Abstract: A network automation system platform is described herein for carrying out a method for automated multi-node performance validation testing on a communications network. The method includes acquiring a test configuration for executing a multi-node performance validation test, wherein the test configuration identifies: a multi-node network performance test, carried out by an application layer, that specifies a technology-independent test script that is generic to particular technologies for providing performance validation-related services, and a node group upon which the multi-node network performance test is to be performed. The method further includes executing the multi-node network performance validation test by the application layer issuing requests to a core layer comprising a set of technology-specific services that issue, in accordance with the application layer requests, technology-specific commands to external services during performance validation of nodes within the node group.

Abstract: An auditory prosthesis comprising an actuator for providing mechanical stimulation to a recipient. The auditory prosthesis comprises a measurement circuit for use in determining the resonance peak(s) of the actuator. In an embodiment, the measurement circuit measures the voltage drop across the actuator and/or current through the actuator during a frequency sweep of the operational frequencies of the actuator. These measured voltages and/or currents are then analyzed for discontinuities that are indicative of a resonance peak of the actuator. In another embodiment, rather than using a frequency sweep to measure voltages and/or currents across the actuator, the measurement circuit instead applies a voltage impulse to the actuator and then measure the voltage and/or current across the actuator for a period of time after application of the impulse. The measured voltages and/or currents are then analyzed to identify resonance peak(s) of the actuator.

Abstract: A time domain reflectometry measurement apparatus and method is provided. Measurement data of a time domain reflectometry measurement are analyzed with respect to previously acquired empirical measurement data of error-free or faulty devices with known failures. In this way, failures can be identified in the device under test without the need of opening the device.

Abstract: This invention relates to a method of classification of images among different classes comprising: performing a dimensionality reduction step for said different classes on a training set of images whose classes are known, and then classifying one or more unknown images among said different classes with reduced dimensionality, said dimensionality reduction step being performed on said training set of images by machine learning including processing, for at least a first matrix and for at least a second matrix, a parameter representative of a product of two first and second matrices to assess to which given classes several first given images respectively belong: first matrix representing the concatenation, for said several first given images, of the values of the pixels of each said first given image, second matrix representing the concatenation, for said several first given images, of the values of differences between the pixels of each said first given image and the pixels of a second given image different fro

Abstract: A hands-off detection device includes: a first steering angle acquisition unit configured to acquire a first steering angle of a steering wheel; a second steering angle acquisition unit configured to acquire a second steering angle of a steering mechanism connected to the steering wheel via a torsion bar; a steering angle estimation unit configured to obtain an estimation angle of the first steering angle in a state where the steering wheel is not being grasped on a basis of the second steering angle; and a grasping state determination unit configured to determine a grasping state of the steering wheel on a basis of the frequency component of a angle difference between the first steering angle and the estimation angle and a reference frequency component being the frequency component of the angle difference in the state where the steering wheel is not being grasped.

Abstract: The subject technology relates to synthetic aperture to image leaks and sound sources. Other methods and systems are also disclosed. The subject technology includes drilling a wellbore penetrating a subterranean formation. The subject technology includes logging the wellbore using the stationary acoustic sensor and the moving acoustic sensor of the logging tool to obtain logged measurements, and obtaining an actual acoustic signal associated with a leak source in the wellbore using logged measurement data. The subject technology also includes determining a synthetic acoustic signal indicating an estimated leak source in the wellbore, and determining a correlation between the synthetic acoustic signal and the actual acoustic signal. The subject technology also includes generating a probability map from the determined correlation, in which the probability map indicates a likelihood of the leak source being located at a given location in the wellbore based on the probability map.

Abstract: Quantum file migration is disclosed. A first quantum computing system receives a request for the first quantum computing system to provide a quantum file that resides on the first quantum computing system to a second quantum computing system. The quantum file includes a qubit header portion and a qubit data portion. The qubit header portion is stored in one or more qubits implemented by the first quantum computing system, and the qubit data portion is stored in one or more other qubits. In response to the request, the first quantum computing system moves, to the second quantum computing system, the qubit header portion from the one or more qubits implemented by the first quantum computing system to one or more qubits implemented by the second quantum computing system.

