Digital All-pass Filters Research Articles

A Phase Correction Model for Fourier Transform Spectroscopy

In Fourier transform spectroscopy (FTS), the conventional Mertz method is commonly used to correct phase errors of recovered spectra, but it performs poorly in correcting nonlinear phase errors. This paper proposes a phase correlation method–all-pass filter (PCM-APF) model to correct phase errors. In this model, the proposed improved phase correlation method can correct linear phase errors, and all-pass filters are applied to correct the residual nonlinear phase errors. The optimization algorithm for the digital all-pass filters employs an improved algorithm which combines the subtraction-average-based optimizer (SABO) and the golden sine algorithm (Gold-SA). The proposed PCM-APF model demonstrates high correction precision, and the optimization algorithm for the filters converges faster than traditional intelligent optimization algorithms.

Audibility of Group-Delay Equalization

This paper discusses the audibility of group-delay variations. Previous research has found limits of audibility as a function of frequency for different test signals, but extracting the tolerance for group delay to help audio reproduction system designers is hard. This study considers four critical test signals, three synthetic and one recorded, modified with digital allpass filters. The signals are filtered to produce a positive or negative group-delay peak covering the most sensitive frequency range from 500 Hz to 4 kHz, without changing the delay at other frequencies. ABX listening tests using headphones reveal the audibility thresholds for each signal. The perception is highly dependent on the signal, and the unit impulse and pink impulse are the most critical test signals. Negative group-delay variations are more easily audible than positive ones. The smallest mean threshold for the negative group delay was $-$0.56 ms and 0.64 ms for the positive group delay, obtained with a pink impulse. The thresholds are smaller than those obtained in previous studies. A synthetic hi-hat sound decaying 60 dB in 80 ms hides a positive group-delay variation. The variation is more difficult to hear in a recorded castanet sound than in the most critical synthetic signals. This work demonstrates how the group-delay response of headphones and loudspeakers can be perceptually tested, and leads to a better understanding of how audio systems should be equalized to avoid audible group-delay distortion.

Compensation Module Design for Overlapping Band in Band-Interleaved Data Acquisition Systems Based on Hybrid Particle Swarm Optimization Algorithm

The band interleaved data acquisition system (BI-DAS) is an attractive structure to improve the bandwidth of the acquisition system. However, the non-ideal characteristic of the spectrum analysis filter in BI-DAS results in an overlapping frequency band between two adjacent frequency sub-bands. Phase misalignment (PM) between two sub-bands in the overlapping band may cause those signals canceled or partially canceled to each other when sub-bands’ signal are merged. In this paper, a compensation module with a digital all-pass filter (APF) is proposed for the PM of the overlapping bands in BI-DASs. Based on this compensation module, a hybrid Particle Swarm Optimization (PSO) algorithm, along with the Levenberg-Marquardt (LM) algorithm is proposed to design coefficients of the compensation module. The compensation module and corresponding method proposed in this paper are verified in a BI-DAS with 20Gsps sampling rate and 5.5GHz bandwidth. The experimental results show that the proposed compensation module can effectively compensate the PM between the sub-bands in the overlapping band. The proposed hybrid PSO-LM (HPSOLM) algorithm combines the flexibility and reliability inherent in the PSO with the fast convergence and precision of the LM algorithm. It can effectively design the compensation module with stable APF while consuming less time and obtaining better compensation results than the conventional PSO method.

Group Delay Equalization of Polynomial Recursive Digital Filters in Maximal Flat Sense

The paper presents the development of an algorithm to obtain stable allpass filter, which acts as a group delay equalizer, with the aim to equalize group delay of the polynomial IIR filter in a maximal flat sense. The proposed method relies on a set of nonlinear equations, derived directly from the flatness conditions of the group delay response at the origin in the [Formula: see text]-plane, with the order to obtain the unknown values of the allpass filter coefficients. The algorithm implemented in the MATLAB platform returns the coefficients of allpass filter. In the given example, first we construct a minimum phase polynomial IIR digital filter with a maximally flat magnitude at origin, next we augment the system with cascade connection of nonminimum allpass digital filter with order to equalize the group delay response of the whole filter in a maximally flat sense.

