Allpass Filter Design Research Articles

All-Pass Filter Design Using Unimodular Interpolation

Many signal processing applications involve designing an all-pass filter with a desired phase response. Earlier methods have largely focused on approximating the desired response using an optimisation based approach, or by using numerical computations of the group delay at specific frequencies with Blaschke interpolation. The former method does not offer any guarantee to match the estimated phase response at given points, whereas the latter one matches the phases at the input points, but is sensitive to the numerical precision of the specified group delays. In this work, we present a unimodular interpolation-based method to obtain all-pass filter coefficients that match the desired phase response at the given points without the need for group delays at the interpolating points. Through detailed simulations, we show that the proposed method is more suited for obtaining all-pass filters that match the target phases when compared to earlier approaches.

Design of discrete-time matrix all-pass filters using subspace Nevanlinna pick interpolation

Unitary matrix-valued functions of frequency are matrix all-pass systems, since they preserve the norm of the input vector signals. Typically, such systems are represented and analyzed using their unitary-matrix valued frequency domain characteristics, although obtaining rational realizations for matrix all-pass systems enables compact representations and efficient implementations. However, an approach to obtain matrix all-pass filters that satisfy phase constraints at certain frequencies was hitherto unknown. In this paper, we present an interpolation strategy to obtain a rational matrix-valued transfer function from frequency domain constraints for discrete-time matrix all-pass systems. Using an extension of the Subspace Nevanlinna Pick Interpolation Problem (SNIP), we design a construction for discrete-time matrix all-pass systems that satisfy the desired phase characteristics. An innovation that enables this is the extension of the SNIP to the boundary case to obtain efficient time-domain implementations of matrix all-pass filters as matrix linear constant coefficient difference equations, facilitated by a rational (realizable) matrix transfer function. We also show that the derivative of matrix phase constraints, related to the group delay at the interpolating points, can be optimized to control the all-pass transfer matrices at the unspecified frequencies. Simulations show that the proposed technique for unitary matrix filter design performs as well as traditional DFT based interpolation approaches, including Geodesic interpolation and the popular Givens rotation based matrix parameterization.

A 4-bits active inductor-based lattice 24.5–50 ps all-pass filter

In this paper, a lattice network-based second-order all-pass filter (APF) design is presented. Unlike previously published works, floating active inductors (FAIs) are used in the lattice topology. Inductance (L) and quality factor (Q) tunability of Q-enhanced FAIs are employed to ensure the designed APF is robust to process-voltage-temperature (PVT) variations and to make the filter’s group delay responses are constant for a wide frequency range. The operation of the proposed APF is verified by post-layout simulations using Cadence Design Suite in TSMC 65-nm CMOS technology. The operating frequency of the designed filter reaches 5 GHz with a delay range of 24.5-50 ps. The designed filter has a gain of -0.15 dB, which varies up to 1.47 dB in the operating frequency range. The group delay error is 114 fs, which is a 0.294% variation in the nominal case. The input-referred 1 dB compression point (P1dB) and the third-order interception point (IIP3) values are attained as -5.21 dBm and +9.19 dBm, respectively. At the nominal condition, the noise figure is achieved as 16.7 dB. The circuit occupies only 0.0189 μm2 while drawing 29 mA from a 1.5 V supply.

Design and practice of simple first-order all-pass filters using commercially available IC and their applications

First-order all-pass filter circuits, both non-inverting and inverting, could be the focus of this article, which could include the design and implementation of first-order all-pass filter circuits. Using a standard integrated circuit (IC): AD830, as well as a single resistor and a single capacitor, the proposed first-order all-pass filters could well be built. The AD830 is an integrated circuit (IC) manufactured by Analog Devices Corporation that is available for purchase. The pole frequency and phase response of the proposed all-pass filters could well be directly modified by attuning the resistor in the circuit. Aside from that, the output voltage has a low impedance, making it appropriate for use in voltage-mode circuits. In addition, the proposed first-order all-pass filter is used to design the multiphase sinusoidal oscillator, which serves as an example of an application wherein the oscillation condition can be adjusted without impacting the frequency. The gain and phase responses of the proposed all-pass filters, as well as their phase response adjustment, time-domain response, and total harmonic distortion of signals, are all shown via computer simulation using the PSPICE software, as well as their experimental results. For the proposed circuits, a statistical analysis is coupled with a Monte Carlo simulation to estimate the performance of the circuits. In accordance with the results of this study, a theoretical design suitable for developing a worksheet for teaching and learning in electrical and electronic engineering laboratories has already been developed

