Abstract: A method for determining a property of a fluid includes: receiving at a computing device an admittance spectrum created by application of an excitation to a resonator contacting the fluid, the spectrum covering a first frequency range and having real and imaginary components; determining a resonant frequency of the admittance spectrum, the resonant frequency being a frequency at which a magnitude of the imaginary component is about zero; determining a bandwidth of the spectrum; and determining the property based on one or both of the resonant frequency and the bandwidth of the resonant frequency.

Abstract: Methods, systems and computer program products for identifying components of an unknown mixture using spectral analysis techniques. The method includes comparing the spectrum of the unknown mixture with the spectra of library compounds to obtain candidate mixture combinations. A model is generated for each of the candidate mixture combinations based on a modeling metric. A residual spectrum is computed corresponding to each of the candidate mixture combinations by removing the spectrum of each of the compounds of the candidate mixture combination from the spectrum of the unknown mixture. One or more potential compounds are identified by comparing the residual spectrum with the spectrum of library compounds. The potential compounds are added to the candidate mixture combinations to generate an updated list of the candidate mixture combinations. The search algorithm repeats the steps described above on the updated candidate mixture combinations, until a first termination condition is satisfied.

Abstract: A time qualified frequency mask trigger triggers on signals that violate a frequency mask for at least a specified time duration. A frame of digital data representing an input signal is transformed into a frequency spectrum having at least one frequency bin, with each frequency bin having a power amplitude value. A trigger signal is generated when any of the power amplitude values violates an associated reference power level for at least a specified time duration.

Abstract: A model refinement system refines initial split rules that define an initial decision tree to generate final split-rules. The model refinement refines the initial split rules by removing clauses that are satisfied by match scores that are less than a threshold match score to generate initial trimmed rules. Using the initial trimmed rules, the model refinement system classifies an initial training set and filters the initial training set to remove negative training pairs that are classified as duplicate pairs resulting in a filtered training set. An intermediate decision tree defined by intermediate split-rules is generated based on the filtered training set. Final split-rules are generated based on the intermediate split rules and input pairs of data records are classified as duplicate pairs based on attribute values of the input pairs and the final split-rules.

Abstract: A power trigger is provided having time qualified and sequential event capability. Digital data representing an input signal is converted into a power signal. The power signal is compared to a trigger level. A trigger signal is generated when the power signal violates the trigger level for either at least or less than a specified time duration. Alternatively, the trigger signal may be generated on the occurrence of a sequence of such violations.

Abstract: A realtime spectrum trigger system on a realtime oscilloscope considers both the magnitude and phase of an input signal having a periodic component so that successive acquisitions of the input signal are time aligned. A user inputs a frequency, threshold and phase for triggering on the periodic component. Input signal samples are filtered by quadrature filters according to the frequency input to produce quadrature signal components. The square of the magnitude of the input signal is computed from the quadrature signal components, as well as the phase ratio and sign, for comparison with calculated values. When enabled by the magnitude of the input signal, a phase crossing determinator compares the phase ratio and sign with calculated values to determine the phase crossing to generate a trigger, resulting in successive acquisitions of the input signal being in time alignment.

Abstract: Systems, methods, and computer program products for graphically displaying audio data are provided. In some implementations, a method is provided. The method includes displaying a graphical visual representation of digital audio data, the representation displaying a feature of the audio data on a feature axis with respect to time on a time axis. The method also includes receiving an input in the graphical visual representation selecting a range with respect to the feature and automatically extending the selected range with respect to time to define a selected region of the visual representation, where the extended range with respect to time is predefined and ignoring any component of the received input with respect to time.

Abstract: A frequency offset estimating apparatus includes an nth power computing module and a spectrum analyzing module. By raising a received signal to nth power to generate an nth power signal and analyzing the spectrum of the nth power signal, the present invention is capable of quickly and accurately estimating a frequency offset of the received signal. As being unaffected by channel characteristics, the estimating frequency offset apparatus is suitable for all channel environments.

Abstract: Electromagnetic field distribution is measured by considering time variations of a measured electric and/or magnetic field value. In response to scanning performed with a probe at an arbitrary set of measurement coordinates in a predetermined measurement plane in the vicinity of an object to be measured, a signal is detected at each of plural sets of coordinates in a measurement plane. Electric and magnetic fields are computed during a measurement time period at each set of measurement coordinates in the measurement plane based on measurement coordinates where the probe is positioned and the signal is detected with the probe. Amplitude probability distribution during the time period at each set of measurement coordinates in the vicinity of the object is computed based on the computed intensity, then mapped and displayed.

