Abstract: A measuring device for measuring the envelope power and the mean-power value of a high-frequency signal. The measuring device includes a detector for detecting the high-frequency signal and for generating an analog detector signal, an analog/digital converter for generating a digital signal and an evaluation device for evaluating the digital signal. A dither supply device for the supply of a dither signal is disposed between the detector and the analog/digital converter, and a dither elimination device for eliminating the dither signal is disposed between the analog/digital converter and the evaluation device. The dither supply device supplies a different dither signal for the measurement of the envelope power than for the measurement of the mean-power value.

Abstract: A method and a device for measuring the phase noise of a signal registers the measurement signal (V) with a given measurement frequency (f1) and with a superimposed phase noise (f1(t)), divides the measurement signal (V) into a first and second measurement signal (V1?, V2?), derives a first signal (V1) with a first frequency ((f1+f1(t))/N) reduced relative to the measurement frequency (f1) and the superimposed phase noise (f1(t)) and a second signal (V2) with a second frequency ((f1+f1(t))/M) reduced relative to the measurement frequency (f1) and the superimposed phase noise (f1(t)), determines a third signal (V3) with a third frequency (f3(t)) compensated by the measurement frequency (f1) relative to the first frequency ((f1+f1(t))/N) of the first signal (V1) and a fourth signal (V4) with a fourth frequency (f4(t)) compensated by the measurement frequency (f1) relative to the second frequency ((f1+f1(t))/M) of the second signal (V2) and determines a correlation spectrum from the third and fourth signal (V3,

Abstract: Provided is a spectrum analysis system that measures a signal component at each frequency of an input signal, comprising a sampling section that samples the input signal at prescribed bandwidths to digitize the input signal, and outputs a resulting digital output signal; a converting section that converts the digital output signal from the sampling section into the signal component at each frequency of a unit bandwidth; and an output section that (i) outputs the digital output signal output by the sampling section when a frequency span, which is a frequency range in which the measurement result of the signal component at each frequency of the input signal is output, is greater than or equal to a predetermined reference bandwidth and (ii) outputs the signal component at each frequency converted by the converting section when the frequency span is less than the predetermined reference bandwidth.

Abstract: An apparatus for measuring spectral components of a signal is described. The apparatus comprises a measurement acquisition unit configured to receive an input signal and to provide a measurement trace. The apparatus also comprises a model module configured to model one or more of a phase noise from the apparatus, a broadband noise from the apparatus, and a third order intermodulation (TOI) product from the apparatus. The apparatus also comprises a display configured to show one or more of the phase noise from the apparatus, the broadband noise from the apparatus, and the TOI product from the apparatus.

Abstract: A computationally implemented method comprises providing a plurality of spectral data display and manipulation options on a display displaying spectral data, the plurality of data display and manipulation options including providing a region further including a plurality of selectable tabs, and displaying a pictorial representation of the spectral data display and manipulation options, further including displaying the region further including a plurality of selectable tabs.

Abstract: A method for identifying and reducing spurious frequency components is provided. A method in accordance with at least one embodiment of the present disclosure may include generating a digital sinusoidal waveform at a direct digital synthesizer (DDS) and receiving the digital sinusoidal waveform at an audio digital-to-analog converter. The method may further include converting the digital sinusoidal waveform to an analog sinusoidal waveform containing spurious frequency components, combining the analog sinusoidal waveform with an analog distortion correction waveform to generate a composite output waveform and receiving the composite output waveform at notch filter circuitry. The method may also include filtering the composite output waveform to generate a filtered composite output waveform and amplifying a difference between the filtered composite output waveform and a signal from a circuit-under-test (CUT) to generate an amplified analog signal.

Abstract: A frequency characteristic measuring apparatus measures a device under test in which the frequency of an input signal and the frequency of an output signal differ from each other, simplifying the configuration of a tracking generator and peripheral circuits associated with the tracking generator, and simultaneously measuring the characteristics of the input signal and the output signal of the device under test. A spectrum analyzer has mixers, local oscillators and IF sections as first and second measuring units for measuring frequency characteristics of two input signals by performing frequency sweep in correspondence with a first or second frequency range, a mixer and an oscillator as a tracking generator section which operates by being linked to the frequency sweep operation in the first measuring unit, and a section which generates a trigger signal designating measurement start timing.