Abstract: Example methods and systems for pre-validation of network configuration are disclosed. One example may comprise: detecting a request for network configuration to be implemented in a physical network environment; and identifying a set of physical network elements associated with the network configuration. The method may further comprise emulating the set of physical network elements to determine a physical network behaviour caused by the network configuration; and assessing validity of the network configuration based on the physical network behaviour. The set of physical network elements may be emulated using (a) multiple first physical network element emulators and (b) a second physical network element emulator that aggregates the multiple first physical network element emulators.

Abstract: This physical property value measurement device irradiates a specimen with a heating beam arrived at through intensity-pulse modulation of output light of a heating laser and irradiates the specimen with a temperature probe beam that is output light from a temperature probe laser and is delayed relative to the heating beam. The component of a detection signal for the reflected light of the temperature probe beam that is synchronous with the frequency of the intensity-pulse modulation is amplified using a lock-in amplifier, and a computer that performs regression analysis on the thermoreflectance signal obtained from the lock-in amplifier.

Abstract: Multi-phase interleaving control in a power supply device is accelerated. In addition, in accelerating the multi-phase interleaving control in the power supply device, acceleration in detecting a feedback signal and stabilization of a control system in a high-frequency band are promoted. Eliminating the need of the feedback signal according to a slow response detector, and using a detection signal obtained by a detector for detecting an AC signal capable of rapid response, thereby accelerating the multi-phase interleaving control in the power supply device. Then, the control system is stabilized, by satisfying a condition where gain is equal to 1 or less in a transfer function of the control system including an LC circuit, and a condition where a phase shift caused by dead time of switching time does not affect the sampling cycle.

Abstract: A computing device in tiding a data port for receiving power. A detector can determine if a cable attached to the data port is capable of providing power greater than a threshold level to the computing device. A controller can generate an error signal to alert a user that the cable does not provide power over the threshold level to the computing device.

Abstract: Techniques and systems for concurrent formal verification of logic synthesis are described. A synthesis tool can write intermediate checkpoint designs that embody the state of an integrated circuit (IC) design under synthesis as optimization progresses. Meanwhile, formal equivalence checking proceeds in parallel with synthesis and checks the intermediate checkpoint designs for equivalence.

Abstract: A digital receiver for decoding input data having three states includes a first input coupled to a first data line, a second input coupled to a second data line, a third input coupled to a third data line, and a fourth input coupled to a fourth data line. A first decoder is coupled to a first output, wherein the first decoder is for outputting first data signals in response to the sign of input data on the first data line minus input data on the second line. A second decoder is coupled to a second output, wherein the second decoder is for outputting second data signals in response to the sign of input data on the third data line minus input data on the fourth data line.

Abstract: One embodiment of the invention includes an accelerometer sensor system. The system includes a sensor comprising a proofmass and electrodes and being configured to generate acceleration feedback signals based on control signals applied to the electrodes in response to an input acceleration. The system also includes an acceleration component configured to measure the input acceleration based on the acceleration feedback signals. The system further includes an acceleration controller configured to generate the control signals to define a first scale-factor range associated with the sensor and to define a second scale-factor range associated with the sensor. The control system includes a calibration component configured to calibrate the accelerometer sensor system with respect to range-dependent bias error based on a difference between the measured input acceleration at each of the first scale-factor range and the second scale-factor range.

Abstract: A circuit design description may have registers and combinational gates. Circuit design computing equipment may perform register retiming on the circuit design description, whereby registers are moved across combinational gates, information about the register moves are recorded, and ultimately a modified circuit design description is created. The circuit design computing equipment may perform sequential equivalence checking to ensure that the circuit design description and the modified circuit design description are sequentially equivalent. To facilitate the sequential equivalence checking, the circuit design computing equipment may augment the two circuit design descriptions based on the information recorded during register retiming.

Abstract: In a sensor signal processing apparatus, a control unit executes at least one of a temperature measurement process and a calculation process in parallel with a signal conversion process. In the temperature measurement process, the control unit causes a second A/D converter to execute the A/D conversion of a temperature signal. In the calculation process, the control unit calculates an offset and a conversion gain of a first A/D converter base on an A/D conversion value output from the second A/D converter and pre-prepared temperature characteristic data of a physical quantity sensor. In the signal conversion process, the control unit sets the calculated offset and the calculated conversion gain to the first A/D converter, and causes the first A/D converter to execute the A/D conversion of the sensor signal.