Abstract: A state detecting apparatus S for detecting a current operating state of an LM (linear motion) system includes an AE sensor 1 generating a detection signal Sae by detecting an AE wave elastically generated when a plurality of balls contained in the LM system revolve in a circulation portion while spinning themselves; and a signal processing unit 4 generating a parameter indicating an intensity of the AE wave based on only the detection signal Sae corresponding to an operating frequency of the ball, and uses the parameter to determine a lubrication state of the LM system. Thereby, it is possible to provide the state detecting apparatus capable of predicting failure occurrence in the LM system; providing an improved maintenance to a user of the LM system and further longer lifetime thereof; and providing a performance guarantee and an improved quality of a device or equipment manufactured using the LM system.

Abstract: System and method implementations for testing a cooling fan in an electronic device are disclosed. As one example, a method of testing a cooling fan of a sample electronic device is disclosed that includes generating an audio input at an audio speaker and receiving an audio output at an audio microphone to obtain an audio output signal. The method further includes processing the audio output signal to identify frequency modulation in the audio output signal, and identifying a state of motion of fan blades of the cooling fan based, at least in part, on the frequency modulation.

Abstract: Method, apparatus, and system, including computer program products, implementing and using techniques for time series analysis, wherein the time series exhibit trend and/or seasonality. Model parameters of the time series data are determined by selecting and/or suggesting a most appropriate combination of trend and seasonality of the time series data based on analysis of variances of transformed time series data.

Abstract: Frequencies of plural peak signals which appear in a band ½ of a sampling frequency are detected from a spectrum obtained from a measuring target signal sampled with the sampling frequency in order to detect the repetition frequency of the measuring target signal having plural harmonic components with a similar power. Each of the plural peak signals is successively assumed to be a fundamental wave beat component originating from the fundamental wave of the measuring target signal and theoretical frequencies of harmonic beat components originating from harmonic components of the measuring target signal are successively calculated. The theoretical frequencies are compared with the frequencies of the plural peak signals to determine one of the plural peak signals as a fundamental wave beat component originating from the fundamental wave of the measuring target signal.

Abstract: A moored buoy floating at the ocean surface and anchored to the seafloor precisely measures acceleration, pitch, roll, and Earth's magnetic flux field of the buoy over a limited sampling period.

Abstract: A frequency mask trigger having frequency selective amplitude discrimination capability is provided for triggering when selected frequency components of an input signal fail to reach a desired power level. A frame of digital data representing an input signal is transformed into a frequency spectrum having at least one frequency bin, each frequency bin having a power amplitude value. Each power amplitude value is compared to an upper lower reference power levels and a lower reference power level. A trigger signal is generated when the power amplitude value in any frequency bin is above the lower reference power level and below the upper reference power level for a specified time duration.

Abstract: A method for calibrating an apparatus for ellipsometric measurements performed on an arbitrarily large or continuously moving sample, using a visible sample reference frame, and one or more laser sources in order to calibrate the ellipsometer for variations in the distance between the ellipsometer apparatus and the sample of interest. Included are techniques for projecting a first laser beam spot from an incident laser source onto a sample, then analyzing the position of the first laser beam spot relative to the center of the sample reference frame using human-aided measurements and confirmations and/or computer vision techniques. Then adjusting pivot points and/or apparatus-to-sample distance to achieve a first beam spot being located about the center of the sample reference frame, and concurrently intersecting the plane of the sample. Other techniques include changing the incidence and reflectance angle using a semi-circular track arc design with a stepping motor activating each goniometer arm.

Abstract: A spectrum analyzer is provided that includes components to achieve from below 9 kHz to above 20 GHz operation range while remaining hand-held. Components of the spectrum analyzer include an integrated precision stand-alone step attenuator that does not rely on printed circuit board (PCB) mounted circuit elements within the signal path. Further, a PIN diplexing switch separates signals into different base-band and highband paths. The baseband path includes a pre-amplifier for low frequency signals, while the higher frequency bands may not necessarily include a pre-amplifier. The baseband path further provides improved broadband termination of its 1st mixer IF port by incorporating a new quadrature-coupled directional (QCD) filter that includes a ring resonator. An inexpensive air dielectric multi-cavity baseband filter is also used to suppress 2nd mixer IF images. The highband path incorporates multi-throw MMIC PIN diode switches to selectively filter different bands of input signals.

