All-pass Transfer Function Research Articles

Current-mode biquad using OTAs and CF

A novel current-mode biquad using operational transconductance amplifiers (OTAs) and current follower (CF) is presented. The circuit can realise lowpass, bandpass, highpass, band-stop and all-pass transfer functions without any circuit matching conditions. The circuit parameters can also be tuned independently by the transconductance gains of the OTAs. The proposed biquad enjoys very low sensitivities with respect to the circuit elements.

Versatile voltage-mode active-only biquad with lossless and lossy integrator loop

This paper presents a realization of a voltage-mode active-only biquad using operational amplifiers (OAs) and operational transconductance amplifiers (OTAs). The circuit configuration is obtained from a second-order integrator loop structure with lossless and lossy integrators. The proposed circuit can realize low-pass, band-pass, high-pass, band-stop and all-pass transfer functions by a suitable choice of input and output terminals. The circuit characteristics can be electronically tuned through adjustment of the transconductance gains of the OTAs. An example is given, together with simulated results by PSPICE. The circuit configuration is very suitable for implementation in both bipolar and CMOS technologies.

Linear Fractional Transformations and Balanced Realization of Discrete-Time Stable All-Pass Systems

The tangential Schur algorithm provides a means of constructing the class of multivariable discrete-time stable all-pass transfer functions of a fixed finite McMillan degree. In each iteration step a linear fractional transformation is employed which is associated with a J-inner rational matrix of McMillan degree 1. In this set-up, the emphasis is exclusively on transfer functions. In the present contribution we present a unified framework in which linear fractional transformations on transfer functions are represented by corresponding linear fractional transformations on state-space realization matrices. When applied to the case of the tangential Schur algorithm, minimal balanced realizations of stable all-pass systems in terms of the parameters used are obtained. The balanced state-space approach of (Hanzon and Peeters, 2000) is incorporated as a special case.

The monogenic signal

This paper introduces a two-dimensional (2-D) generalization of the analytic signal. This novel approach is based on the Riesz transform, which is used instead of the Hilbert transform. The combination of a 2-D signal with the Riesz transformed one yields a sophisticated 2-D analytic signal: the monogenic signal. The approach is derived analytically from irrotational and solenoidal vector fields. Based on local amplitude and local phase, an appropriate local signal representation that preserves the split of identity, i.e., the invariance-equivariance property of signal decomposition, is presented. This is one of the central properties of the one-dimensional (1-D) analytic signal that decomposes a signal into structural and energetic information. We show that further properties of the analytic signal concerning symmetry, energy, allpass transfer function, and orthogonality are also preserved, and we compare this with the behavior of other approaches for a 2-D analytic signal. As a central topic of this paper, a geometric phase interpretation that is based on the relation between the 1-D analytic signal and the 2-D monogenic signal established by the Radon (1986) transform is introduced. Possible applications of this relationship are sketched, and references to other applications of the monogenic signal are given.

Voltage-mode active-only biquad

This paper presents a realization of a voltage-mode active-only biquadratic circuit. The proposed circuit is constructed employing solely operational amplifiers and operational transconductance amplifiers (OTAs). The circuit configuration is obtained from a second-order structure with two integrator loops. The circuit can realize low-pass, band-pass, high-pass, band-stop, low-pass notch, high-pass notch and all-pass transfer functions by suitably choosing the input and output terminals, and the circuit characteristics can be electronically tuned through adjusting the transconductance gains of OTAs. Some examples are given together with simulated results by PSPICE. The circuit configuration is very suitable for implementation in both bipolar or CMOS technologies.

Universal two-input two-output current-mode active biquad using FTFNs

A universal active biquad using the four-terminal floating nullors (FTFNs) is presented. The proposed circuit uses two FTFNs, two capacitors and two resistors. The proposed circuit has two input currents and can provide two highimpedance output currents. Without changing the circuit topology, the output currents can realize lowpass, highpass, bandpass, and allpass transfer functions. A notch transfer function can be obtained by adding a voltage-to-current converter using an additional FTFN. The proposed circuit enjoys low passive sensitivities and orthogonal tuning of the parameters ωo and ωo/Qo.

A versatile current-mode biquad using operational amplifiers

A versatile current-mode biquadratic filter using three operational amplifiers and nine passive elements is proposed. By suitably choosing the output branch, lowpass, bandpass, highpass, bandstop and allpass transfer functions are realized simultaneously without changing the circuit configuration and elements. Two circuits, one is for low frequency application and the other for high frequency, are proposed. The center frequency, quality factor and gain constants of the circuit can be tuned independently. Simulated results show that the circuits work successfully.

Current-Mode Universal Filter Using FTFNs

A new current-mode universal filter is presented. The proposed filter uses three four-terminal floating nullors (FTFNs), three grounded capacitors, and four grounded resistors. The proposed filter has three inputs and one output and can realize lowpass, highpass, bandpass, notch, and allpass transfer functions without changing the circuit topology. The proposed filter enjoys low active and passive sensitivities and independent control of the parametersω0andω0Q0using grounded elements.

Versatile Active Biquad Using FTFNs

A universal active biquad using the four-terminal floating nullors (FTFNs) is presented. The propsed circuit uses two FTFNs, three capacitors and two resistors. The proposed circuit has three input voltages and can simultaneously provide a high-impedance output current and/or an output voltage. Without changing the circuit topology, the output voltage can realise lowpass, highpass, bandpass, notch and allpass transfer functions and the output current can realise bandpass and highpass transfer functions. The proposed circuit enjoys low active and passive sensitivities and independent control of the parametersωoandω0/Q0.