Abstract: A circuit and method for controlling internal test mode entry of an Asynchronous Static Random Access Memory (ASRAM) chip wherein the circuit includes an address code comparator for detecting whether address codes inputted via an address bus of the ASRAM chip match a predefined validation code; a test mode detector for determining whether to let the ASRAM chip enter into an internal test mode; a test mode clock generator for generating a clock signal for the test mode decoder; and a test mode decoder for generating a test control signal. The circuit of the present application uses the existing pins of the ASRAM chip to input a special section of codes to trigger the ASRAM to enter into its internal test mode, thereby reducing the difficulty of testing the products.

Abstract: A method includes receiving data associated with operation of an industrial process system. The method also includes identifying a model defining a behavior of the industrial process system using the data, an orthonormal bases function, and an ordinal spline bases function. The orthonormal bases function can be generated using estimated poles of the industrial process system. The ordinal spline bases function can be generated using a specified set of cubic splines. The ordinal spline bases function can also be generated using a distribution of knots and multiple ordinal spline functions associated with the knots. More knots can be associated with a more nonlinear portion of the industrial process system, and fewer knots can be associated with a less nonlinear portion or a linear portion of the industrial process system.

Abstract: Method and devices for testing a headphone with increased sensation are provided. The headphone can filter and amplify low frequency audio signals, which are then sent to a haptic device in the headphone. The haptic device can cause bass sensations at the top of the skull and at both ear cups. The testing system can evaluate the haptic and acoustic sensations produced by the headphone to evaluate if they have been properly assembled and calibrate the headphones if necessary.

Abstract: A control system for optimizing a chemical loop system includes one or more sensors for measuring one or more parameters in a chemical loop. The sensors are disposed on or in a conduit positioned in the chemical loop. The sensors generate one or more data signals representative of an amount of solids in the conduit. The control system includes a data acquisition system in communication with the sensors and a controller in communication with the data acquisition system. The data acquisition system receives the data signals and the controller generates the control signals. The controller is in communication with one or more valves positioned in the chemical loop. The valves are configured to regulate a flow of the solids through the chemical loop.

Abstract: The present invention is directed to an apparatus and method for remotely measuring surface air pressure. In one embodiment, the method of the present invention utilizes the steps of transmitting a signal having multiple frequencies into the atmosphere, measuring the transmitted/reflected signal to determine the relative received power level of each frequency and then determining the surface air pressure based upon the attenuation of the transmitted frequencies.

Abstract: A continuous scanning method employs one or more moveable sensors and one or more reference sensors deployed in the environment around a test subject. Each sensor is configured to sense an attribute of the test subject (e.g., sound energy, infrared energy, etc.) while continuously moving along a path and recording the sensed attribute, the position, and the orientation of each of the moveable sensors and each of the reference sensors. The system then constructs a set of transfer functions corresponding to points in space between the moveable sensors, wherein each of the transfer functions relates the test data of the moveable sensors to the test data of the reference sensors. In this way, a graphical representation of the attribute in the vicinity of test subject can be produced.

Abstract: A portable medical monitor system generates a current calibration curve for generating the estimate of the level of an analyte, such as glucose, being monitored. The current calibration curve is based on at least two measured data values of the level being monitored. The system determines a transformation function based on the calibration curve and at least one preceding calibration curve such that the transformation function produces a predictive calibration curve, and generates an estimated level value of the level being monitored, based on sensor output from a sensor associated with the portable medical monitor system, in accordance with the predictive calibration curve.

Abstract: In one embodiment, a method for testing a cable includes receiving a read-signal profile read at a receiving-end of a cable upon an initial test signal being input to a sending end of the cable, calculating a cross-correlation function between the read-signal profile and a matched filter output, and determining a peak value of the cross-correlation function. In another embodiment, a system includes a device, the device including logic for receiving a read-signal profile read at a receiving-end of the cable upon an initial test signal being input to a sending end of the cable, logic for calculating a cross-correlation function between the read-signal profile and a matched filter output, logic for determining a peak value of the cross-correlation function, and logic for storing the peak value to a computer readable medium. Other methods, systems, and computer program products are also described according to various embodiments.