Abstract: A computationally implemented method for recognizing devices based on detected signal patterns includes generating a plurality of signal pattern templates for a plurality of radio frequency communication signals, determining a matching signal pattern template for the detected signal pattern, and overlaying the matching signal pattern over the detected signal pattern.

Abstract: A system and method for time-frequency analysis in which acquired signals are modeled as frictionally damped harmonic oscillators having a friction factor that is not a free parameter are provided. The friction factor is selected as a function of the frequency value of the associated oscillator, such that an increase in both temporal and spectral resolution are provided over existing time-frequency analysis methods. The friction factor is also selected to define a spectral band, within which the given oscillator can detect data oscillations. The properly selected friction factor thereby provides the analysis over a broad spectral range that can span many orders of magnitude.

Abstract: Methods and apparatus for spectrum sensing for FM wireless microphone signals are provided. The spectrum sensing algorithm developed makes use of the property that the autocorrelation function of an FM signal is a sinusoidal function provided that the frequency) deviation is much smaller than the carrier frequency and the correlation delay is small. Based on this property, a simple spectrum sensing algorithm for the FM signal is designed by computing the autocorrelation function of the received signal and matched filtering of the sinusoidal function. The spectrum sensor provided by this approach can reliably detect the target signals when a strong adjacent channel interference exists and the signal power is as low as ?114 dBm.

Abstract: A signal parameter estimator includes curve fitting of multiple ideal spectral shapes.

Abstract: In order to detect, localize and interpret a partial discharge occurring in a partial discharge site along an electrical equipment, two measurement probes and a synchronization probe are installed along the electrical equipment. The measurement probes detect pulses travelling in the electrical equipment while the synchronization probe detects a phase angle in the electrical equipment and is usable for calibration purposes. A control unit receives the signals sensed by the probes and conditions them. Digital processing applied on the conditioned signals, involving their correlation, a time-frequency distribution and a form factor estimation, allows establishing a diagnosis indicating a detection of a partial discharge and its localization along the electrical equipment. A wideband magnetic probe may be provided for detecting the pulses traveling in the electrical equipment.

Abstract: Introduced herein is a “resource adaptive” algorithm for spectrum and periodicity estimation on a continuous stream of data. The formulation is based on the derivation of a closed-form incremental computation of the spectrum, augmented by a load-shedding scheme that can adapt to available CPU resources to provide a resource efficient solution for real time spectrum estimation.

Abstract: A method is provided for aligning a measurement instrument that includes a tunable filter. The method includes: (i) applying an output signal of an internal noise source of the measurement instrument to the input of the tunable filter, (ii) applying a control signal to the tunable filter to tune the tunable filter to a selected alignment frequency, (iii) measuring a value for a gain alignment parameter of the tunable filter while the output signal of the internal noise source is applied to the input of the tunable filter and the control signal is applied to the tunable filter, (iv) storing the measured gain alignment parameter value in an alignment table in the memory device, and (v) repeating steps (ii) through (iv) for a plurality of selected alignment frequencies in an operating frequency range of the tunable filter.

Abstract: Log chirp testing where a log chirp may be provided to a device under test and a first time domain response from the device under test may be received. The first time domain response may be in the time domain. The first time domain response may be converted to the angular domain to create an angular domain response. Converting to the angular domain response may include resampling the time domain response from the time domain to the angular domain. The angular domain response may be filtered and/or analyzed. The angular domain response may be converted to a second time domain response. Similar to above, the conversion may include resampling the angular domain response from the angular domain to the time domain. The first time domain response and the second time domain response may be analyzed. Testing results of the device under test may be generated and stored based on said analyzing.

Abstract: In a method for measuring a radiation power, an elliptical mirror is prepared so as to have a elliptical spherical space enclosed by a metal wall surface, the space having a rotating axis passing through two focal points. A device under test is placed in a position of one of the two focal points such that a center of radiation of a radio wave substantially coincides with the focal point, and a receiving antenna is placed in an position of an other one of the two focal points. The device under test is caused to radiate a radio wave and the radiated radio wave is reflected at the wall surface to allow the receiving antenna to receive the radio wave. Then, total radiation power of the radio wave is measured at a measurement end of the receiving antenna in accordance with an output signal from the receiving antenna.

