2M-Band Interleaved DFT Modulated Filter Banks with Perfect Reconstruction

In this paper, we propose a new family of perfect reconstruction (PR) complex filter banks, named interleaved discrete Fourier transform modulated filter banks (Interleaved DFT-FBs). In the filter banks, the analysis filters are generated by interlaced exponential modulating two different analysis prototype filters, and the synthesis filters are generated by two different synthesis prototype filters via the same manner. The filter banks have a simple polyphase structure similar to DFT modulated filter banks (DFT-FBs). More importantly, the proposed Interleaved DFT-FBs can achieve critically sampled PR complex filter bank with FIR analysis and synthesis filters, which is impossible for DFTFBs. We give and prove the PR condition for 2M -band Interleaved DFT-FBs. Utilizing the result, the design procedure of the prototype filters is presented. In addition, by the theoretic analysis and numerical examples, it is shown that the analysis and synthesis filters cannot simultaneously provide good stopband attenuation for the critically sampled PR Interleaved DFT-FBs. Although the limitation always exits, the filter banks can find applications in some subband coding systems of high bit rate.