Improved LBR two-pair extraction methods for low sensitivity digital filter realizations

In this paper, we present two improved lossless bounded-real (LBR) two-pair extraction methods using an allpass input function, which significantly reduce roundoff errors during the extraction process and reduce the amount of computation nearly to a half. Both methods are based on the induced allpass transfer function from the given BR function, which is obtained by replacing the value of the terminating multiplier with 1 or -1. The first method is an LBR two-pair extraction based directly on the allpass input function induced from the given input transfer function. The second extraction method is based on two new real polynomials obtained by further decomposing the induced allpass input function. Even with two polynomials, the involved polynomial division and parameter calculation are simpler in the second method. Consequently, numerical errors are further reduced in the second method. The benefits of employing the two improved methods are confirmed through simulation examples.

The design of 2-D approximately linear phase filters using a direct approach

A novel approach to the design of approximately linear phase recursive digital filters was recently described. The technique exploited a property of allpass transfer functions which allowed the creation of a set of linear simultaneous equations in the filter coefficients which could then be solved in the least-squares sense. This paper extends the design method to 2-D and multi-D filters. These filters find application in many areas including image processing, image coding, filter banks and seismic data processing. Several problems arise which are not present in the 1-D design and the paper looks at ways to overcome them. In addition, there is discussion on the stability issue. Several examples including circularly, elliptically and diamond symmetric lowpass filters and a fan filter are presented. Comparison is made between the proposed technique and those of Gu and Swamy (1994) and Toyoshima et al. (1990).

A note on the orthogonal realization of allpass digital filters and their finite wordlength performance

In this correspondence, a direct method to obtain an orthogonal realization of an allpass transfer function from the entries of the Jury table or the Schur-Cohn test is presented. The performance of this orthogonal realization using fixed- or floating-point implementation is discussed. Based on this formulation, simple formulae for the coefficient sensitivity and output roundoff noise variances are obtained. The results are illustrated with an example.

On the Construction of Orthonormal Basis Functions for System Identification

In this paper we present an alternative derivation of orthonormal rational families in H2, based on previous work by Roberts and Mullis. The construction is based on balanced state space realizations of all-pass transfer functions, and generalizes recent work of Heuberger et al. The emphasis is put on the simplicity of this approach compared with traditional methods. We also present some historical remarks concerning earlier approaches to this problem, as well as completeness ami uniform boundedness conditions for this family of orthonormal functions.

Active-R realization of current-mode biquads

A new circuit configuration for realizing current-mode biquadratic transfer functions using operational amplifier poles is presented. The circuit is composed only of opamps and resistors, and it can realize lowpass, highpass, bandpass, notch and allpass transfer functions.

Adaptive allpass filtering for nonminimum-phase system identification

Efficient algorithms for the recursive identification of nonminimum-phase systems using an adaptive allpass filter together with an adaptive transversal filter are introduced. Both the output and input sequences are assumed to be available, and the proposed technique basically uses a linear predictor at the output of the system to equalise its magnitude response and an allpass filter to match its phase response. The mirror image property of the numerator and denominator polynomials in an allpass transfer function reduces the number of adaptive parameters needed compared to an unconstrained recursive identification scheme. Computer simulations are used to support the claims made in the paper.

Allpass expansions of digital transfer functions

It is well known that digital allpass filters can be efficiently realised by using lossless structures which possess low sensitivity, low roundoff noise and are free from limit cycles on implementation with finite word-length registers. It is established that every rational transfer function of a stable IIR filter can be expressed as a linear combination of a set of stable first-order allpass transfer functions. This leads to two types of implementation for every stable IIR digital filter in the form of a parallel or cascade connection of first-order allpass sections.

All-pass networks using current conveyors

Two circuits, each realizing a second order all-pass transfer function, are described. One circuit uses a grounded capacitor, and is thus suitable from the point of view of IC implementation. The other circuit employs a minimum of active and passive components required for a second order all-pass realization.

On the approximation of phase specifications by discrete‐time or continuous‐time allpass transfer functions

On the approximation of phase specifications by discrete‐time or continuous‐time allpass transfer functions

A Characterization of All Solutions to the Four Block General Distance Problem

All solutions to the four block general distance problem which arises in $H^\infty $ optimal control are characterized. The procedure is to embed the original problem in an all-pass matrix which is constructed. It is then shown that part of this all-pass matrix acts as a generator of all solutions. Special attention is given to the characterization of all optimal solutions by invoking a new descriptor characterization of all-pass transfer functions. As an application, necessary and sufficient conditions are found for the existence of an $H^\infty $ optimal controller. Following that, a descriptor representation of all solutions is derived.

Norms of principal axis realizations: Application of abstract realization theory

Principal axis realizations are an important class of implementations, associated with good numerical properties. The spectral (l/sub 2/) norm of the principal axis realization matrices of arbitrary transfer functions is studied. In particular, it is shown that if the transfer function is contractive, then its principal axis realization matrices have a norm less than square root 2, while the internally balanced realization is conjectured to have a norm of less than 1. Furthermore, if the transfer function is an all-pass transfer function, then the three principal axis realizations become identical and equal to an orthogonal matrix. Abstract realization theory is used to prove these results. >