Abstract: Apparatus for radiation mapping of a region comprises a spectrum analyzer for analyzing a local radiation field according to wavelength, and a positioning unit for obtaining a position reading to correlate with said local radiation field, thereby to provide said radiation mapping. The results may be provided as layers to a map, and different layers may be provided for different frequencies and different times of the day.

Abstract: A method utilizes an optical image processing system. The method includes providing a measured magnitude of the Fourier transform of a complex transmission function of an object or optical image. The method further includes providing an estimated phase term of the Fourier transform of the complex transmission function. The method further includes multiplying the measured magnitude and the estimated phase term to generate an estimated Fourier transform of the complex transmission function. The method further includes calculating an inverse Fourier transform of the estimated Fourier transform, wherein the inverse Fourier transform is a spatial function. The method further includes calculating an estimated complex transmission function by applying at least one constraint to the inverse Fourier transform.

Abstract: A method for improving bandwidth of an oscilloscope involves, in preferred embodiments, the use of frequency up-conversion and down-conversion techniques. In an illustrative embodiment the technique involves separating an input signal into a high frequency content and a low frequency content, down-converting the high frequency content in the analog domain so that it may be processed by the oscilloscope's analog front end, digitizing the low frequency content and the down-converted high frequency content, and forming a digital representation of the received analog signal from the digitized low frequency content and high frequency content.

Abstract: A method and system for detecting the existence of rumble strips on a roadway by a vehicle. Wheel speed data is obtained from a wheel speed sensor, and frequency-based analysis is then performed on the wheel speed data. The presence of a rumble strip can then be detected based on the outcome of the frequency-based analysis. The wheel speed data can be modified before conversion to the frequency domain to reduce wheel-induced cyclic variations in wheel speed. The frequency-based analysis can use an FFT and a peak detection method that analyzes one or more peaks in the FFT data to determine if any are indicative of the presence of a rumble strip. The method can be carried out automatically in real time and used to alert the driver of the detection of the rumble strip.

Abstract: A spectrometer has: Accumulation means to obtain a data set containing N data points, repeating the measurement M times to obtain M spectral data sets or time-domain data sets S1 (d1 to dN) to SM (d1 to dN), and accumulating the M spectral data sets or time-domain data sets. Means for creating sets S1 (dn) to SM (dn) of the data points contained in the M spectral data sets or time-domain data sets S1 (d1 to dN) to SM (d1 to dN). Correlation computing means for finding correlations. Computing means for finding either the product of an accumulated or anticipated spectrum.

Abstract: Embodiments of a method and apparatus for variable sensing using the frequency domain are taught herein. An exposure of a system to a physical variable is determined by periodically sensing the physical variable to produce a plurality of digital samples. The plurality of digital samples is converted to respective frequency domain representations. The exposure is calculated using the frequency domain representations.

Abstract: A frequency spectrum analyzing apparatus for performing a frequency spectrum analysis with respect to a detected value of an operating parameter of an internal combustion engine in synchronism with rotation of the engine, is provided. The operating parameter is sampled at predetermined time intervals, and the sampled value is converted to a digital value. Intensities of first and second elements are calculated with respect to a predetermined number of the sampled values, wherein the first and second elements respectively correspond to a plurality of frequency components contained in the detected value, and a phase of the second element differs from a phase of the first element by 90 degrees. Frequency component intensities corresponding to the plurality of frequencies are calculated in synchronism with rotation of the engine, using the first element intensities and the second element intensities.

Abstract: Method, apparatus, and system, including computer program products, implementing and using techniques for determining a periodic cycle of time series data. A frequency spectrum of the data is provided. The frequency spectrum is processed using at least one of the following steps, resulting in a processed frequency spectrum: filtering the frequency spectrum for reducing noise of the data, truncating the frequency spectrum at low frequencies, and weighting high frequency contributions over low frequency contributions of the frequency spectrum. A periodic cycle is extracted based on the processed frequency spectrum.