Abstract: Sets of time domain data of respective frequency bands from Fd-1 to Fd-n of a periodic input signal Fs are acquired. Sets of the time domain data of the common frequency band are extracted from the sets of the time domain data of the frequency bands Fd-1 and Fd-2 in the acquired frequency bands. Correlativity between the sets of the time domain data of the common frequency band is determined while shifting time relationship between the sets each other to identify the sets of time domain data having correspondence relationship. The sets of the time domain data having the correspondence relationship in the time domain data of the adjacent frequency band Fd-1 and Fd-2 are converted to the sets of the frequency domain data respectively, and the sets of the frequency domain data are combined to produce one set of combined frequency domain data.

Abstract: In a method of detecting a repetition frequency of a measured signal, in order to detect the waveform repetition frequency of the measured signal with high accuracy even in the presence of a frequency fluctuation in the measured signal, the repetition frequency of the measured signal acquired by the conventional method is used as a provisional repetition frequency, and the frequency change amount of the specified signal obtained in the case where the measured signal is sampled sequentially with a sampling frequency greatly changed from the provisional sampling frequency to generate a frequency fold at the time of sampling is detected. Based on the detected frequency change amount of the specified signal and the change amount of the sample number indicating how many times the frequency fold has occurred in the process, the error contained in the sampling number with a frequency fluctuation contained in the measured signal is calculated.

Abstract: A method is disclosed for analyzing an AC voltage signal with a transformation which transforms the signal from a representation in the time-domain to a representation in the frequency-domain. This transformation can be a fast Fourier transform, a discrete Fourier transform or a Laplace transform. By selecting a second higher sampling frequency which is an integer multiple of a first sampling frequency, the zero crossings of the AC voltage signal can be accurately determined.

Abstract: An apparatus and method to recognize tones from human singing or similar characteristics is described. The method used to recognize the tone tries to mimic how human brain interprets tones and reduces errors by use multiple combinations of trial and error to get the closest frequency of the tone.

Abstract: A signal generation circuit includes: a first signal source that generates a first signal; and a variable rate frequency divider section that generates a variable rate frequency-divided signal in which a first frequency-divided signal obtained by frequency-dividing the first signal by a first frequency dividing ratio and a second frequency-divided signal obtained by frequency-dividing the first signal by a second frequency dividing ratio temporally alternately appear in a specified mixing ratio.

Abstract: A frequency measurement device includes: a counter section that counts a supplied pulse stream signal to be measured at a predetermined time interval and outputs a stream of count values corresponding to the frequency of the signal to be measured; and a low-pass filter section that performs a filtering process on the stream of count values, the low-pass filter section including moving average filters in multiple stages, and an output of at least one moving average filter among the moving average filters in multiple stages is downsampled.

Abstract: Apparatus and methods are provided to allow multiple, possibly overlapping, regions of interest within a frequency spectrum to be defined, and managed. Each of these regions of interest may be selected for further testing or identification. Unselected regions are allowed to collapse into narrow bars so as not to interfere with the selected region. Multiple rows are provided to allow for the definition and selection of overlapping regions of interest. Furthermore, in some embodiments aid is provided for identifying the signal type by providing a list of signal type candidates based upon such parameters as region of interest bandwidth, region of interest center frequency and geographic location.

Abstract: A spectrum detection method, system and base station are provided, which relate to the field of communications technology, and improve the spectrum utilization in a cellular multi-hop network. The spectrum detection method includes: receiving an intermediate spectrum detection result sent by each node; and integrating the intermediate spectrum detection results to obtain a final spectrum detection result. The spectrum detection method, system, and base station are mainly applied to cellular multi-hop networks.

Abstract: Provided is a method of selecting a white Gaussian noise sub-band using singular value decomposition (SVD). The method includes selecting a first frequency band, verifying whether a signal is included in the selected first frequency band, determining the first frequency band as a target measurement frequency when the signal is not included in the selected first frequency band, and measuring a background radio noise in the determined target measurement frequency.

Abstract: Power measurements of a signal having a changing frequency are corrected by acquiring samples of the signal, matching the samples of the signal to a sequence of frequencies indexed to correction transforms, and applying the correction transforms to the samples of the signal. Additionally, an apparatus corrects power measurements of a signal having a changing frequency and includes an acquisition block for acquiring samples of the signal, a sequence controller for matching the samples of the signal to a sequence of frequencies indexed to correction transforms and a correction block for applying the correction transforms to the samples of the signal.

