by the numerical examples.