Critically sampled and oversampled complex filter banks via interleaved DFT modulation

This paper presents a new class of complex modulated filter banks, namely, interleaved discrete Fourier transform (DFT) modulated filter banks, where analysis filter bank comprises interleaved exponentially modulated versions of two lowpass analysis prototype filters and synthesis filter bank is generated from two lowpass synthesis prototype filters in the same manner. As compared with DFT modulated filter banks, interleaved DFT modulated filter banks are more flexible in structure and provide more degrees of freedom for design. It is shown that 2M-channel critically sampled interleaved DFT modulated filter banks can be perfect reconstruction (PR) and FIR. However, critical sampling limits stopband attenuation of the filter banks. Further, we investigate the structure of oversampled interleaved DFT modulated filter banks and a bi-iterative quadratic programming algorithm is developed for designing oversampled nearly perfect reconstruction (NPR) interleaved DFT modulated filter banks. Owing to more degrees of freedom for design, oversampled interleaved DFT modulated filter banks achieve better total performance than oversampled DFT modulated filter banks do.