Abstract: The present invention relates to a method and an arrangement based on two-port network (TPN) theory that allows analytically estimating the loop transfer function from open and short-circuited input impedance measurements, e.g. single ended line transmission (SELT) measurements, by utilizing the fact that the line under test (LUT) can be considered reciprocal and by assuming that the LUT is symmetric. Hence, by using the present invention and an estimation of the noise on the line, the attainable bit rate at the customer premises can be determined by means of SELT measurements at the CO. The transfer function of a telephone copper-loop is estimated regardless of its topology by impedance measurements from the CO side. Specifically, such estimation is carried out from the calculation of the transmission parameters of loop, which are expressed only in terms of open and short-circuited input impedance measurements at the CO when reciprocity and symmetry is assumed.

Abstract: A wireless electronic device may serve as a device under test in a test system. The test system may include an array of over-the-air antennas that can be used in performing over-the-air wireless tests on the device under test (DUT). A channel model may be used in modeling a multiple-input-multiple-output (MIMO) channel between a multi-antenna wireless base station and a multi-antenna DUT. The test system may be configured to perform over-the-air tests that emulate the channel model. A design and analysis tool may be used to identify an optimum over-the-air test system setup. The tool may be used in converting a geometric model to a stochastic model for performing conducted tests. The tool may be used in converting a stochastic model to a geometric model and then further convert the geometric model to an over-the-air emulated stochastic model. The over-the-air emulated stochastic model may be used in performing conducted tests.

Abstract: The present invention is a method for capturing a cooling transfer function for a thermally-isolated, self-heating device. The method includes causing the device to undergo a plurality of successive heat-up cycles and cool-down cycles. The method further includes changing durations of time of the successive cool-down cycles. The method further includes deducing the cooling transfer function based upon temperature measurements for the device obtained at the end of the successive cool-down cycles (ex.—at the beginning of the successive heat-up cycles) of the device. The method thereby allows for capture of the cooling transfer function without direct observation of the cooling transfer function.

Abstract: A control system for optimizing a chemical loop system includes one or more sensors for measuring one or more parameters in a chemical loop. The sensors are disposed on or in a conduit positioned in the chemical loop. The sensors generate one or more data signals representative of an amount of solids in the conduit. The control system includes a data acquisition system in communication with the sensors and a controller in communication with the data acquisition system. The data acquisition system receives the data signals and the controller generates the control signals. The controller is in communication with one or more valves positioned in the chemical loop. The valves are configured to regulate a flow of the solids through the chemical loop.

Abstract: In one embodiment, a method for testing a cable includes receiving a read-signal profile read at a receiving-end of a cable upon an initial test signal being input to a sending end of the cable, calculating a cross-correlation function between the read-signal profile and a matched filter output, and determining a peak value of the cross-correlation function. In another embodiment, a system includes a device, the device including logic for receiving a read-signal profile read at a receiving-end of the cable upon an initial test signal being input to a sending end of the cable, logic for calculating a cross-correlation function between the read-signal profile and a matched filter output, logic for determining a peak value of the cross-correlation function, and logic for storing the peak value to a computer readable medium. Other methods, systems, and computer program products are also described according to various embodiments.

Abstract: An apparatus for measuring s-parameters using as few as one pulser and two samplers is described. The apparatus calibrates itself automatically using the internal calibration standards.

Abstract: Disclosed is a test system for determining a frequency response of a virtual power plant connected to a utility grid and including a plurality of distinct power plants. The test system includes a test sequence module for providing a frequency test sequence. The frequency test sequence includes a set of frequency test values; and an injection unit for injecting values of the frequency test sequence simultaneously to nodes of the virtual power plant. A node of the virtual power plant includes any of: a power production unit of a power plant, a power storage unit of a power plant, a plant controller of a power plant. Further described are a virtual power plant and a method of testing a frequency response of a virtual power plant.

Abstract: A method that measures performance of an information appliance comprises a test module receiving, from a client, and recording a request for processing of a sample data by an information appliance. The test module sends the sample data received from the client to the information appliance for processing. If a request to a backend application is present, the test module also sends the request to the backend application for processing and receives and records a response from the backend application. The test module sends the response from the backend application to the information appliance for processing. A generated correlation ID is used to update a performance data table with start time and a stop time of a response for transaction sample data processed by the information appliance.