All-Pass Filter Design Using Blaschke Interpolation

Obtaining a rational all-pass filter that matches a target phase response is a common problem in signal processing. Typical approaches have generally focused on optimizing filter coefficients while minimizing the deviation from the target phase response. However, these approaches typically do not offer a guarantee of exact match of the phase or any conditions on group delay. In this letter, we propose a Blaschke interpolation based all-pass filter design, wherein, if the phase response is known at n distinct frequencies, an all-pass filter that exactly satisfies the target values can be obtained. Moreover, the group delay at the interpolating points can be optimized or tuned to control the phase response for remaining frequencies. Simulations reveal that the design method is able to produce filters that closely match the target phase response accurately with much lower complexity than prior approaches.

Transformation of Ladder Based All Pass and Biquad Filters into Active All Pass and Biquad Filter using CFOA

In this paper ladder based all pass and biquad filters are transformed into CFOA based all pass and biquad filters. The ladder based approach is used for design of prototypes. The new circuits have attractive properties of greater linearity, high dynamic rate, high slew rate and high signal bandwidth. A new technique for the conversion has been proposed. The technique uses signal flow graph and converts the existing LC ladder based filter into CFOA based configurations. The design of all pass and Biquad filter has been realized using the proposed technique. The proposed configuration is implemented using CFOA as an active device and all the capacitors are grounded. The new configurations are suitable for various signal processing applications. Simulation has been carried out using simulation software PSpice (v10.2). The simulation results have been demonstrated and discussed.

Design of IIR All-Pass Filters Using a Neural-Based Learning Algorithm

Least-squares design of infinite impulse response all-pass filter can be formulated as an eigenvector solving problem based on the Rayleigh principle. The eigenfilter is designed by solving a single eigenvector corresponding to the smallest eigenvalue of a real, symmetric, and positive-definite matrix. This paper proposes a minor component analysis-based neural learning algorithm for designing eigenfilter. By appropriately mapping the associated all-pass filter specifications to the simple neural model enables the filter coefficients to be derived from the neural weights. The neural weights eventually approach the optimal filter coefficients of the eigenfilter when the neural model achieves convergence. The proposed neural learning algorithm is demonstrated from simulation results to converge rapidly and achieve accurate performance of eigenfilter design.

An Improved All-Pass Filter Design Using Closed-Form Toeplitz-plus-Hankel Matrix

The least-squares design of infinite impulse response all-pass filter can be formulated as to solve a system of linear equations without directly computing a matrix inversion. The set of linear equations associated matrix is further expressed as a Toeplitz-plus-Hankel matrix such that the optimal filter coefficients are efficiently solved by employing a robust Cholesky decomposition or the split Levinson technique. This paper proposes closed-form expressions for efficiently computing Toeplitz-plus-Hankel matrix based on trigonometric identities. The closed-form expressions of the Toeplitz-plus-Hankel matrix can be directly evaluated as the passband edges are specified without sampling the frequency band as that of the previous computing-efficiency algorithm. The proposed new and simpler closed-form expressions are indicated from simulation results to accurately improve the design performance as well as achieve computational efficiency.

Phase Response Design of Recursive All-Pass Digital Filters Using a Modified PSO Algorithm.

This paper develops a new design scheme for the phase response of an all-pass recursive digital filter. A variant of particle swarm optimization (PSO) algorithm will be utilized for solving this kind of filter design problem. It is here called the modified PSO (MPSO) algorithm in which another adjusting factor is more introduced in the velocity updating formula of the algorithm in order to improve the searching ability. In the proposed method, all of the designed filter coefficients are firstly collected to be a parameter vector and this vector is regarded as a particle of the algorithm. The MPSO with a modified velocity formula will force all particles into moving toward the optimal or near optimal solution by minimizing some defined objective function of the optimization problem. To show the effectiveness of the proposed method, two different kinds of linear phase response design examples are illustrated and the general PSO algorithm is compared as well. The obtained results show that the MPSO is superior to the general PSO for the phase response design of digital recursive all-pass filter.

High speed optical phased array using high contrast grating all-pass filters.