A Wideband Array Beamforming Method of Conformal Array Based by All-pass Digital Filters

In wideband signal beamforming, the traditional phase-shift method causes pattern pointing deviation and sidelobe widening, so the true time delay should be used to compensate the cannel delay accurately. In this paper, in view of the conformal array wideband beamforming of low computational complexity and high delay precision from a real-time processing, it proposes divide the real-time delay into integer and fractional parts. The low-order FIR filter and the high-order FIR filter are cascaded to used to form the digital beam forming device. The simulation result indicates that, the method proposed in this paper can effectively solve the pattern pointing deviation and sidelobe widening problems.

Low‐complexity design framework of all‐pass filters with application in quadrature mirror filter banks design

Digital all-pass filters design problem can be simplified by solving a set of linear equations associated with a Toeplitz-plus-Hankel matrix in the least-squares sense. Consequently, the Cholesky decomposition or split Levinson technique can be appropriately used to obtain the optimal solution. In this study, the determination of the set of linear equations to calculate the all-pass-based quadrature mirror filter banks is achieved by exploiting some trigonometric identities and the frequency sampling method. The proposed simplification allows for expressing a sum of sinusoids by a single expression. The simulation results indicate that the presented new and simpler closed-form expressions of the Toeplitz-plus-Hankel associated matrices can achieve accurate performance with a considerable reduction in computational complexity.

Lattice Structure Realization for The Design of 2-D Digital Allpass Filters With General Causality

This paper presents a lattice structure for the realization of two-dimensional (2-D) recursive digital allpass filters (DAFs) with general causality. We employ four basic lattice sections to realize 2-D recursive DAFs with wedge-shaped coefficient support region like a nonsymmetric half-plane (NSHP) support region. The theory and transfer functions of the realized 2-D lattice DAFs are derived. Some variations of the 2-D lattice structure are also presented. We use the Roesser state space model to verify the minimal realization of the proposed 2-D recursive lattice DAF. We present a least-squares design technique and a minimax design technique to solve the nonlinear optimization problems of the proposed 2-D lattice DAF structure. The novelty of the presented lattice structure is that it not only inherits the desirable attributes of 1-D Gray-Markel lattice allpass structure but also possesses the advantage of better performance over the existing 2-D lattice allpass structures. Finally, several design examples are provided for conducting illustration and comparison.

The Phase Characteristics for the Stability of 2-D Nonsymmetric Half-Plane Digital Allpass Filters

The phase-response property for the bounded-input bounded-output (BIBO) stability of a two-dimensional (2-D) causal recursive digital allpass filter (DAF) with nonsymmetric half-plane (NSHP) support region is presented. Both cases of filters with real coefficients and complex coefficients are explored. Moreover, the effect of the numerator polynomial of a 2-D NSHP DAF on stability is also considered. The presented phase-response property has several applications. A remarkable application is that it can be utilized to enforce stability for a 2-D NSHP DAF design by choosing an appropriate phase specification. The eigenfilter design of 2-D NSHP DAFs for this application is also presented. Design examples are given to show these applications and the stability of a 2-D NSHP DAF is also inspected by the 2-D spectral factorization-based algorithm and a zeros-examining method presented by Ekstrom and Woods for confirmation.

Phase Characteristics for the Stability of 2-D Quarter-Plane Recursive Digital All-Pass Filters

In this brief, the monotone phase-response property of a 2-D causal digital all-pass filter (DAF) with real coefficients or complex coefficients in the quarter plane (QP) support region is presented. Regarding the circumstance of real coefficients, we also prove that the previously proposed stability criterion on the viewpoint of unwrapped phase by Pei and Shyu is necessary and sufficient for 2-D separable DAFs but is only sufficient for QP DAFs. The resultant property possesses the advantage of increasing the freedom of phase design over the previously proposed one. A remarkable application of the presented property is choosing an appropriate specification for the desired phase response of a 2-D DAF design. A design example is given to show this application, and the stability is also inspected by the 2-D spectral factorization algorithm and the root maps for confirmation.

Digital All-Pass Filter Modeling Based on Desired Group Delay Using Advanced Material: A Review on the Signal Processing Part

This paper presents a review on three types of techniques in designing digital all-pass filters based on group delay. All the three methods use the same basic concept rooting back to the requirement of a stable transfer function of the filter which should be a minimum-phase type, and the denominator group delay. The most optimized of the three is chosen to be implemented in MATLAB in order to decrease the group delay variation of a 5th order Chebyshev low-pass filter with cut-off frequency of 160 MHz. The digital transfer function of the low-pass filter is obtained from the analog transfer function by means of bilinear transformation. The sampling frequency of the digital LPF is 100 times the cut-off ffrequency to retain the response of the analog LPF. Both of the filters are then cascaded together and the overall group delays variations are analyzed. The variations of group delay shows a reduction but the price paid is the increase of the overall group delay of the system.

