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

On arbitrary-level IIR and FIR filters

A recently published method for designing IIR (infinite-impulse-response) digital filters with multilevel magnitude responses is reinterpreted from a different viewpoint. On the basis of this interpretation, techniques for extending these results to the case of finite-impulse-response (FIR) filters are developed. An advantage of the authors' method is that, when the arbitrary-level filter is implemented, its power-complementary filter, which may be required in specific applications, is obtained simultaneously. Also, by means of a tuning factor (a parameter of the scaling matrix), it is possible to generate a whole family of arbitrary-level filters

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

It is shown that a wide 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 of the complex allpass filter corresponds to one of the transfer functions G(z) (for example, low-pass), whereas the imaginary part of the output sequence corresponds to its "complementary" filter H(z) (for example, highpass). Since the resulting implementation is structurally lossless, G(z) and H(z) have very low passband-sensitivity. Numerical design examples are included to demonstrate the ideas

Some properties of IIR power-symmetric filters

Power-symmetric IIR filters have in the past been used in two-channel filter banks. If appropriately designed, such filters have allpass polyphase components, and this induces useful properties in the filter bank. For example, IIR orthonormal filter banks have in the past been designed in this way, and generate orthonormal basis functions. In this paper we study some theoretical properties of IIR power symmetric filters in a more general perspective. This includes the derivation of a general analytical form, and a study of pole locations

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

Reduced order strip Kalman filtering using singular perturbation method

Includes bibliographical references.Strip Kalman filtering for restoration of images degraded by linear shift invariant (LSI) blur and additive white Gaussian (WG) noise is considered. The image process is modeled by a 1-D vector autoregressive (AR) model in each strip. It is shown that the composite dynamic model that is obtained by combining the image model and the blur model takes the form of a singularly perturbed system owing to the strong-weak correlation effects within a window. The time scale property of the singularly perturbed system is then utilized to decompose the original system into reduced order subsystems which closely capture the behavior of the full order system. For these subsystems the relevant Kalman filtering equations are given which provide the suboptimal filtered estimates of the image and the one-step prediction estimates of the blur needed for the next stage. Simulation results are also provided

Lattice structures for optimal design and robust implementation of two-channel perfect-reconstruction QMF banks

A lattice structure and an algorithm are presented for the design of two-channel QMF (quadrature mirror filter) banks, satisfying a sufficient condition for perfect reconstruction. The structure inherently has the perfect-reconstruction property, while the algorithm ensures a good stopband attenuation for each of the analysis filters. Implementations of such lattice structures are robust in the sense that the perfect-reconstruction property is preserved in spite of coefficient quantization. The lattice structure has the hierarchical property that a higher order perfect-reconstruction QMF bank can be obtained from a lower order perfect-reconstruction QMF bank, simply by adding more lattice sections. Several numerical examples are provided in the form of design tables

Minimal structures for the implementation of digital rational lossless systems

Digital lossless transfer matrices and vectors (power-complementary vectors) are discussed for applications in digital filter bank systems, both single rate and multirate. Two structures for the implementation of rational lossless systems are presented. The first structure represents a characterization of single-input, multioutput lossless systems in terms of complex planar rotations, whereas the second structure offers a representation of M-input, M-output lossless systems in terms of unit-norm vectors. This property makes the second structure desirable in applications that involve optimization of the parameters. Modifications of the second structure for implementing single-input, multioutput, and lossless bounded real (LBR) systems are also included. The main importance of the structures is that they are completely general, i.e. they span the entire set of M×1 and M×M lossless systems. This is demonstrated by showing that any such system can be synthesized using these structures. The structures are also minimal in the sense that they use the smallest number of scalar delays and parameters to implement a lossless system of given degree and dimensions. A design example to demonstrate the main results is included

Residual echo signal in critically sampled subband acoustic echo cancellers based on IIR and FIR filter banks

Published versio

DESIGN OF COMPLEMENTARY RECURSIVE DIGITAL FILTERS BASED ON GROUP DELAY APPROXIMATION

This paper describes a new procedure for design of complementary IIR digital filters based on group delay approximation. The filters are realized as parallel sum of two all-pass filters, a structure for which low complexity implementations exist. Problem with phase warping which is inevitable if filter design is made through phase approximation will be removed using proposed method. Adequate initial solution is also proposed. Realized amplitude characteristics of complementary filters will be approximately equriripple. The design examples illustrate that the proposed algorithm is very efficient in term of computation time and number of iterations