We report a high speed 8x8 optical phased array using tunable 1550 nm all-pass filters with ultrathin high contrast gratings (HCGs) as the microelectromechanical-actuated top reflectors. The all-pass filter design enables a highly efficient phase tuning (1.7 π) with a small actuation voltage (10 V) and actuation displacement of the HCG (50 nm). The microelectromechanical HCG structure facilitates a high phase tuning speed >0.5 MHz. Beam steering is experimentally demonstrated with the optical phased array.

Single MIMO-OTA and single-grounded-capacitor-based first-order allpass filter design

A novel first-order voltage-mode allpass (AP) filter employing a single multiple-input-multiple-output operational-transconductance-amplifier (MIMO-OTA) and a single grounded capacitor is introduced in this article. Compared to the corresponding already published topologies, the offered benefits are as follows: it employs minimum number of active and passive components; the only capacitor is grounded, which is good for a monolithic integration of an IC; and the absence of any matching condition for its realisability. The performance of the proposed circuit has been evaluated through simulation results, utilising the analogue design environment of Cadence software.

Allpass filter design with waveguide loss compensation

A major artifact of realistic photonic filters is the waveguide power loss. Its detrimental effect on the allpass structure is particularly alarming because the phase response is highly sensitive to perturbations. While the loss can be simply captured into a variation on the unit delay in signal processing analysis, its non-linearity makes it mathematically difficult to address. We present an allpass filter design algorithm that is able to provide filter coefficients that compensate for the waveguide power loss. By absorbing the loss parameter into the design cost function, the optimization problem becomes non-convex and NP hard. Our approach solves this problem by utilizing an iterative algorithm in conjunction with the branch and bound global optimization technique. The proposed algorithm is expected to improve the performance and increase the utilization of allpass filters for optical signal phase based applications such as distortion compensation and group delay equalization.

Neural Network-Based IIR All-Pass Filter Design

This paper presents a neural network-based Lyapunov energy function for the weighted least-squares design of IIR all-pass filters. In the proposed method, the error reflecting the difference between the desired phase response and the phase of the designed IIR all-pass filter is formulated as a Lyapunov error criterion. Based on the neural network architecture and suitable Hopfield parameters, the optimal filter coefficients can be obtained when convergence is achieved. Furthermore, a weight updating function is proposed to achieve accurate approximation of the equiripple response. The simulation results indicate that the proposed technique can achieve high performance in a parallel manner.

Improved Computing-Efficiency Least-Squares Algorithm with Application to All-Pass Filter Design

All-pass filter design can be generally achieved by solving a system of linear equations. The associated matrices involved in the set of linear equations can be further formulated as a Toeplitz-plus-Hankel form such that a matrix inversion is avoided. Consequently, the optimal filter coefficients can be solved by using computationally efficient Levinson algorithms or Cholesky decomposition technique. In this paper, based on trigonometric identities and sampling the frequency band of interest uniformly, the authors proposed closed-form expressions to compute the elements of the Toeplitz-plus-Hankel matrix required in the least-squares design of IIR all-pass filters. Simulation results confirm that the proposed method achieves good performance as well as effectiveness.

A Voltage Gain-Controlled Modified CFOA And Its Application in Electronically Tunable Four-Mode All-Pass Filter Design

This paper presents a new active building block (ABB) called voltage gain-controlled modified current feedback amplifier (VGC-MCFOA) based on bipolar junction transistor technology. The versatility of the new ABB is demonstrated in new first-order all-pass filter structure design employing single VGC-MCFOA, single grounded capacitor, and three resistors. Introduced circuit provides all four possible transfer functions at the same configuration, namely current-mode, transimpedance-mode, transadmittance-mode, and voltage-mode. The pole frequency of the circuit can be easily tuned by means of DC bias currents. The theoretical results are verified by SPICE simulations based on bipolar transistor arrays AT&T ALA400-CBIC-R process parameters.

Robust, Efficient Design of Allpass Filters for Dispersive String Sound Synthesis

An efficient allpass filter design method is introduced to match the dispersion characteristics of vibrating stiff strings. The proposed method designs an allpass filter in cascaded biquad form directly from the target group delay, placing the poles at frequencies at which the group delay area function achieves odd integer multiples of ?, and fixing the pole radii according to a smoothness parameter. The pole frequencies are seen to be roots of quartic polynomials, and an efficient approximation to the desired roots is provided. Design examples show the method to outperform a previous closed-form design. Furthermore, the proposed method can achieve an arbitrarily wide bandwidth of good approximation by increasing the filter order, as the method is numerically robust and yields stable allpass filters.