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.

Design of Two-Channel Quadrature Mirror Filter Banks Using Minor Component Analysis Algorithm

The design of two-channel quadrature mirror filter banks can be constructed based on real infinite impulse response (IIR) all-pass digital filters without yielding magnitude distortion. The design problem is first formulated as a phase optimization using IIR all-pass filters in the least-squares sense. Then the nonlinear phase optimization is further converted into solving an eigenproblem of an appropriate real, symmetric, and positive-definite matrix. In this paper, the minor component analysis algorithm based on the neural learning rule is exploited to the design of eigenfilter. When the learning algorithm achieves convergence, the weights of the neural system approximate the smallest eigenvector, which are the optimal filter coefficients of the IIR all-pass filters. The simulation results confirm that the proposed neural-based method can achieve accurate performance by incorporating the simple neural model.

Design of digital allpass-based two-channel quincunx QMF banks

This paper presents a novel structure for constructing two-channel quincunx quadrature mirror filter (QQMF) banks. The analysis and synthesis filters of the QQMF bank are composed of two-dimensional (2-D) recursive digital allpass filters with symmetric half-plane support regions. Using the 2-D doubly complementary half-band property possessed by the analysis and synthesis filters, we facilitate the design of the digital allpass-based two-channel QQMF banks. For finding the coefficients of the 2-D recursive symmetric half-plane digital allpass filters, the design problem is appropriately formulated to result in an optimization problem that can be solved by using a weighted least-squares algorithm in the minimax (L∞) optimal sense. The novelty of the proposed design method is that the designed 2-D QQMF bank achieves perfect magnitude response and possesses satisfactory phase response without requiring extra phase equalizer. Simulation results are also provided for illustration and comparison. Copyright © 2012 John Wiley & Sons, Ltd.

Design of 2-D interpolation/decimation filters using a general 2-D digital allpass filter

Two-dimensional (2-D) interpolation/decimation digital filters are widely used for sampling rate conversion. A general structure consisting of a 2-D recursive digital allpass filter (DAF) and a 2-D pure delay block is presented for designing 2-D recursive interpolation/decimation filters. We utilize a 2-D DAF with symmetric half-plane (SHP) support for its filter coefficients to comply with the symmetry possessed by 2-D interpolation/decimation filters. The structure also possesses a preferable doubly complementary half-band (DC-HB) property that reduces the number of required independent coefficients for designing 2-D interpolation/decimation filters. We appropriately formulate the design problem to obtain a simple linear optimization problem that minimizes the phase error of the 2-D recursive SHP DAF in the pth norm (Lp) sense. Simulation results are provided for illustration and comparison.

Efficient digital filters with variable cut-off based on all-pass and sharpening digital filters

All-pass digital filters are known as excellent prototype filters in many applications, such as control systems, signal processing and communications. Efficient filters can be designed because transfer function is very robust to small element changes. The drawback of digital filters based on all-pass filter sections is that they are not suitable for tuning and the design of filters with variable cut-off frequency. In this paper there is proposed a new design method suitable for the design of filters that may satisfy different attenuation specifications and variable cut-off based on low-order wave digital filters. The method is derived using computer algebra system.

Two‐dimensional recursive digital filters with nearly circular‐symmetric magnitude response and approximately linear phase

AbstractThis paper presents a general structure using 1‐D and two‐dimensional (2‐D) recursive digital all‐pass filters (DAFs) for the design of 2‐D recursive circularly symmetric digital low‐pass filters (CS‐DLFs). The general structure is a cascade of two stages composed of all‐pass building blocks. The first stage is a parallel connection of a 2‐D recursive DAF with a symmetric half‐plane (SHP) support for its filter coefficients and a 2‐D pure delay block. The second stage composed of a parallel connection of a 1‐D recursive DAF and a 1‐D pure delay block is used for eliminating the unwanted pass‐band induced by the first stage. As a result, the design of a 2‐D CS‐DLF in either the least‐squares or the minimax sense can be formulated in a simple linear optimization problem in terms of the weighted‐phase response error for each DAF. Design results with nearly circularly symmetric magnitude response and approximately linear phase are also provided for illustration and comparison. Copyright © 2010 John Wiley & Sons, Ltd.

