scispace - formally typeset
Search or ask a question

Showing papers on "Linear phase published in 2008"


Journal ArticleDOI
TL;DR: A simple and efficient linear phase lead compensation repetitive control scheme for engineers to develop high-performance power converter systems that helps a repetitive controller to achieve faster convergence rate, higher tracking accuracy, and wider stability region.
Abstract: This paper presents a simple and efficient linear phase lead compensation repetitive control scheme for engineers to develop high-performance power converter systems. The linear phase lead compensation helps a repetitive controller to achieve faster convergence rate, higher tracking accuracy, and wider stability region. In the proposed scheme, the phase lead compensation repetitive controller is plugged into generic state-feedback-controlled converter systems. Its comprehensive synthesis, which involves principle, analysis, design, modeling, implementation, and experiments, is systematically and completely presented in great detail. A complete series of experiments is successfully carried out to verify the solution.

239 citations


Journal ArticleDOI
TL;DR: A linear phase FIR filter is designed using particle swarm optimization (PSO) and genetic algorithms (GA) and it is found that the PSO outperforms the GA in some of the presented design cases.

193 citations


Journal ArticleDOI
TL;DR: The results constitute the first quantitative assessment of the time course of phase information processing by the human visual brain and are interpreted in a framework that focuses on image statistics and single-trial analyses.
Abstract: The present paper examines the visual processing speed of complex objects, here faces, by mapping the relationship between object physical properties and single-trial brain responses. Measuring visual processing speed is challenging because uncontrolled physical differences that co-vary with object categories might affect brain measurements, thus biasing our speed estimates. Recently, we demonstrated that early event-related potential (ERP) differences between faces and objects are preserved even when images differ only in phase information, and amplitude spectra are equated across image categories. Here, we use a parametric design to study how early ERP to faces are shaped by phase information. Subjects performed a two-alternative force choice discrimination between two faces (Experiment 1) or textures (two control experiments). All stimuli had the same amplitude spectrum and were presented at 11 phase noise levels, varying from 0% to 100% in 10% increments, using a linear phase interpolation technique. Single-trial ERP data from each subject were analysed using a multiple linear regression model. Our results show that sensitivity to phase noise in faces emerges progressively in a short time window between the P1 and the N170 ERP visual components. The sensitivity to phase noise starts at about 120–130 ms after stimulus onset and continues for another 25–40 ms. This result was robust both within and across subjects. A control experiment using pink noise textures, which had the same second-order statistics as the faces used in Experiment 1, demonstrated that the sensitivity to phase noise observed for faces cannot be explained by the presence of global image structure alone. A second control experiment used wavelet textures that were matched to the face stimuli in terms of second- and higher-order image statistics. Results from this experiment suggest that higher-order statistics of faces are necessary but not sufficient to obtain the sensitivity to phase noise function observed in response to faces. Our results constitute the first quantitative assessment of the time course of phase information processing by the human visual brain. We interpret our results in a framework that focuses on image statistics and single-trial analyses.

95 citations


Journal ArticleDOI
TL;DR: An extension of Nomarski differential interference contrast microscopy enables isotropic linear phase imaging through the combination of phase shifting, two directions of shear, and Fourier space integration using a modified spiral phase transform.
Abstract: An extension of Nomarski differential interference contrast microscopy enables isotropic linear phase imaging through the combination of phase shifting, two directions of shear, and Fourier space integration using a modified spiral phase transform. We apply this method to simulated and experimentally acquired images of partially absorptive test objects. A direct comparison of the computationally determined phase to the true object phase demonstrates the capabilities of the method. Simulation results predict and confirm results obtained from experimentally acquired images.

83 citations


Journal ArticleDOI
TL;DR: In this paper, a planar UWB filter with circular slots in ground is presented and the authors used a new technique by etching a wideband circular-shape slot resonator in the ground plane of the filters.
Abstract: In this paper, miniature planar UWB filters with circular slots in ground is presented and we are using a new technique by etching a wideband circular-shape slot resonator in the ground plane of the filters. The proposed filters have compact size of 15 × 12.4 mm2. Two filters are introduced and the final design achieves flat insertion loss and linear phase of S12 throughout the passband (3.14–8.28 GHz) but occasional slight ripple occurs. Two different results are shown and the minimum insertion loss is less than 0.13 dB for both of presented filters.