Abstract: An analyser for measuring the response of an electronic device (DUT 206) to an RF input signal from a signal generator 240a is described. An active load pull circuit 201 is connected to the DUT 206, which receives an output signal from the DUT 206 and then feeds a modified signal back to the DUT 206. The signal is modified by a signal processing circuit 237 in view of input signals x, y to control the magnitude gain and phase change effected by the feedback circuit 237. Thus, positive feedback loops are avoided and better control of the analyser is permitted. A network analyser, or other signal measuring device 242, logs the waveforms (from which s-parameters derived) observed at ports of the DUT 206, thereby allowing the behaviour of the DUT 206 under various load conditions to be analysed.

Abstract: A system comprising user interface software configured to provide a plurality of spectral data display and manipulation options on a display displaying spectral data, a user interface processor configured to display a pictorial representation of the spectral data display and manipulation options, and a user interface instruction engine configured to provide a plurality of data display and manipulation instructions to the user interface processor to provide display and manipulation of the displayed spectral data. The plurality of data display and manipulation instructions are received from a control device connected to a computing system and the manipulation of the displayed spectral data is based on a user response to the displayed spectral data manipulation options or a pre-determined selection of the displayed spectral data display manipulation options.

Abstract: A spectrogram mask trigger is generated in response to multiple or complex frequency events within a signal being monitored. A sequence of frequency masks over a period of time is generated according to a frequency trajectory, frequency hops or other complex frequency events expected in the signal to form a spectrogram mask. The spectrogram mask is then applied to multiple spectra or spectrogram of the signal to determine whether an anomalous frequency event has occurred within the time period or to identify a particular frequency pattern within the signal. Depending upon the results of the spectrogram mask application, the spectrogram mask trigger is generated for storing a block of data from the signal surrounding the triggering event for further analysis.

Abstract: The invention relates to a measuring device, especially for a machine tool and/or a manual measuring device, comprising a measuring unit (12a-d) that is adapted to measure and an external signal recognition unit (14a-d). The invention is characterized in that the external signal recognition unit (14a-d) is adapted to recognize an external signal during and/or prior to a measurement of the measuring unit (12a-d).

Abstract: A measuring device for measuring the envelope power and the mean-power value of a high-frequency signal. The measuring device includes a detector for detecting the high-frequency signal and for generating an analog detector signal, an analog/digital converter for generating a digital signal and an evaluation device for evaluating the digital signal. A dither supply device for the supply of a dither signal is disposed between the detector and the analog/digital converter, and a dither elimination device for eliminating the dither signal is disposed between the analog/digital converter and the evaluation device. The dither supply device supplies a different dither signal for the measurement of the envelope power than for the measurement of the mean-power value.

Abstract: Method and system for detecting magnetic contaminants in products (160). The product (160) is transported past magnetic sensors (170, 180) which return a first sensed signal S1 (172) and a second sensed signal S2 (182) being time-spaced received versions of the source signal produced by the product (160). From the sensed signals (172, 182) it is determined whether a magnetic contaminant has been detected. Gradiometry may be applied between the signals (172, 182). A so-called auto-cross-correlation comprising +/?(CC1+CC2?AC1?AC2) derived from the cross-correlation (CC1) of S1 with S2, the cross-correlation (CC2) of S2 with S1, the autocorrelation (AC1) of S1 and the autocorrelation (AC2) of S2, may be used to improve signal recovery from noise. The auto-cross-correlation may be applied in other applications.

Abstract: It is possible to provide a frequency characteristics measuring device which can simplify the configuration for performing a measurement and reduce the undue effort required for the measurement. A spectrum analyzer (10) includes: two sets of measuring units having mixers (110, 210), local oscillators (112, 212), and IF sections (120, 220) for separately measuring frequency characteristics of two input signals; a trigger generation section (310) which generates a trigger signal for specifying a measurement start timing in each of the two sets of measuring units; a sweep control section (300) which simultaneously sends an instruction to the two local oscillators (112, 212) when a trigger signal is inputted and performs a sweep control so that the two local oscillators (112, 212) output local oscillation signals of the same frequency at the same timing.

