On the construction of a digital transfer function from its real part on unit circle

It is shown in this correspondence that the system function H(z) of a linear time invariant (LTI) causal digital filter with real impulse response coefficients can be obtained from the real part of its frequency response HR(ejω) given in the form of a rational trigonomentric function, using algebraic methods rather than complex contour integration techniques

Realization of perfect reconstruction non-uniform filter banks via a tree structure

Obviously, a tree structure filter bank can be realized via a non-uniform filter bank, and perfect reconstruction is achieved if and only if each branch of the tree structure can provide perfect reconstruction. In this paper, the converse of this problem is studied. We show that a perfect reconstruction non-uniform filter bank with decimation ratio {2,4,4} can be realized via a tree structure and each branch of the tree structure achieves perfect reconstruction

Generalized polyphase representation and application to coding gain enhancement

Generalized polyphase representations (GPP) have been mentioned in literature in the context of several applications. In this paper, we provide a characterization for what constitutes a valid GPP. Then, we study an application of GPP, namely in improving the coding gains of transform coding systems. We also prove several properties of the GPP

A complete factorization of paraunitary matrices with pairwise mirror-image symmetry in the frequency domain

The problem of designing orthonormal (paraunitary) filter banks has been addressed in the past. Several structures have been reported for implementing such systems. One of the structures reported imposes a pairwise mirror-image symmetry constraint on the frequency responses of the analysis (and synthesis) filters around π/2. This structure requires fewer multipliers, and the design time is correspondingly less than most other structures. The filters designed also have much better attenuation. In this correspondence, we characterize the polyphase matrix of the above filters in terms of a matrix equation. We then prove that the structure reported in a paper by Nguyen and Vaidyanathan, with minor modifications, is complete. This means that every polyphase matrix whose filters satisfy the mirror-image property can be factorized in terms of the proposed structure

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

Coding gain in paraunitary analysis/synthesis systems

A formal proof that bit allocation results hold for the entire class of paraunitary subband coders is presented. The problem of finding an optimal paraunitary subband coder, so as to maximize the coding gain of the system, is discussed. The bit allocation problem is analyzed for the case of the paraunitary tree-structured filter banks, such as those used for generating orthonormal wavelets. The even more general case of nonuniform filter banks is also considered. In all cases it is shown that under optimal bit allocation, the variances of the errors introduced by each of the quantizers have to be equal. Expressions for coding gains for these systems are derived

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

Composite Filler Characterization by Scanning Electron Microscopy, Image Analysis and Thermogravimetry

The morphological and compositional characterization of the filler particles in selected dental composites has been accomplished by a combination of backscattered electron imaging, digital imaging , energy dispersive X-ray analysis and thermogravimetry. Backscattered electron images provide excellent composition contrast between the filler and the matrix in this analysis . Qualitative energy dispersive spectroscopy was used to classify the filler composition in the composites studied. The digital imaging technique of feature analysis was utilized to quantitatively characterize the particle morphological parameters and their distributions. Several parameters were determined of which the particle area, breadth, height and Waddel diameter are emphasized. Particle size distribution histograms were also obtained. The filler contents in commercial composites were also determined by thermogravimetry. Thus a comprehensive method has been developed and applied to characterize filler morphology in particulate dental composites, which include both commercial and experimental systems. The commercial systems show variations in filler composition, filler size and distribution as well as filler loading levels. The experimental systems confirm variations in particle size and size distributions as a function of filler processing time

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