Design of doubly-complementary IIR digital filters using a single complex allpass filter, with multirate applications

It is shown that a large class of real-coefficient doubly-complementary IIR transfer function pairs can be implemented by means of a single complex allpass filter. For a real input sequence, the real part of the output sequence corresponds to the output of one of the transfer functions G(z) (for example, lowpass), whereas the imaginary part of the output sequence corresponds to its "complementary" filter H(z)(for example, highpass). The resulting implementation is structurally lossless, and hence the implementations of G(z) and H(z) have very low passband sensitivity. Numerical design examples are included, and a typical numerical example shows that the new implementation with 4 bits per multiplier is considerably better than a direct form implementation with 9 bits per multiplier. Multirate filter bank applications (quadrature mirror filtering) are outlined

Tree-structured complementary filter banks using all-pass sections

Tree-structured complementary filter banks are developed with transfer functions that are simultaneously all-pass complementary and power complementary. Using a formulation based on unitary transforms and all-pass functions, we obtain analysis and synthesis filter banks which are related through a transposition operation, such that the cascade of analysis and synthesis filter banks achieves an all-pass function. The simplest structure is obtained using a Hadamard transform, which is shown to correspond to a binary tree structure. Tree structures can be generated for a variety of other unitary transforms as well. In addition, given a tree-structured filter bank where the number of bands is a power of two, simple methods are developed to generate complementary filter banks with an arbitrary number of channels, which retain the transpose relationship between analysis and synthesis banks, and allow for any combination of bandwidths. The structural properties of the filter banks are illustrated with design examples, and multirate applications are outlined

Optimality and duality of the turbo decoder

Proceedings of the IEEE, 95(6): pp. 1362-1377.The near-optimal performance of the turbo decoder has been a source of intrigue among communications engineers and information theorists, given its ad hoc origins that were seemingly disconnected from optimization theory. Naturally one would inquire whether the favorable performance might be explained by characterizing the turbo decoder via some optimization criterion or performance index. Recently, two such characterizations have surfaced. One draws from statistical mechanics and aims to minimize the Bethe approximation to a free energy measure. The other characterization involves constrained likelihood estimation, a setting perhaps more familiar to communications engineers. The intent of this paper is to assemble a tutorial overview of these recent developments, and more importantly to identify the formal mathematical duality between the two viewpoints. The paper includes tutorial background material on the information geometry tools used in analyzing the turbo decoder, and the analysis accommodates both the parallel concatenation and serial concatenation schemes in a common framework

Computing frequency transformations for lattice digital all-pass filters

Une méthode numérique est décrite pour le calcul des transformations spectrales des filtres passe-tout en treillis. Elle peut être appliquée aux fonctions de transfert de deux circuits passe-tout en parallèle, pour réaliser un filtre accordé, par exemple. La méthode s'appuie sur la configuration Hessenburg orthogonal de la description de la variable d'état d'un filtre en treillis, et l'algorithme ainsi obtenu démontre une excellente stabilité numérique

A finite-interval constant modulus algorithm

A finite-interval constant modulus algorithm is developed which is vastly simpler than the Analytic Constant Modulus Algorithm and, unlike that algorithm, can claim to minimize a constant modulus criterion. It requires one QR decomposition of a data matrix, followed by a power iteration. Step size bounds which ensure monotonic convergence are obtained in analytic form, and proper tuning leads to an algorithm which converges typically within a few iterations. The algorithm thus gives a computationally feasible method for implementing constant modulus signal restoration in packet-based transmission systems. 1