Abstract: Disclosed are systems and methods for prognostic health management (PHM) of electronic systems. Such systems and methods present challenges traditionally viewed as either insurmountable or otherwise not worth the cost of pursuit. The systems and methods are directed to the health monitoring and failure prediction of electronic systems, including the diagnostic methods employed to assess current health state and prognostic methods for the prediction of electronic system failures and remaining useful life. The disclosed methodologies include three techniques: (1) use of existing electronic systems data (circuit as a sensor); (2) use of available external measurements as condition indicators and degradation assessor; and (3) performance assessment metrics derived from available external measurements.

Abstract: A method and a device for determining a reaction signal for a selected location in an information processing system (2) in response to at least one input signal (XIn) over an application period T. The effect of an input signal (XIn) on the information processing system is determined by: a) applying input signal(s) (X) to the information processing system (2), b) detecting output signal(s) (Yout) associated with a selected location in the information processing system in response to the input signal(s) (XIn), c) forming a value set (XIn, YOut, Zt) for an output signal (YOut) at the selected location in response to an input signal (XIn) for a given time (Zt), and d) determining the reaction signal (YOutMax) for the selected location.

Abstract: An adjustment test apparatus for AI module is disclosed, which includes a signal generator supplying analog electric quantity to a plurality of the same type of AI modules, and a maintenance PC connected to each AI module, the maintenance PC being connected to each AI module through a USB hub having a port corresponding to each AI module and a USB-RS232 converter connected to each port, the maintenance PC having a function of selecting a port to communicate with each AI module, and a function of monitoring a digital output value corresponding to an input signal provided by the signal generator to each AI module at the time of communication and setting each AI module to correct the output value to a proper value.

Abstract: A method is provided for de-embedding measurements from a given network containing mixtures of devices with known and unknown S-parameters given a description of the network and the known S-parameters of the overall system.

Abstract: A control system for industrial water systems that utilizes multiple measurements of information and models to decide optimal control actions to maximize corrosion/scaling/fouling inhibition and particulate dispersancy performance and minimize cost of water and treatment chemicals. This system is capable of automatic operation for a wide range of process conditions, ensures multiple performance objectives, achieves robust operation under a variety or un-measurable disturbances and achieves the least costly solution delivery.

Abstract: A method is provided for preventing islanding of a power source connected to an electric AC grid via an interface. The method senses an output voltage waveform of the interface, controls an output current waveform of the interface to track a reference current waveform having a mathematical relationship with the sensed output voltage waveform, and discontinues the output current waveform when the output voltage waveform is sensed to be outside a predetermined waveform range.

Abstract: Embodiments provide histogram-based methods and system to estimate the transfer function of an ADC, and subsequently to linearize a non-linear ADC transfer function. Embodiments include blind algorithms that require no a priori knowledge of the input signal distribution. Embodiments can be implemented using cumulative (i.e., cumulative distribution function (CDF)) or non-cumulative (i.e., probability density function (PDF)) histograms. According to embodiments, a non-linear transfer function can be estimated by linearly approximating successive local intervals of the transfer function. Linearly approximated successive local intervals of the transfer function can then be used to fully characterize and closely estimate the transfer function.

Abstract: A verification tool receives a finite precision definition for an approximation of an infinite precision numerical function implemented in a processor in the form of a polynomial of bounded functions. The verification tool receives a domain for verifying outputs of segments associated with the infinite precision numerical function. The verification tool splits the domain into at least two segments, wherein each segment is non-overlapping with any other segment and converts, for each segment, a polynomial of bounded functions for the segment to a simplified formula comprising a polynomial, an inequality, and a constant for a selected segment. The verification tool calculates upper bounds of the polynomial for the at least two segments, beginning with the selected segment and reports the segments that violate a bounding condition.

Abstract: A method and device for high speed broadband testing of systems and substances using a binary, spectrally sparse sequence (SSS) as a periodic excitation waveform. The sequences with controllable frequency and magnitude spectra content are designed by component manipulation method or by edge manipulation method. The excitation waveform is typically pre-calculated, and kept in waveform memory, from where it is shifted out into digital to physical quantity converter (DQC). The sparse spectrum of the SSS makes it easy to create plenty of uncorrelated frequency sets with adjacent, but sufficiently different frequencies to form multi-path test systems, where all the paths can be measured simultaneously. The response of the sample under test (SUT) is sampled and the complex transfer function is calculated directly or indirectly via Impulse Response by Discrete Fourier Transform technique and its derivatives. The sequence bit interval and sampling interval have a predetermined ratio.