A Fault Ride-Through Technique of DFIG Wind Turbine Systems Using Dynamic Voltage Restorers

This paper proposes a low-voltage ride-through technique of a doubly fed induction generator (DFIG) wind turbine system using a dynamic voltage restorer (DVR). For effective control of the DVR, digital all-pass filters are used for extracting the positive-sequence component from the unbalanced grid voltage since they have the advantages of giving a desired phase shift and no magnitude reduction over conventional low- or high-pass filters. Using the positive-sequence component, the phase angles for the positive- and negative-sequence components of the grid voltage are derived. A control algorithm for the DVR that is dual voltage controllers only is implemented for the two sequence components in the dq synchronous reference frame. In order to achieve the power rating reduction of the DVR, the stator power reference for the DFIG is reduced during faults. In addition, a control scheme of pitch angle system is applied to stabilize the operation of the wind turbine system in the event of grid faults. PSCAD/EMTDC simulations show the effectiveness of the proposed technique and a feasibility of reducing the power rating of DVR for the fault ride-through capability of DFIG. The validity of the proposed control scheme for the DVR has also been verified by experimental results.

Two-Channel Parallelogram QMF Banks Using 2-D NSHP Digital All-Pass Filters

This paper presents a novel structure for the analysis and synthesis filters of two-channel parallelogram quadrature mirror filter (PQMF) banks. Two-dimensional recursive digital all-pass filters (DAFs) with nonsymmetric half-plane (NSHP) support regions are used as the basic sections for building this structure. With an appropriate combination of the 2-D NSHP DAFs, the resultant analysis/synthesis filters possess a 2-D doubly complementary symmetry that facilitates the design and implementation of two-channel PQMF banks. Moreover, the proposed PQMF bank provides approximately linear-phase response without magnitude distortion. The design problem of the proposed PQMF bank is appropriately formulated to result in a minimization of the linear-phase error associated with the 2-D NSHP DAFs in the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$p$</tex></formula> th-norm <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$(L_{p})$</tex></formula> sense. Efficient design techniques are developed to solve the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$L_{p}$</tex> </formula> optimization problems. Simulation results for illustration and comparison are also provided.

Current-mode operational transconductance amplifier-capacitor biquad filter structures based on Tarmy–Ghausi Active-RC filter and second-order digital all-pass filters

The Tarmy-Ghausi (TG) active resistor-capacitor (RC) filters using op-amps and its modification by Moschytz are well known to active RC filter designers. These use first-order all-pass networks in a negative feedback loop. New current-mode universal operational transconductance amplifier-capacitor (OTA-C) biquad filters based on the TG active RC filter are considered here. These are based on a recently proposed OTA-C based first-order all-pass network. Three different feedback arrangements are investigated in the proposed filter structure so as to reduce the pole-Q sensitivity. The proposed biquad filters are shown to implement all different types of filters like low-pass, high-pass, band-pass, symmetric notch, all-pass, low-pass notch and high-pass notch. The synthesis of the general biquad is carried out in a novel way by invoking the analogy with direct-form digital filter structures. The special case of all-pass filter realisation derived from the proposed universal filter needs additional hardware for realising the feed-forward coefficients. Hence alternative OTA-C based all-pass filter implementations based on Mitra-Hirano and Gray-Markel second-order digital filter structures are derived in which the coefficients that are used to realise the denominator are shared in the realisation of numerator also. All the proposed circuits are compared with the other structures available in the literature. The simulation results of the proposed circuits are also presented.

Two-Channel Quincunx QMF Banks Using Two-Dimensional Digital Allpass Filters

This paper presents a novel structure for the analysis and synthesis filters of two-channel quincunx quadrature mirror filter (QQMF) banks. This structure uses an appropriate combination of 2-D recursive digital allpass filters (DAFs) with symmetric half-plane (SHP) support regions. The proposed analysis/synthesis filters possess a 2-D doubly complementary half-band (DC-HB) property that facilitates the design and implementation of the proposed two-channel QQMF banks. Moreover, the proposed structure provides approximately linear-phase response without magnitude distortion. The design problem of the proposed QQMF banks is appropriately formulated to result in a linear optimization problem that only minimizes the linear-phase error associated with the 2-D SHP DAFs in the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> th-norm ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Lp</i> ) sense. Efficient design techniques are developed to solve the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Lp</i> optimization problem for finding the coefficients of the 2-D recursive SHP DAFs. Finally, we provide simulation results for illustration and comparison.