Abstract: A measurement system is provided for measuring a complex transfer function of a system under test. The measurement system comprises a signal source for generating an input signal to be applied to the system under test, a signal detection device for detecting a response signal of the system under test in response to the input signal; and a signal analysing system for determining the gain and phase shift of the system under test by comparing the response signal to the input signal. The signal analysing system includes phase adjustment means to adjust a relative phase difference of the detected response signal and input signal; and curve fitting means to identify a phase difference adjustment of the phase adjustment means which gives the best fit of the response signal to the input signal. The phase measurement of the response signal is determined from the best fit phase difference adjustment.

Abstract: In one embodiment, a spectral map for performing nonlinear calibration of a signal path is developed by 1) identifying a set of frequency locations for a set of particular output signal spurs that result from applying one-tone and two-tone input signals covering a bandwidth of interest to the signal path; 2) developing, based on the set of frequency locations, a spectral map for predistorting, in the frequency domain, signals that are applied to, or received from, the signal path in the time domain; and 3) saving the spectral map for performing nonlinear calibration of the signal path.

Abstract: A method of processing an input signal to perform frequency analysis is disclosed. The input signal comprises a desired signal and an interference signal. A crosslation is performed to generate a representation of the frequency content of the input signal. The representation comprises initial crosslation values predominantly corresponding to interference and subsequent crosslation values corresponding to the desired signal. For the crosslation values corresponding to interference, a maximum value and slope are calculated. These are used as parameter indicators of the interference and also to identify which values should be discarded in the processing of the desired signal. With the crosslation values corresponding to interference discarded, the remaining crosslation values are processed to calculate properties of the desired signal.

Abstract: Disclosed is a method of equalization of a vector/signal analyzer including: providing a structured test signal within a selected frequency range. The structured test signal includes a plurality of frequency components each having a respective amplitude and phase. The method includes inputting the test signal to the analyzer; the analyzer operating to condition the test signal; determining information representative of frequency distortion of the conditioned test signal introduced by the analyzer; generating a set of equalization coefficients based on the information representative of the frequency distortion, the set of coefficients corresponding to the selected frequency range; and storing the set of equalization coefficients and the correspondence of the set of coefficients to the selected frequency range.

Abstract: A system for measuring the time interval of a signal. The second signal has a frequency higher than a frequency of the first signal. According to one embodiment, the system includes an electronic circuit for determining an approximation of the time based on a period of the second signal and for determining an adjustment to the approximation based on the second signal and a third signal corresponding to the second signal and aligned with the first signal. The length of the adjustment is less than the period of the second signal.

Abstract: The process for measuring peak and power values of an audiofrequency signal S including: digitization of the original signal, calibration of the digitized signal, determination of update instants of the measurements of the signal on the basis of a criterion associated with the value of the signal itself, setting of a fast sequence for measuring the peak of the digitized and calibrated signal, setting of a fast sequence for measuring the power of the digitized and calibrated signal, acquisition of representative peak and power measurements of the digitized and calibrated signal according to the update instants of the signal, optimization of the fastness of the measurement according to the nature of the digitized and calibrated signal, optimization of the pertinence of the measurement on a digitized and calibrated, broad-band signal of a large dynamic range.

Abstract: Implementations are presented herein that include a test circuit and a reference circuit.

Abstract: Systems and methods may be provided for threshold determinations for spectrum sensing. The systems and methods may include receiving a false alarm rate, where the false alarm rate is associated with false occupancy identifications of a spectrum segment, determining a noise floor as a function of a noise figure and characteristics of a multi-resolution spectrum sensing (MRSS) window, and calculating a sensing threshold based at least in part upon the false alarm rate and the noise floor. The systems and methods may also include determining whether a portion of an RF spectrum is occupied based at least in part on the calculated sensing threshold.

Abstract: A method for spectral analysis of a signal (s1(t)) in several frequency bands with different frequency resolution adapts the two spectra of the signal (s1(t)) from adjacent frequency bands relative to one another in the transitional range of the two frequency bands. The associated device contains a unit for discrete convolution (3), which implements a smoothing of the discrete power spectra (|S1(k)|2) of the discrete signal (s1(k)) from adjacent frequency bands in the transitional range of the two frequency bands.