75 citations


Journal ArticleDOI
01 Jan 2008
TL;DR: In this article, a coherent optical phase-locked loop (PLL) was proposed for linear phase demodulation at low frequency and a coherent coherent receiver was demonstrated at high frequency.
Abstract: In this paper, we present a coherent receiver based on an optical phase-locked loop (PLL) for linear phase demodulation. The receiver concept is demonstrated at low frequency. For high-frequency operation, monolithic and hybrid integrated versions of the receiver have been developed and experimentally verified in an analog link. The receiver has a bandwidth of 1.45 GHz. At 300 MHz, a spurious free dynamic range (SFDR) of 125 dB ldr Hz2/3 is measured.

74 citations


Journal ArticleDOI
TL;DR: Low residual timing jitter of 10 GHz pulses from a 1.55 ?
Abstract: We demonstrate low residual timing jitter of 10 GHz pulses from a 1.55 ?m optical frequency comb generator based on a doubly-resonant electro-optic modulator. The comb spectral phase is shown to be linear but of different slopes for the two sides of the optical spectrum. The linear phase delay predicts well the measured timing delay of the two pulse trains from the comb generator. The pulse timing jitter is analyzed, and we illustrate that the pump laser's linewidth plays a dominant role in the timing jitter. For Fourier frequencies from 1 Hz to 10 MHz, integrated residual timing jitter at 10 GHz was reduced from approximately 94 fs to approximately 8 fs when the pump laser's linewidth was reduced from approximately 10 MHz to approximately 1 kHz. An electronic servo was then used to stabilize the Fabry-Perot cavity in the comb generator. Integrated residual timing jitter was further reduced to approximately 6 fs, and the corresponding residual phase noise power density is -105 dBc/Hz at 1 Hz frequency offset from the 10 GHz pulse carrier.

70 citations


Journal ArticleDOI
TL;DR: In this article, a dual-band bandpass filter using defected stepped impedance resonator (DSIR) and microstrip step impedance resonators (MSIR) is proposed.
Abstract: This letter presents a novel approach to design dual-band bandpass filter by using defected stepped impedance resonator (DSIR) and microstrip stepped impedance resonator (MSIR). A pair of MSIRs on the upper plane forms a cross coupled filtering passage, and a pair of DSIRs at the lower plane constructs a linear phase filtering passage. Both of them are fed by a common T-shaped microstrip feed line with source-load coupling. Then they are directly combined to construct a compact dual-band filter with two passbands centering at 2.35 GHz and 3.15 GHz, respectively. The measurement results agree well with the full-wave electromagnetic designed responses.

66 citations


Journal ArticleDOI
TL;DR: A group of multi-step phase calculation algorithms for evaluation of interferometric measurements using the phase-shifting technique, with a constant but arbitrary phase shift between captured frames of the irradiance of the interference field is proposed.

61 citations


Journal ArticleDOI
TL;DR: A systematic study of the dependence of the excitation efficiency on the phase dispersion of theexcitation pulses is presented, which reveals surprising opportunities for improved pulse sequence performance.

59 citations


Patent
Zhenning Tao1, Lei Li1, Hisao Nakashima1
20 Nov 2008
TL;DR: In this article, a phase error estimator, a coherent receiver and a phase estimation method are presented, where the phase error estimation consists of a pre-decider, for judging a phase of data in said base band electric signal in accordance with said feedback phase error; a phase-error complex value extracting section, for extracting a real part and an imaginary part of the phase errors extracted by the predecider.
Abstract: The present invention relates to a phase error estimator, a coherent receiver and a phase error estimating method. The phase error estimator estimates a phase error in an inputted base band electric signal and feeds back said phase error; said phase error estimator comprises: a pre-decider, for judging a phase of data in said base band electric signal in accordance with said feedback phase error; a phase error complex value extracting section, for extracting a real part and an imaginary part of the phase error in accordance with the judgment result of said pre-decider; a phase error determining section, for determining said phase error in accordance with the real part and the imaginary part of the phase error extracted by the phase error complex value extracting section; and a time delay feeding back section, for delaying said phase error by N number of symbols and feeding back the delayed phase error to said pre-decider, wherein N is an integer greater than 1.

