Complex-valued Filter Banks Research Articles

Biorthogonal exponentially modulated filter bank

This paper explores modulated filter banks (MFBs) utilizing polyphase domain analysis. The MFB theory offers a variety of configuration alternatives and to narrow down the diversity our emphasis is on critically sampled perfect reconstruction systems in odd-stacked configuration. Into this MFB subclass, we introduce biorthogonal exponentially modulated filter bank (EMFB). The biorthogonal EMFB is suitable for subband processing of complex-valued signals and the analysis–synthesis reconstruction delay is an adjustable parameter. The EMFB is represented with its polyphase components and we develop a unified framework for analyzing different classes of complex-valued filter banks, covering perfect reconstruction conditions and metrics for residual distortion effects. In addition, it is shown how the EMFB can be converted into even-stacked configuration through frequency shifting. This provides a link with the modified discrete Fourier transform filter bank, but even-stacked EMFB solves the subsignal handling in a simplified manner.

Phase Watermarking of Images with Complex-Valued Linear-Phase Subband Filter Banks

A new algorithm is proposed for digital watermarking by applying complex-valued linear-phase filter banks to low frequency-band coefficients of images in the DCT domain. The watermark is conveyed in the phase spectrum of the subband coefficients. The robustness of the algorithm is examined in JPEG encoding with different qualities and compared with the DFT-based approach. Because only low frequency-band DCT coefficients are applied to complex-valued filter banks, the computational load introduced by the complex-valued filter banks is kept low. The watermark decoding is only accessible to users with the key information, i.e., impulse responses of the complex-valued linear-phase filter banks that designed with time-frequency spread property.

Symmetric Orthogonal Complex-Valued Filter Bank Design by Semidefinite Programming

A new design method for complex-valued two-channel finite impulse response (FIR) filter banks with both orthogonality and symmetry properties is developed. Based on a novel linear matrix inequality (LMI) characterization of trigonometric curves, the optimal design of perfect-reconstruction filter banks is cast into a semidefinite programming (SDP) problem. The dimension of the resulting SDP problem is further reduced by exploiting convex duality. Consequently, the globally optimal solution can be found for any practical filter length and desired regularity order.

A study of two-channel complex-valued filterbanks and wavelets with orthogonality and symmetry properties

We investigate two-channel complex-valued filterbanks and wavelets that simultaneously have orthogonality and symmetry properties. First, the conditions for the filterbank to be orthogonal, symmetric, and regular (for generating smooth wavelets) are presented. Then, a complete and minimal lattice structure is developed, which enables a general design approach for filterbanks and wavelets with arbitrary length and arbitrary order of regularity. Finally, two integer implementation methods that preserve the perfect reconstruction property of the filterbank are proposed. Their performances are evaluated via experimental results.

Design of near perfect reconstruction oversampled filter banks for subband adaptive filters

In this brief, a design algorithm for real-valued and complex-valued oversampled filter banks which yield a low level of inband alias and enable simple subband adaptive structures is presented. The filter banks are either based on complex modulation of a real-valued low-pass prototype or on the direct or modulated setups of real-valued filter banks. If real-valued filter banks are required, then the different channels will have different subsampling ratios so that the bandpass sampling theorem is not violated. This brief also presents design examples of real-valued and complex-valued filter banks.