Abstract: A signal analyzer repetitively memorizes waveform data of a signal under test to detect peaks P1-P6 of the waveform data. Waveform widths of the waveform data at a mask reference level, or a predetermined level down from the respective peaks, are evaluated as mask reference widths and then masks of the respective peaks are set using the mask reference level and mask reference widths. Hence the masks are automatically set, so a user can easily obtain time domain data and/or frequency domain data including characterizing portions in the signal under test.

Abstract: A novel and useful apparatus for and method of local oscillator (LO) generation with non-integer multiplication ratio between the local oscillator and RF frequencies. The LO generation schemes presented are operative to generate I and Q square waves at a designated frequency while avoiding the well known issue of harmonic pulling. The input signal is fed to a synthesizer timed to a rational multiplier of the RF frequency L/N fRF. The clock signal generated is divided by a factor Q to form 2Q phases of the clock at a frequency of L(N*Q)fRF, wherein each phase undergoes division by L. The phase signals are input to a pulse generator which outputs a plurality of pulses. The pulses are input to a selector which selects which signal to output at any point in time. By controlling the selector, the output clock is generated as a TDM based signal. Any spurs are removed by an optional filter.

Abstract: A spectrum analyzer is provided with frequency-scalable circuit architectures that extend the bandwidth of the spectrum analyzer using an array of couplers. The array of couplers is distributed along the RF signal path at one end, and interfaced to one or more frequency-translation devices such as mixers or samplers at the other. In a first architecture, a single mixer is employed with an LO signal applied to one input and coupler outputs providing RF signals to another input, with switching controlled to select one coupler's RF output to provide to the mixer. In a second architecture, a separate mixer is used, one for each coupler RF signal, with switches selecting one of the mixer IF outputs to select a desired output frequency. Both the first and second embodiments eliminate switching and its associated loss and frequency limitations from the main RF signal path to enable wideband high-dynamic-range spectrum analysis.

Abstract: The invention relates to a measuring device comprising a signal unit (20) for emitting a measuring signal (22.1, 22.2) in a measuring frequency range (60, 62, 68, 70) adapted for measurement and an evaluation unit (36) for the spectral evaluation of an evaluation signal (34.1, 34.2) induced by the measuring signal (22.1, 22.2) to a measuring result. According to the invention, the measuring device comprises a signal processing unit (30) adapted to displace a generation signal (26) for generating a measuring signal (22.1, 22.2) in a generation frequency range (48) from the generation frequency range (48) to the measuring frequency range (60, 62, 68, 70).

Abstract: It is possible to provide a frequency component measuring device capable of narrowing the range of transmission frequency of a local oscillator, preventing degradation of the level measurement accuracy, and measuring the level of a modulation wave. The device includes: a local oscillator (24) capable of performing sweep in a predetermined frequency range; a mixer (22) for mixing a local oscillation signal outputted from the local oscillator (24) and a measured signal so as to subject the measured signal to a frequency conversion; a plurality of intermediate-frequency filters (44, 46) for extracting and outputting components of different intermediate frequencies from a signal outputted from the mixer (22); and an image removal processing section (66) for performing image removal according to the plurality of intermediate-frequency signals separately outputted from the intermediate-frequency filters (44, 46) corresponding to frequency sweep operations performed by the local oscillator (24) more than once.

Abstract: The process eliminates image rays generated in a frequency converting device generating actual rays and image rays from frequency rays of an input signal. The frequency converting device comprising a mixer mixing the input signal and a signal provided by a local oscillator and a filter assembly filtering the mixed signals output by the mixer. In a first sweep and a second sweep, the frequency of the oscillator is varied and the signal level at the output of the frequency converting device is recorded for a set of converted frequencies. The second sweep is carried out so that the frequency of the actual ray generated in the second sweep by an input ray is the same as the frequency of the actual ray generated in said first sweep by said input ray, and the frequency of the image ray generated in the second sweep by an input ray is not the same as the frequency of the image ray generated in said first sweep by said input ray.

Abstract: To produce data of an initial analysis range and a range zooming a part of it while updating them in parallel. [Means for resolution] A first frequency analysis range and a second frequency analysis range that is narrower than the first one are set with an operation panel 34, etc. A first signal path 171 produces first time domain data of a frequency converted signal under test according to a first data production rate that is set depending on the first frequency analysis range. A second signal path 172 produces second time domain data of frequency converted signal under test according to a second data production rate that is set depending on the second frequency analysis range and is slower than the first data production rate.