Abstract: A testing system includes a computer system and an enhanced small form-factor pluggable (SFP+) transceiver. The computer system send a testing data to the SFP+ transceiver via an SFP+ interface to be tested. The SFP+ transceiver includes a loopback address and receives the testing data and returns the testing data to the computer system via the loopback address. The computer system compares the returned testing data and the testing data it sends to determine whether or not there is data loss occurring.

Abstract: A method for predicting a value of a first variable based on values of a plurality of additional variables. The method is usable in, for example, predicting by-products of a process based on values of variables relating to operation of the process.

Abstract: A method and system for test automation is described. The method may include creating a test case on a client computer; generating expected testing results by manually executing the test case on a computer system; performing automated testing on the computer system using the test case to generate automated testing results; validating the test case by comparing the automated testing results with the expected testing results; marking the test case as automatable, if the automated testing results match the expected testing results; and storing the automatable test case for later execution.

Abstract: A dimension-gauging system to determine at least one dimension of a non-ferrous, electrically conducting object produces a magnetic field inside the object and changes the excitation of the magnetic field. A signal processing unit measures the reaction of the magnetic field to the change in excitation, obtains an actual field transfer function between the excitation and the measured field reaction and determines the at least one dimension of the object by fitting the measured field transfer function to a predetermined field transfer function, where the predetermined field transfer function represents the dynamic behavior between the excitation and the measured field reaction with the one dimension as a parameter.

Abstract: A test structure for gathering switching history effect statistics includes a waveform generator circuit that selectively generates a first test waveform representative of a 1SW transistor switching event, and a second test waveform representative of a 2SW transistor switching event; and a history element circuit coupled to the waveform generator circuit, the history element circuit including a device under test (DUT) therein, and a variable delay chain therein, wherein a selected one of the first and second test waveforms are input to the DUT and the variable delay chain; wherein the history element circuit determines fractional a change in signal propagation delay through the DUT between the 1SW and 2SW transistor switching events, with the fractional change in signal propagation delay calibrated with timing measurements of a variable frequency ring oscillator; and wherein the test structure utilizes only external low-speed input and output signals with respect to a chip.

Abstract: A method and apparatus for modeling the characteristics of memristor devices. The invention provides methods and an apparatus for accurately characterizing the linear and non-linear Lissajous current-voltage behavior of actual memristor devices and incorporating such behavior into the resultant model. The invention produces a model that is adaptable to large scale memristor device simulations.

Abstract: The systems and methods described herein allow for automatic identification experiments in a closed loop, where the old control strategy, already tuned and tested, is utilized. The strategy is modified to inject additional signal optimized for identification. The experimenting time may be reduced by performing only those system manipulations which explore model uncertainties important to potential degradation of controller performance by discrepancy between the system and the model. The disruptions are reduced by keeping the control loop closed, which eliminates waiting for steady state before applying steps to the inputs and reduces the risk of process limits crossing. The energy of additional signal can be set to meet the maximum allowable disruption requirements. The energy of additional signal is in a direct relation to the speed of identification related information gathering. It can be varied in time to follow the needs of system operators.

Abstract: An electrical wire includes a core comprising an electrically conductive material that conducts electricity along the length of the electrical wire. The core also includes an acoustic conductive material that conducts acoustic waves along the length of the electrical wire. The core also includes an acoustic waveguide that provides internal reflection for the acoustic waves conducted through the core, and that guides the acoustic waves along the length of the electrical wire. The response acoustic wave signals may be compared against a failure model for the wire in order to determine the reliability of the electrical wire.

Abstract: The invention relates to a process for determining an averaged frequency-dependent transfer function for a perturbed linear time-invariant system by means of an evaluation device, wherein the process comprises providing frequency-dependent reference signals derived from excitations input in a linear time-invariant system, providing frequency-dependent measuring signals for the linear time-invariant system associated with the frequency-dependent reference signals, and determining an averaged frequency-dependent transfer function for the linear time-invariant system, in that, using signal deconvolution of mutually associated measuring and reference signals, frequency-dependent transfer functions are determined and the frequency-dependent transfer functions are averaged, and wherein during determination of the averaged frequency-dependent transfer function at least a part of the determined frequency-dependent transfer functions is included in the averaging corresponding to a respectively associated frequency-dep