Abstract: Methods and systems for determining information about a sample are disclosed. The methods can include measuring spectral information for a sample and determining a quantity related to a signal-to-noise ratio for the spectral information, repeating the measuring and determining until a value of the quantity is beyond a threshold value, and comparing the spectral information to reference information to determine information about the sample.

Abstract: Chromatograms and mass spectra produced by an LC/MS system are analyzed by creating a two-dimensional data matrix of the spectral and chromatographic data. The two-dimensional matrix can be created by placing the spectra generated by the mass spectrometer portion of the LC/MS system in successive columns of the data matrix. In this way, the rows of the data matrix correspond to chromatographic data and the columns of the data matrix correspond to the spectra. A two-dimensional filter is specified and applied to the data matrix to enhance the ability of the system to detect peaks associated with ions. The two-dimensional filter is specified according to desired criteria. Rank-1 and rank-2 filters can be specified to improve computational efficiency. One method of applying the two-dimensional filter is through convolution of the data matrix with the two-dimensional filter to produce an output data matrix. Peaks corresponding to detected ions are identified in the output data matrix.

Abstract: An excitation signal generator (“ESG”) is described. The ESG generates an minimized excitation signal for use in a test system to generate a functional model of a device under test (“DUT”) where extreme values of the minimized excitation signal are increased toward a central value without changing the power spectrum at the DUT.

Abstract: The invention related to a method and circuit that is used to compensate for S-parameters of a passive circuit which do not satisfy passivity. The method includes the following steps: (1) getting S-parameters which do not satisfy passivity, these S-parameters being composed of an S-parameter matrix S; (2) computing matrix [S×S?], wherein matrix S? is a complex conjugate transposed matrix of the S-parameter matrix S; (3) computing the eigenvalues of the matrix [S×S?], and choosing an eigenvalue ? whose real part real(?) is the biggest; (4) computing a compensating value ?, the compensating value ? being equal to real(?)1/2×(1+?), wherein the ? is a very small positive number; and (5) dividing each of the S-parameters by the compensating value ? to get the compensated S-parameters.

Abstract: A method of processing Fourier Transform Mass Spectrometry (FTMS) data includes performing a Fourier Transform of a part of a time domain transient and identifying from that transformed data signal peaks representative of the presence of ions. After peak identification, the full transient is then transformed, and the peaks identified in the partial transient transform are used to locate true peaks in the transformed full transient. The number of ‘false’ peaks resulting from random noise has been found to correlate to the resolution, so that using a partial transient to identify true peaks reduces the risk of false peaks being included; nevertheless this information can then be applied to the full data set when transformed. As an alternative, different parts of the full data set can be transformed and then correlated; because any noise will be random, false peaks should occur at different places in the two partial transforms.

Abstract: A frequency spectrum analyzing apparatus for performing a frequency spectrum analysis with respect to a detected value of an operating parameter of an internal combustion engine in synchronism with rotation of the engine, is provided. The operating parameter is sampled at predetermined time intervals, and a sampled value is converted to a digital value. Intensities of first and second elements are calculated with respect to a predetermined number of the sampled values. The first elements and second elements respectively correspond to a plurality of frequency components contained in the detected value, and a phase of the second element differs from a phase of the first element by 90 degrees. Frequency component intensities corresponding to the plurality of frequency components are calculated in synchronism with rotation of the engine, using the first element intensities and the second element intensities.

Abstract: Method and computer program for accepting controlled-source electromagnetic (“CSEM”) source and receiver data (40) as time series, transforming these data into the time-frequency domain, and reducing these data and survey metadata to a form suitable for interpretation or inversion. The invention includes: a number of processing tools or programs (30), each designed to take a specific action on CSEM data or metadata, combine data types in some way, and/or provide a visual representation of data; a Graphical User Interface (32) to specify the action of specific tools (34) on specific data, supply parameters to tools, and monitor progress of the processing project; and a specified common internal data format, so that processing tools may be applied in various orders (36) during different processing flows and processed CSEM data can be passed on to interpretation or inversion systems.

Abstract: Methods, systems and computer program products for identifying components of an unknown mixture using spectral analysis techniques. The method includes comparing the spectrum of the unknown mixture with the spectra of library compounds to obtain candidate mixture combinations. A model is generated for each of the candidate mixture combinations based on a modeling metric. A residual spectrum is computed corresponding to each of the candidate mixture combinations by removing the spectrum of each of the compounds of the candidate mixture combination from the spectrum of the unknown mixture. One or more potential compounds are identified by comparing the residual spectrum with the spectrum of library compounds. The potential compounds are added to the candidate mixture combinations to generate an updated list of the candidate mixture combinations. The search algorithm repeats the steps described above on the updated candidate mixture combinations, until a first termination condition is satisfied.