Abstract: A methods and devices for polyphase resampling are presented which may comprise a coefficient generator which provides a plurality of coefficients and an interpolation arrangement used to carry out the resampling by means of the coefficients applied to input data provided for resampling in order to provide output data. In one possible implementation the coefficient generator is constructed and/or controlled so as to provide the coefficients for the resampling in the form of linearly interpolated coefficients. In another alternative implementation, a plurality of at least two data interpolation filters are provided for the interpolation of a corresponding number of parallel input data, wherein the coefficients are input to each of the data interpolation filters.

Abstract: A measurement technique that provides a full solution to the gated local oscillator sweep measurement and improves the accuracy of signal analyzers in gated sweep mode by pre-sweeping the local oscillator at the beginning of a gate pulse and over-sweeping the local oscillator at the end of each gate pulse.

Abstract: A system for detecting a direct current (DC) component of a pulse-width modulated (PWM) signal includes a modulator configured to provide at least one PWM signal to an input of an amplifier. A DC detector is configured to detect a DC component of a selected one of the at least one PWM signal as a function of a switching frequency of the selected PWM signal. The DC detector provides at least one report signal that indicates a level of the DC component of the selected PWM signal relative to a predetermined threshold.

Abstract: Spectrum analyzer circuits and methods are provided which implement “zero-IF” (direct conversion) or “near-zero IF” (or very low IF) architectures that enable implementation of integrated (on-chip) spectrum analyzers for measuring the frequency spectrum of internal chip signals. An integrated spectrum analyzer circuit, which comprises a zero IF or near-zero IF framework, enables a low-power compact design with sufficient resolution bandwidth for on-chip implementation and diagnostics of internal chip signals.

Abstract: The present invention is directed to an apparatus and methodology for performing spurious-free dynamic range (SFDR) measurements on an RF circuit, such as a mixer, using a single analog input port. The present invention is designed for use when access to the intermediate frequency (IF) port in a radio frequency (RF) front-end circuit is not available, when the traditional two-port method for making an SFDR measurement is inadequate. Passing the analog input through a directional coupler between the RF combiner and the mixer facilitates the performance of the traditional third order intermodulation (IMD) test. Key differences between the single-port and traditional two-port setups are considered and examined, and experimental data obtained using the single-port setup is compared to data obtained using the traditional two-port set-up for different mixer models. Comparison of similar results yields confirmation and a calibration to account for the additional losses introduced by the directional coupler.

Abstract: Mass analysis method and mass spectrometer in which the S/N of mass spectra does not deteriorate due to accumulation if an ionization method, such as MALDI, producing spectral intensities that are not uniform in time is employed. Every given number of collected mass spectra are accumulated and stored to produce primary accumulation mass spectra. After the measurements, some of the stored primary accumulation spectra are selected according to a given rule based on a time trace of the intensities of the primary accumulation mass spectra. The selected spectra are accumulated to produce a secondary accumulation mass spectrum.

Abstract: Transmit equalization over high speed digital communication paths may be compensated in a receiver for a probe on that path. In one example, a probe input provides a signal from an electronic communications path, the signal having been processed by a transmit equalizer. A filter circuit processes the signal to compensate for the transmit equalizer, and a decoder decodes the processed signal and produces an output for use by test equipment.

Abstract: A receiver for receiving a broadcast channel comprising a spectrum analyzer physically integrated into the receiver and operative to receive an intermediate frequency signal and process the spectral contents of the receive signal.

Abstract: The present invention exploits extreme sensitivity to initial conditions in ray-chaotic enclosures to create a method to distinguish nominally identical objects through their unique “wave fingerprints.” The fingerprint can be measured through transmission of a pulsed microwave signal as a function of carrier frequency and time. When internal components are re-arranged, the Electromagnetic Fingerprints (EMF) changes in significant ways. The EMF can be detected by direct injection measurements of the enclosure or through remote measurement.

Abstract: A frequency detector includes an error measurement unit measuring a time interval between zero-crossing points of an input signal that is modulated. An error conversion unit quantizes the measured time interval using one of modulation time intervals. An error calculation unit calculates a frequency error based upon a difference between the measured time interval and the quantized time interval. An error generation control unit controls whether to output the frequency error based upon the quantized time interval, the calculated frequency error, and a predetermined critical value.