Very low sensitivity FIR filter implementation using 'structural passivity' concept

The concept of "structurally bounded" or "structurally passive" FIR filter implementation is introduced, as a means of achieving very low passband sensitivities. The resulting filter structures, called FIRBR structures, can easily be transformed into very low-sensitivity "passive" two-dimensional FIR filter structures. From a layout point of view, the new structures are not any more complicated than the well-known cascade form. The FIRBR structures do not depend, for synthesis, upon continuous-time filter circuits

Polyphase networks, block digital filtering, LPTV systems, and alias-free QMF banks: a unified approach based on pseudocirculants

The relationship between block digital filtering and quadrature mirror filter (QMF) banks is explored. Necessary and sufficient conditions for alias cancellation in QMF banks are expressed in terms of an associated matrix, derived from the polyphase components of the analysis and synthesis filters. These conditions, called the pseudocirculant conditions, make it possible to unite QMF banks with the framework of block digital filtering directly. Absence of amplitude distortion in an alias-free QMF bank translates into the 'losslessness' property of the pseudocirculant matrix involved

Low passband sensitivity digital filters: A generalized viewpoint and synthesis procedures

The concepts of losslessness and maximum available power are basic to the low-sensitivity properties of doubly terminated lossless networks of the continuous-time domain. Based on similar concepts, we develop a new theory for low-sensitivity discrete-time filter structures. The mathematical setup for the development is the bounded-real property of transfer functions and matrices. Starting from this property, we derive procedures for the synthesis of any stable digital filter transfer function by means of a low-sensitivity structure. Most of the structures generated by this approach are interconnections of a basic building block called digital "two-pair," and each two-pair is characterized by a lossless bounded-real (LBR) transfer matrix. The theory and synthesis procedures also cover special cases such as wave digital filters, which are derived from continuous-time networks, and digital lattice structures, which are closely related to unit elements of distributed network theory

A new approach to the realization of low-sensitivity IIR digital filters

A new implementation of an IIR digital filter transfer function is presented that is structurally passive and, hence, has extremely low pass-band sensitivity. The structure is based on a simple parallel interconnection of two all-pass sections, with each section implemented in a structurally lossless manner. The structure shares a number of properties in common with wave lattice digital filters. Computer simulation results verifying the low-sensitivity feature are included, along with results on roundoff noise/dynamic range interaction. A large number of alternatives is available for the implementation of the all-pass sections, giving rise to the well-known wave lattice digital filters as a specific instance of the implementation

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

Passivity properties of low-sensitivity digital filter structures

A general representation of a class of low passband sensitivity digital filter structures is proposed. The proposed representation for a transfer function of orderNconsists of an(N + 1)-pair memoryless system terminated atN-pairs by delays. The(N + 1)-pair system contains only adders and multipliers, and is described by an orthogonal transfer matrix. The set of terminating delays can be looked upon as anN-pair system with transfer matrixz^{-1}{bf 1}. Certain wave digital filter structures, Gray-Markel lattice structures and the coupled-form biquadratic section belong to the general form advanced here. Several properties satisfied in these special cases are derived in a unified manner using the generalized representation. Also, a quantization scheme that makes the structure free from zero-input limit cycles even under time-varying conditions is advanced, unifying similar such results independently reported for the above well-known structures

A unified structural interpretation of some well-known stability-test procedures for linear systems

A number of well-known stability-test procedures for continuous-and discrete-time systems are re-examined in a unified manner, leading to well-defined network-theoretic interpretations. The representation and network interpretation are based on the fact that the stability of any linear system (scalar or multivariable) is equivalent to the stability of a related all-pass system, which in turn can always be synthesized as a cascade of (scalar or matrix) two-pair all-pass (lossless) networks. The original system of interest is stable if and only if each all-pass two-pair is stable (and hence "lossless bounded real"). As a result of this interpretation, a number of related issues, such as enumeration of unstable poles, prematured terminations, and singularity situations can all be approached in a unified manner, based only on "two-pair extraction formulas." In addition, the network interpretation also leads to direct test procedures for testing relative stability, and the stability of multi-input, multi-output systems