FIR, Allpass, and IIR Variable Fractional Delay Digital Filter Design

This paper presents two-step design methodologies and performance analyses of finite-impulse response (FIR), allpass, and infinite-impulse response (IIR) variable fractional delay (VFD) digital filters. In the first step, a set of fractional delay (FD) filters are designed. In the second step, these FD filter coefficients are approximated by polynomial functions of FD. The FIR FD filter design problem is formulated in the peak-constrained weighted least-squares (PCWLS) sense and solved by the projected least-squares (PLS) algorithm. For the allpass and IIR FD filters, the design problem is nonconvex and a global solution is difficult to obtain. The allpass FD filters are directly designed as a linearly constrained quadratic programming problem and solved using the PLS algorithm. For IIR FD filters, the fixed denominator is obtained by model reduction of a time-domain average FIR filter. The remaining numerators of the IIR FD filters are designed by solving linear equations derived from the orthogonality principle. Analyses on the relative performances indicate that the IIR VFD filter with a low-order fixed denominator offers a combination of the following desirable properties including small number of denominator coefficients, lowest group delay, easily achievable stable design, avoidance of transients due to nonvariable denominator coefficients, and good overall magnitude and group delay performances especially for high passband cutoff frequency ( ges 0.9pi) . Filter examples covering three adjacent ranges of wideband cutoff frequencies [0.95, 0.925, 0.9], [0.875, 0.85, 0.825], and [0.8, 0.775, 0.75] are given to illustrate the design methodologies and the relative performances of the proposed methods.

Tunable dispersion filter design for piano synthesis

The tunable dispersion filter is a new design approach presented in this letter to provide dispersion modeling for digital waveguide synthesis of musical instruments, which do not produce extremely inharmonic sounds, such as the piano. We propose to use a cascade of second-order allpass filters for modeling dispersion. The filter coefficients can be calculated by using simple formulae based on the Thiran allpass filter design, which is usually used for fractional delay approximation. Unlike the previous allpass filter approximations, this filter design is easily scalable to produce various inharmonicity values for a wide range of fundamental frequencies.

An allpass filter design method with application to piano string synthesis

A nonparametric allpass filter design method for matching a desired group delay as a function of frequency is presented. The technique is useful in physical modeling synthesis of musical instruments exhibiting dispersive wave propagation in which different frequency bands travel at different speeds. While current group delay filter design methods suffer from numerical difficulties except at low filter orders, the technique presented here is numerically robust, producing an allpass filter in cascaded biquad form, and with the filter poles following a smooth loop within the unit circle. The technique was inspired by the observation that a pole-zero pair arranged in allpass form has 2π total group delay when integrated around the unit circle, regardless of the pole location. To match a given group delay characteristic, the method divides the frequency axis into sections containing 2π total group delay, and assigns a pole-zero allpass pair to each. In this way, the method incorporates an order selection technique, and by adding a pure delay to the desired group delay, allows the trading of increased filter order for improved fit to the frequency-dependent group delay. Results are presented for modeling the group delay of a stiff piano string under several computational constraints.

Phase Correction of Interferograms Using Digital All-Pass Filters

A method for the phase correction of interferograms in Fourier transform infrared spectroscopy is presented. It is shown that phase error can be canceled to within an arbitrary angular precision by a low-order digital all-pass filter. Such a filter only modifies the phase of the Fourier transform of the interferogram and keeps the magnitude unchanged, like the Mertz method, for example. However, our method minimizes the asymmetric apodization that results in photometric errors when using the Mertz method alone. A practical example is provided in which phase correction over a frequency range of 800 cm(-1) to 4000 cm(-1) using a 9-pole all-pass filter resulted in a photometric error of <0.01%, much less than the 0.3% error of the Mertz method. An alternative and faster (approximately 100 ms) approach is to use an all-pass filter with lower angular precision followed by the Mertz method. Removing most of the phase error with the filter brings the interferogram to an optimal state so that the residual phase error can be completely removed with the Mertz procedure without introducing photometric error. The method can be used in most experiments, including emission spectroscopy, where conventional techniques are inadequate. A simple all-pass filter design algorithm is given.