Synthesis Of Transfer Functions Research Articles

Ear Centering for Accurate Synthesis of Near-Field Head-Related Transfer Functions

The head-related transfer function (HRTF) is a major tool in spatial sound technology. The HRTF for a point source is defined as the ratio between the sound pressure at the ear position and the free-field sound pressure at a reference position. The reference is typically placed at the center of the listener’s head. When using the spherical Fourier transform (SFT) and distance-varying filters (DVF) to synthesize HRTFs for point sources very close to the head, the spherical symmetry of the model around the head center does not allow for distinguishing between the ear position and the head center. Ear centering is a technique that overcomes this source of inaccuracy by translating the reference position. Hitherto, plane-wave (PW) translation operators have yield effective ear centering when synthesizing far-field HRTFs. We propose spherical-wave (SW) translation operators for ear centering required in the accurate synthesis of near-field HRTFs. We contrasted the performance of PW and SW ear centering. The synthesis errors decreased consistently when applying SW ear centering and the enhancement was observed up to the maximum frequency determined by the spherical grid.

Temporal multilayer structures for designing higher-order transfer functions using time-varying metamaterials

Temporal metamaterials are artificial materials whose electromagnetic properties change over time. In analogy with spatial media and metamaterials, where their properties change smoothly or abruptly over space, temporal metamaterials can exhibit a smooth variation over time, realizing a temporal non-homogeneous medium, or a stepwise transition, and the temporal version of dielectric slabs or multilayer structures. In this Letter, we focus our attention on temporal multilayer structures, and we propose the synthesis of higher-order transfer functions by modeling the wave propagation through a generalized temporal multilayer structure, consisting of a cascade over time of different media. The tailoring of the scattering response of the temporal structure as a function of frequency is presented, deriving the corresponding scattering coefficients for a properly designed set of medium properties, i.e., permittivity and permeability, and application time, in analogy with what is typically done in optical and electromagnetic spatial multilayered structures. This allows us to design novel electromagnetic and optical devices with higher-order transfer functions by exploiting the temporal dimension instead of the spatial one.

SFG Synthesis of General High-Order All-Pass and All-Pole Current Transfer Functions Using CFTAs

An approach of using the signal flow graph (SFG) technique to synthesize general high-order all-pass and all-pole current transfer functions with current follower transconductance amplifiers (CFTAs) and grounded capacitors has been presented. For general nth-order systems, the realized all-pass structure contains at most n + 1 CFTAs and n grounded capacitors, while the all-pole lowpass circuit requires only n CFTAs and n grounded capacitors. The resulting circuits obtained from the synthesis procedure are resistor-less structures and especially suitable for integration. They also exhibit low-input and high-output impedances and also convenient electronic controllability through the g m-value of the CFTA. Simulation results using real transistor model parameters ALA400 are also included to confirm the theory.

Coupling matrix synthesis of dissipative microwave filters

This study reviews the coupling matrix synthesis of dissipative microwave filters. It compares it to the synthesis of lossless transfer functions and shows that by correctly interpreting the mathematical operations in the lossless case, that is especially the matrix product of vectors and matrices, the same procedure can be adopted for the case including losses. Beyond this, necessary and sufficient conditions are provided guaranteeing that a proper coupling matrix, that is which is symmetric, is obtained at the end. Two examples show the application of the procedure and demonstrate that the correct filter transfer functions are indeed obtained.

Classical circuit theory

This book begins with the basic principles of circuits, derives their analytic properties in both the time and frequency domains, and states and proves the two important theorems. It then develops an algorithmic method to design common and uncommon types of circuits, such as prototype filters, lumped delay lines, constant phase difference circuits, and delay equalizers. The material also discusses the relation between gain and phase, linear and minimum phase functions, group delay, sensitivity functions, scattering matrix, synthesis of transfer functions, approximation of filter functions, all-pass circuits, and circuit design by optimization. This book fills a need for a modern text on the mathematical foundations of passive circuits in general and passive filter design in particular. The mathematical foundations are what classical circuit theory, which is the subject of this book, is all about. It is old, but it has survived the test of time and it is still relevant today because it is basic.

Investigation of phase distortion in the synthesis of head-related transfer functions

Synthesizing over headphones the free-field to ear-canal transfer functions, or head-related transfer functions (HRTFs), of the human auditory system poses several difficulties from the standpoint of digital signal processing. Since the order of the HRTF is unknown, it is necessary to assume a particular value when estimating the HRTF from responses obtained in an anechoic chamber. Additionally, while standard filter designs minimize the squared error between the desired and designed response, applications such as HRTF synthesis are likely to require error metrics that are sensitive to disparities between the log magnitude response of each system. A new design algorithm is proposed that is based on a logarithmic distortion metric and it is shown how this algorithm can be used to obtain minimum phase, low-order pole-zero approximations to HRTFs. Psychophysical results characterizing audibility sensitivity to such HRTF approximation errors are presented in order to establish an audible limit for the distortion in such designs. These results are compared with similar experimental results for the widely used least-squares metric. [Research supported by a grant from the NIDCD of the National Institute of Health.]

Two-pupil Synthesis of Three-dimensional Optical Transfer Functions

We investigate the defocusing imaging effect of a two-pupil interactive system and discuss the synthesis of 3D optical transfer functions (OTFs) from defocused 2D OTFs. Through analytical and simulation results we show the synthesis of 3D OTFs, using as examples two spatially separated Gaussian pupils, and two superposed Gaussian pupils apodized by complementary Fresnel zone plates. Simulation results indicate the low frequency de-emphasis of the obtainable 3D OTFs.