Abstract: A method and a device for determining a frequency mask disposed above or below a frequency spectrum of a detected signal determines every individual ordinate value of a first envelope curve disposed completely above or below the frequency spectrum as the maximum value or minimum value of a given number of respectively adjacent ordinate values of the frequency spectrum linked to a window function. Following this, each individual ordinate value of a second envelope curve disposed completely above or below the frequency spectrum and completely above or below the first envelope curve is determined as the maximum value or minimum value of a given number of respectively adjacent ordinate values of the frequency spectrum linked to a window function.

Abstract: An in-line directional radio-frequency (“RF”) power meter for measuring power and other parameters in a transmission line. The meter simultaneously measures complex voltage-waves traveling in the forward and reverse directions of a connected transmission line and processes measured voltages to compute forward and reverse power, standing wave ratio, and impedance values. The apparatus includes a microprocessor having microcode for digitally computing RF power parameters, and a field programmable gate array (“FPGA”) having microcode for executing complex Fast Fourier Transforms (“FFT”) to calculate voltages and frequencies, a microprocessor with attached firmware to make a series of complex calculations relative to sensed electrical values in the transmission line and to pass certain calculated values to the device to communicate RF power parameters to a user. The configuration of the apparatus allows for measurement of RF power parameters in a relatively economical package.

Abstract: A data compression technique is disclosed for Fourier Transform Mass Spectrometry (FTMS). A statistical analysis is applied to the data in the frequency domain since most of this data is a result of randomly distributed electronic noise. A fit of the whole frequency dataset to the distribution is made to determine preliminary moments of the distribution. The data in the tail of that distribution (which is mainly the peak data) is then removed and the remaining data points are re-fitted to the distribution, to identify the moments of distribution of that remaining noise data. A noise threshold for the mass spectrum is then applied using the calculated moments. The data above the threshold is kept. The whole spectrum can be reconstituted by storing the moments of distribution along with the peak data and then regenerating the noise from those moments and adding it to the peak data.

Abstract: A method of digitizing an analog signal is provided, comprising the steps of separating the analog signal spanning a frequency range into a plurality of frequency bands, and then translating at least one of the signals to a lower frequency band in accordance with a local oscillator and digitizing the at least one translated signal with digitizing elements having a frequency range less than the analog signal frequency range. A fixed relationship of the phase of the local oscillator and a repetitive signal generated in accordance with a writing to a circular buffer of the digitized representation of the at least one of the plurality of frequency bands is then defined. Signals corresponding to the other of the plurality of frequency bands are digitized and written to corresponding circular buffers. Finally, a digital representation of the analog signal is formed from the digitized signals.

Abstract: A calculation method of electromagnetic interference reduction through spectrum diffusion that is for reducing the electromagnetic interference, in which, when a center frequency of a measurement bandwidth is changed so that a spectrum having the maximum amplitude is included in the measurement bandwidth, of a plurality of spectra generated from the frequency spectrum of an electromagnetic interference signal through the spectrum diffusion, the amplitudes of all spectra included in the measurement bandwidth are added up and the maximum total sum of the amplitudes is divided by the amplitude of the electromagnetic interference signal, hence to estimate the electromagnetic interference reduction.

Abstract: There is provided a probability density function separating apparatus that separates a predetermined component in a given probability density function, including: a domain transforming section that is supplied with the probability density function and transforms the probability density function into a spectrum in a frequency domain; and a standard deviation computing section that computes standard deviation of a random component included in the probability density function based on the spectrum.

Abstract: A man-portable locator system for locating buried or otherwise inaccessible pipes, conduits, cables, wires and inserted transmitters using detector arrays and stochastic signal processing and similar techniques to analyze and display multiple target objects at differing frequencies in a layered user interface (UI). For example, the locator UI may be adapted to present a target plurality sorted by proximity of target conductor to the locator operator together with other useful information specifying the multiple objects, frequencies and changes in the subterranean landscape by means of a useful combination of graphical, numeric and acoustic representations.

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.