Journal ArticleDOI
TL;DR: In this paper, a phase field model was proposed to describe the Rayleigh-Taylor instability of two immiscible fluids in the limit of small Atwood numbers by means of a phase-field description, where the sharp fluid interface is replaced by a thin, yet finite, transition layer where the interfacial forces vary smoothly.
Abstract: The Rayleigh--Taylor instability of two immiscible fluids in the limit of small Atwood numbers is studied by means of a phase-field description. In this method the sharp fluid interface is replaced by a thin, yet finite, transition layer where the interfacial forces vary smoothly. This is achieved by introducing an order parameter (the phase field) whose variation is continuous across the interfacial layers and is uniform in the bulk region. The phase field model obeys a Cahn--Hilliard equation and is two-way coupled to the standard Navier--Stokes equations. Starting from this system of equations we have first performed a linear analysis from which we have analytically rederived the known gravity-capillary dispersion relation in the limit of vanishing mixing energy density and capillary width. We have performed numerical simulations and identified a region of parameters in which the known properties of the linear phase (both stable and unstable) are reproduced in a very accurate way. This has been done both in the case of negligible viscosity and in the case of nonzero viscosity. In the latter situation only upper and lower bounds for the perturbation growth-rate are known. Finally, we have also investigated the weakly-nonlinear stage of the perturbation evolution and identified a regime characterized by a constant terminal velocity of bubbles/spikes. The measured value of the terminal velocity is in perfect agreement with available theoretical prediction. The phase-field approach thus appears to be a valuable tecnhique for the dynamical description of the stages where hydrodynamic turbulence and wave-turbulence enter into play.

Patent
15 Apr 2008
TL;DR: In this paper, an array of individual phase comparators, all operating at essentially the same operating point, are used to interpolate two adjacent phase outputs of a multi-phase VCO.
Abstract: A novel interpolating phase detector for use in a multiphase PLL is described comprising an array of individual phase comparators, all operating at essentially the same operating point which permits the circuits to be designed simultaneously for high speed and for low power consumption. Two adjacent phase outputs of a multi-phase VCO may be selected and interpolated in between, by selectively attaching a variable number of phase comparators to each phase output and summing their phase error outputs. By varying the number of phase comparators attached to each phase output, interpolation can be achieved with high linearity.

Patent
02 Jun 2008
TL;DR: In this article, variable phase ring oscillators are used to provide a linear phase progression between adjacent elements in an antenna array by providing a symmetric ring configuration of tuned amplifiers and a single phase shifter.
Abstract: Variable phase ring oscillators are described that provide a linear phase progression between adjacent elements in an antenna array by providing a symmetric ring configuration of tuned amplifiers and a single phase shifter. The ring topology is coupled to a single PLL that allows for direct modulation and demodulation of arbitrary waveforms without using RF up/down converting mixers. The PLL distributes the transmit waveforms to all antenna elements in the transmit mode and combines the received waveforms in the receive mode without any complicated power distribution network. Ultra-wideband architectures and methods are described that utilize a first reference signal source, a VPRO, and a second reference signal source. Related methods are controlling an array and beam steering are also described.

Journal ArticleDOI
TL;DR: An eigen filter-based approach for the design of two-channel linear-phase FIR perfect-reconstruction (PR) filter banks and shows that, by an appropriate choice of the length of the filters, it can ensure the existence of a solution to the constrained eigenfilter design problem for the complementary-synthesis filter.
Abstract: We present an eigenfilter-based approach for the design of two-channel linear-phase FIR perfect-reconstruction (PR) filter banks. This approach can be used to design 1-D two-channel filter banks, as well as multidimensional nonseparable two-channel filter banks. Our method consists of first designing the low-pass analysis filter. Given the low-pass analysis filter, the PR conditions can be expressed as a set of linear constraints on the complementary-synthesis low-pass filter. We design the complementary-synthesis filter by using the eigenfilter design method with linear constraints. We show that, by an appropriate choice of the length of the filters, we can ensure the existence of a solution to the constrained eigenfilter design problem for the complementary-synthesis filter. Thus, our approach gives an eigenfilter-based method of designing the complementary filter, given a ldquopredesignedrdquo analysis filter, with the filter lengths satisfying certain conditions. We present several design examples to demonstrate the effectiveness of the method.