Synthesis of biquad transfer functions using modified continued fraction expansion and NICs

A new method for synthesizing second-order transfer functions is proposed. The method utilizes the negative immitance converter (NIC) as the active device. To generate the necessary passive elements (R and C), and to determine their manner of interconnection, a modified form of Cauer's continued fraction expansion is used. The synthesis procedure is illustrated by some examples and experimental results.

Synthesis of current-mode transfer functions using a single current conveyor

This paper proposes three circuit configurations for the synthesis of current-mode transfer functions using a current conveyor and four or six passive elements. The circuits have low active/passive sensitivities and very high output impedances which are suitable for current sources, and passive element values in the circuits can be chosen so as to be suitable for integrated circuit implementation. The measured frequency responses of the various types of transfer functions (TF), such as a lowpass TF, a highpass TF, a bandpass TF, a bandstop TF and an allpass TF, are shown, and the experimental results agree well with the theoretical characteristics.

Realisation of current-mode transfer function using four-terminal floating nullor

Active-RC synthesis of transfer functions using four-terminal floating nullors (FTFNs) is proposed, and it is shown that an FTFN is a more flexible and all-round building block than an operational amplifier (OA) or a current conveyor (CC II).

Synthesis of arbitrary rational transfer functions in s using uniform distributed RC active circuits

A synthesis technique is described whereby network functions that are rational in s are realized with uniform distributed RC elements and active elements. In contrast to previous distributed synthesis approaches, the technique works directly in the s plane without complex mathematical transformations, uses only grounded rectangular single-layer uniform distributed RC structures, and can realize many network topologies. Classical approximation functions, such as Butterworth and Chebyshev, and well-known filter topologies can be used. Experimental results for a band-pass biquad are presented, and practical implementation possibilities are discussed. >

Bias evaluation and reduction in linear least squares procedures for the synthesis of transfer functions

Following A.H. Whitfield's (1987) discovery that established linear least squares procedures used in the synthesis of transfer functions generally lead to biased parameter estimates, the present work analyses in detail how such bias arises from imperfections in the frequency response data. Procedures are classified according to their order accuracy. A simple improvement to the well-known Sanathanan and Koerner procedure is given.

Non‐reciprocal network synthesis using the generalized richards transformation

AbstractA generalization of the Richards transformation is presented and its properties are derived. the new transformation is appropriate for the canonic synthesis of non‐reciprocal network sections based on the transformation of an impedance, and it is shown that under certain constraints a transformerless realization is possible. the generalized Richards transformation can also be applied to the synthesis of network sections without degree reduction of the impedance to be transformed. This kind of application is important for the realization of transfer functions. A dual transformation for an admittance is established. Finally, it is shown how to use the generalized Richards transformation for the synthesis of transfer functions by doubly terminated lossless two‐ports.

On the synthesis of all-pass digital transfer functions based on LBR two-pair extraction procedure†

In this paper a simple explicit expression is provided for the parameter a in LBR two-pairs used in the synthesis of all-pass digital transfer functions. The result can be of interest in automated procedures for digital filter design. Further, canonical realizations for this type of two-pairs are given.

Synthesis of digital control systems using discrete Walsh polynomials

The use of discrete Walsh polynomials to synthesize a digital control system and determine suitable internal system structure from its prescribed external (input/output) behaviour is studied in this paper. Algorithms for the synthesis of discrete system transfer functions and state equations are presented. The discrete Walsh approach method transforms the original model difference equations into computationally convenient algebraic forms. Two examples in which a transfer function and a state equation are synthesized illustrate the discrete Walsh technique.

Synthesis of arbitrary digital transfer functions using allpass-based structures derived via LBR two-pair extraction procedure

The implementation of a digital filter transfer function with all transmission zeros on the unit circle is developed via the synthesis of an appropriate allpass function. The synthesis procedure is based on the “LBR-extraction” approach. The resulting structure is in the form of a doubly terminated cascade of lossless (LBR) two-pairs, with each two-pair realizing a single real or a pair of complex transmission zeros. The Concepts of complete and partial “1” removals, and “1” shifting are introduced and utilized during the synthesis process. The resulting structures have several properties in common with the Gray and Markel lattice filters, but do not require tap coefficients for numerator realization. The building blocks used in this paper are similar to those in certain wave-digital filters and orthogonal filters.

Two-pupil synthesis of optical transfer functions: 2: Pupil function relationships

Although different methods have been proposed for realizing bipolar point spread functions in hybrid two-channel incoherent spatial filtering systems, each method relies either on interference or noninterference between the two channels to achieve the desired synthesis. It is shown that the pupil functions appropriate for synthesis in these two regimes are related through a linear transformation. Furthermore, the pupil functions appropriate for a noninteractive synthesis can be used to specify pupil functions appropriate for any other synthesis.

A general theorem for degree-reduction of a digital BR function

A general theorem is developed for the degree reduction of a bounded real (BR) digital filter transfer function, and is related to the extraction of a digital lossless two-pair from a BR function in such a manner that the remainder function is reduced order BR. The theorem finds applications in the synthesis of digital filter transfer functions in the form of a cascade of lossless two pairs.

Direct synthesis of filter transfer functions

In this paper we propose a new procedure for the direct synthesis of complex transfer functions for a new class of selective filter. Conditional mean square approximation with Chebyshev weights, with three Lagrangian multipliers (for transfer-function values at cutoff frequency, at the origin (ω = 0) and for the phase at the cutoff frequency) gives a new class of filter derived in explicit form. By the choice of the transfer-function phase we can control the shape of amplitude characteristic in the passband or the filter selectivity.

Synthesis of switched-capacitor filters using FDNR-type second-order time-dependent capacitors in p-domain

A switched-capacitor (SC) version of an FDNR-like second-order time-dependent capacitor in p-domain is obtained by using two building blocks each offering two-terminal negative input impedance. The two-terminal compound block is used to illustrate the synthesis of various switched-capacitor transfer functions.