Patent
11 Feb 2008
TL;DR: In this article, the phase error performance in a phase locked loop (PLL) at integer channels is minimized by adjusting the phase of the interfering signal such that its impact on the reference signal is minimized.
Abstract: A novel and useful apparatus for and method of minimizing the impact of interference on the phase error performance in a phase locked loop (PLL) at integer channels by adjustment of the phase of the interfering signal such that its impact on the reference signal is minimized. Phase control is achieved by use of the digital architecture of the ADPLL and its insensitivity to an arbitrary phase bias introduced between its digitally represented output and reference phase signals. The optimal phase relationship for each integer channel is determined through a calibration procedure in which the phase is swept and the optimal phase is recorded. Before the transmission of a payload on an integer channel, the phase relationship between the output RF signal and the input reference signal is adjusted to the value found to be optimal for that frequency, based on the values previously recorded during the calibration procedure.

Proceedings ArticleDOI
08 Dec 2008
TL;DR: A comparative study between genetic algorithm and particle swarm optimization in FIR filter design demonstrates that PSO is better than GA, not only in the convergence speed but also in the performance of the filter.
Abstract: A comparative study between genetic algorithm and particle swarm optimization in FIR filter design is presented in this paper. FIR filter design involves multi-parameter optimization, on which the existing optimization algorithms donpsilat work efficiently. Given the filter specification to be designed, both algorithms generate a set of filter coefficients and try to meet the ideal frequency characteristic. For the problem at hand, the simulation of designing FIR filters have been done and the simulation results demonstrate that PSO is better than GA, not only in the convergence speed but also in the performance of the filter.

Patent
02 May 2008
TL;DR: In this paper, a method for slice selection is provided in an MRI process, the method involves controlling a transmit array by adding low flip angle RF pulses interspersed between refocusing pulses that are used to move a k-space weighting function with respect to one or more B 1 fields used to deposit energy according to a desired K-space Weighting function.
Abstract: Herein a method for slice selection is provided in an MRI process, the method involves controlling a transmit array by adding low flip angle RF pulses interspersed between refocusing pulses that are used to move a k-space weighting function with respect to one or more B 1 fields used to deposit energy according to a desired k-space weighting function. The low flip angle pulses deposit energy so that an envelope traced by the low flip angle pulses in the k-space weighting function is related to a desired spatially excited region of the sample volume, for example by a Fourier transform, if the phase encoding directions are linear axes that coordinatize the sample volume, and the B 1 fields have linear phase gradients.

Journal ArticleDOI
TL;DR: In this paper, a particle swarm optimization (PSO) algorithm was applied to design a higher-order differentiator that contains two different structures of even and odd orders, and four cases of linear phase finite impulse response (FIR) filters were designed to match the prescribed differentiation frequency response by using PSO algorithm.

Journal ArticleDOI
TL;DR: This paper presents a new optimization method for the design of various frequency-response-masking (FRM)-based linear-phase finite-impulse response (FIR) digital filters based on a batch back-propagation neural network algorithm (NNA), taken as a variable learning rate mode.

Journal ArticleDOI
TL;DR: It is demonstrated that successive application of the two‐step process to data from a dual‐echo Dixon technique provides a “1‐2 punch” to the overall phase errors and can overcome local water and fat separation failures that are observed when the region‐growing–based algorithm is applied alone.
Abstract: Large and spatially-linear phase errors along the frequency-encode direction may be induced by several common and hard-to-avoid system imperfections such as eddy currents. For data acquired in dual-echo Dixon techniques, the linear phase error can be more aggravated when compared to that acquired in a single echo and can pose challenges to a phase-correction algorithm necessary for successful Dixon processing. In this work, we propose a two-step process that first corrects the linear component of the phase errors with a modified Ahn-Cho algorithm (Ahn CB and Cho ZH, IEEE Trans. Med. Imaging 6:32, 1987) and then corrects the residual phase errors with a previously-developed region-growing algorithm (Ma J, Magn. Res. Med. 52:415, 2004). We demonstrate that successive application of the two-step process to data from a dual-echo Dixon technique provides a “1-2 punch” to the overall phase errors and can overcome local water and fat separation failures that are observed when the region-growing–based algorithm is applied alone. Magn Reson Med 60:1250–1255, 2008. © 2008 Wiley-Liss, Inc.

Patent
Jungo Arai1
06 Feb 2008
TL;DR: In this paper, a phase noise correction device for correcting phase noise generated in a local oscillator is presented. But the phase difference detection section detects a phase difference between the divided signal and the generated reference signal and gives a phase rotation to a baseband signal in the direction that cancels the phase noise according to the detected phase difference.
Abstract: A phase noise correction device having a function for accurately detecting a phase noise component and capable of reducing a load on a reception device is provided. A phase noise correction device for correcting a phase noise generated in a local oscillator includes: a division section that divides a signal generated in the local oscillator; a reference signal generation section that generates a signal of the same frequency as that of the divided signal; a phase difference detection section that detects a phase difference between the divided signal and the generated reference signal; and a phase noise correction section that gives a phase rotation to a baseband signal in the direction that cancels the phase noise according to the detected phase difference as a phase noise component.

Proceedings ArticleDOI
01 Sep 2008
TL;DR: A multirate architecture with linear phase low-pass filter working at low sampling rate is presented for removal of the baseline wander and the optimal decimation factor with respect to complexity and filter delay is determined.
Abstract: Baseline wander makes manual and automatic analysis of ECG records difficult, especially the measuring of ST-segment deviation. Since the spectrum of baseline wander and low frequency component of ECG signal usually overlaps, removing of baseline wander can cause distortion of important clinical information, particularly ST-segment distortion. The use of digital linear phase high-pass filter minimizes this undesirable effect, but it requires large computational complexity. A multirate architecture with linear phase low-pass filter working at low sampling rate is presented for removal of the baseline wander. Design tradeoff between transition band width and filter delay was considered. We determined the optimal decimation factor with respect to complexity and filter delay. For testing and assessment of behavior of baseline filter we used test signals, normal and wide QRS complexes with different heat rate.

Journal ArticleDOI
TL;DR: This paper proposes the design of VDFs with minimum integral squared error and constraints on the maximum error deviation in conjunction with flatness group delay specification or phase constraints, which allow the VDF's to have approximately linear phase, especially in the passband.
Abstract: In this paper, we consider the design of finite-impulse response variable digital filters (VDFs) with variable cutoff frequency or variable fractional delay. We propose the design of VDFs with minimum integral squared error and constraints on the maximum error deviation in conjunction with flatness group delay specification or phase constraints. These specifications allow the VDFs to have approximately linear phase, especially in the passband. As these specifications are required to be satisfied for all the filters generated by the VDF with controllable spectral characteristics, the linear constraints resulting from the flatness specification are relaxed to inequality constraints. To make the optimization problem tractable for the phase constrained problem, suitable approximations are employed in the paper. The design problem is formulated as an optimization problem with a quadratic cost function and infinite number of constraints. A numerical scheme with adaptive grid step size is proposed for solving the optimization problem.

Journal ArticleDOI
TL;DR: This paper presents a 5-Gb/s clock and data recovery (CDR) circuit which implements a calibration circuit to correct static phase offsets in a linear phase detector.
Abstract: This paper presents a 5-Gb/s clock and data recovery (CDR) circuit which implements a calibration circuit to correct static phase offsets in a linear phase detector. Static phase offsets directly reduce the performance of CDR circuits as the incoming data is not sampled at the center of the eye. Process nonidealities can cause static phase offsets in linear phase detectors by adversely affecting the circuits in a way which is difficult to design for, making calibration an attractive solution. Both the calibration algorithm and test chip implementation are described and measured results are presented. The CDR circuit was fabricated in a 0.18-mum, six metal layer standard CMOS process. With a pseudorandom bit sequence of 27 - 1 calibration improved the measured bit error rate from 4.6 x 10-2 to less than 10-13.

Proceedings ArticleDOI
08 Dec 2008
TL;DR: It is shown that as far as estimating the single sinusoid angle parameters is concerned, the phase of the received signal samples alone is a sufficient statistic, provided that the phase noise is modeled by the a posteriori PDF, which has a Tikhonov distribution.
Abstract: The exact statistical models for the measurement phase noise in estimating the frequency and phase of a single sinusoid over the additive white Gaussian noise channel are derived. The a posteriori probability density function (PDF) and the a priori PDF of the phase noise derived are given by explicit, closed-form expressions that are valid for arbitrary signal-to-noise ratios. It is shown that as far as estimating the single sinusoid angle parameters is concerned, the phase of the received signal samples alone is a sufficient statistic, provided that the phase noise is modeled by the a posteriori PDF, which has a Tikhonov distribution. Furthermore, we illustrate that the results derived can yield various phase noise models as special cases, and the underlying physical insights and interconnections that exist among these models are revealed. The application of these models to the design of linear minimum variance estimator is presented, and their estimation performances are compared through computer simulations.

Journal ArticleDOI
TL;DR: In this article, the authors derived the correlation functions of intrachannel four-wave mixing (IFWM)-induced phase and amplitude noises in phase-modulated optical communication systems and derived analytical approximations to the probability distribution of IFWM-induced phase noise for PSK and differential PSK systems.
Abstract: We have analytically derived the correlation functions of intrachannel four-wave mixing (IFWM)-induced phase and amplitude noises in phase-modulated optical communication systems. The phase and amplitude noises are correlated with each other for binary phase-shift keying (PSK) systems but uncorrelated for M-ary PSK systems with M > 2. We have also derived analytical approximations to the probability distribution of IFWM-induced phase noise for PSK and differential PSK systems. Furthermore, we have studied the performance of an optimal linear phase-noise predictor derived from the IFWM-induced phase-noise autocorrelation function. This yields a performance improvement of 1.8 dB when IFWM-induced phase noise is the dominant impairment, and an improvement of 0.8 to 1.2 dB in the presence of amplified spontaneous emission noise and nonlinear phase noise in typical terrestrial links.

Journal ArticleDOI
TL;DR: In this paper, a metamaterial-enabled approach is presented that allows one to engineer the dispersion of a log-periodic dipole array antenna (LPDA) to make it more suitable for wide bandwidth pulse transmission.
Abstract: A metamaterial-enabled approach is presented that allows one to engineer the dispersion of a log-periodic dipole array antenna (LPDA) to make it more suitable for wide bandwidth pulse transmission. By modifying the LPDA with electrically small transmission line metamaterial-based negative and positive phase shifters, the phase of each element of the LPDA are adjusted such that in the main beam direction, the phase shifts between each element approximates a linear phase variation. The performance characteristics of the resulting dispersion-engineered LPDA are obtained numerically with HFSS and MATLAB simulations. By measuring in the far field the fidelity between the actual transmitted pulse and the idealized output waveform, the required component values of the phase shifters are optimized. Significant improvements in the fidelity of the pulses transmitted are demonstrated with eight and ten element LPDAs.

Patent
Suguru Fujita1, Lei Huang1, Ping Luo1
30 Jan 2008
TL;DR: In this article, a phase shifter (174) adjusts the capacitance of a phase modulation device to correct an I/Q orthogonal shift and reduce degradation of the ON/OFF ratio.
Abstract: Provided is a modulation device which generates a phase modulation signal and an amplitude modulation signal and can correct an I/Q orthogonal shift and reduce degradation of the ON/OFF ratio. In the device, a phase shifter ( 174 ) controls voltage applied to a capacitor in accordance with a control signal outputted from a phase control unit ( 180 ) and adjusts the capacitance so as to shift the phase of a carrier generated by an oscillator ( 173 ). The phase control unit ( 180 ) estimates a phase shift of a phase shifter ( 174 ) in accordance with an output RF signal (S 140 ) by using the phase shift estimation method. Furthermore, the phase control unit ( 180 ) performs tuning of the phase shifter ( 174 ) according to the estimated value of the phase shift of the phase shifter ( 174 ) so that a phase difference between carries of an I signal (S 125 ) and a Q signal (S 135 ) is 90 degrees.

Journal ArticleDOI
22 Dec 2008-Chaos
TL;DR: It is established that the local maxima in the current correspond to the borders of these Arnold tongues; in this way, the link between optimal transport in ratchets and phase synchronization is established and the deterministic dynamics in the underdamped case is considered.
Abstract: The phenomenon of phase synchronization for a particle in a periodic ratchet potential is studied. We consider the deterministic dynamics in the underdamped case where the inertia plays an important role since the dynamics can become chaotic. The ratchet potential is tilted due to a constant external force and is rocking by an external periodic forcing. This potential has to be tilted in order to obtain a rotator or self-sustained nonlinear oscillator in the absence of the external periodic forcing; this oscillator then acquires an intrinsic frequency that can be locked with the frequency of the external driving. We introduced an instantaneous linear phase, using a set of discrete time markers, and the associated average frequency, and show that this frequency can be synchronized with the frequency of the driving. We calculate Arnold tongues in a two-dimensional parameter space and discuss their implications for the chaotic transport in ratchets. We show that the local maxima in the current correspond to the borders of these Arnold tongues; in this way we established a link between optimal transport in ratchets and phase synchronization.