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Showing papers on "Noise (signal processing) published in 1989"


Journal ArticleDOI
TL;DR: Although discussed in the context of direction-of-arrival estimation, ESPRIT can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise.
Abstract: An approach to the general problem of signal parameter estimation is described. The algorithm differs from its predecessor in that a total least-squares rather than a standard least-squares criterion is used. Although discussed in the context of direction-of-arrival estimation, ESPRIT can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise. It exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure. The technique, when applicable, manifests significant performance and computational advantages over previous algorithms such as MEM, Capon's MLM, and MUSIC. >

6,273 citations


Journal ArticleDOI
TL;DR: An FFT-based measurement technique, which can be easily used to determine accurately the frequency, amplitude, and phase of all the harmonic and interharmonic components of a distorted signal, is examined in this paper.
Abstract: An FFT-based measurement technique, which can be easily used to determine accurately the frequency, amplitude, and phase of all the harmonic and interharmonic components of a distorted signal, is examined Suitable windows and interpolation algorithms are examined in order to reduce undesirable effects due to spectral leakage caused by a sampling process that is not synchronized Several results concerning the application of different windows on a set of simulated signals are compared to verify the capability of the proposed procedure The influence of the noise is examined to study the filtering properties of the weighting functions >

382 citations


PatentDOI
TL;DR: In this paper, the autocorrelation coefficients of the impulse response of an Nth order FIR inverse noise filter derived from LPC analysis of previous non-speech signal frames are used to provide a measure M which depends on the power within that part of the spectrum containing no noise.
Abstract: Voice activity detector (VAD) for use in an LPC coder in a mobile radio system uses autocorrelation coefficient R 0 , R 1 . . . of the input signal, weighted and combined, to provide a measure M which depends on the power within that part of the spectrum containing no noise, which is thresholded against a variable threshold to provide a speech/no speech logic output. The measure is formula (I), where H i are the autocorrelation coefficients of the impulse response of an Nth order FIR inverse noise filter derived from LPC analysis of previous non-speech signal frames. Threshold adaption and coefficient update are controlled by a second VAD response to rate of spectral change between frames.

167 citations


Journal ArticleDOI
TL;DR: A procedure based on the removal of periodic noise by notch filtering in the frequency domain and the isolation of sensor noise and intrapixel variability using the semivariogram was applied easily and successfully to five sets of AVIRIS data from the 1987 flying season and could be applied to remotely sensed data from broadband sensors.
Abstract: To make the best use of narrowband Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data, an investigator needs to know the signal-to-noise ratio (SNR) The signal is land cover dependent and varies with both wavelength and atmospheric absorption, and random noise comprises sensor noise and intrapixel variability (ie variability within a pixel) The three existing methods for estimating the SNR are inadequate, since typical laboratory methods inflate, while typical dark-current and image methods deflate the SNR value The authors propose a procedure called the geostatistical method that is based on the removal of periodic noise by notch filtering in the frequency domain and the isolation of sensor noise and intrapixel variability using the semivariogram This procedure was applied easily and successfully to five sets of AVIRIS data from the 1987 flying season and could be applied to remotely sensed data from broadband sensors >

166 citations


Journal ArticleDOI
TL;DR: Two methods for estimation of noise correlations along an array of sensors are presented, both rely on a parametric (autoregressive moving average) noise model that has the advantage of describing the noise correlations by a small number of parameters.
Abstract: Two methods for estimation of noise correlations along an array of sensors are presented. Both rely on a parametric (autoregressive moving average) noise model. The model has the advantage of describing the noise correlations by a small number of parameters and can be applied to a great variety of physical noises. The first method is related to the calculation of the likelihood of whitened observations, and the second is related to Pisarenko's method (1973) applied to whitened observations. Both methods are obtained by optimization of a criterion and are iterative. The noise estimates can be used for sensor-output whitening and it then provides a means to improve array processing performance. The two methods perform well, both on simulated and real data. However, the first method seems simpler and more robust than the second. >

143 citations


Journal ArticleDOI
TL;DR: In this paper, the gated detection technique and recent progress in optical time-domain reflectometry (OTDR) are presented, as well as future optical network diagnostics are discussed.
Abstract: Advances in optical time-domain reflectometry (OTDR), such as enlargement of dynamic range, enhancement in resolution, reduction of noise intrinsic to single-mode fibers, and increase in user friendliness of the equipment, are reviewed. The gated detection technique and recent progress in OTDR are presented. Future optical network diagnostics are discussed. >

120 citations


Journal ArticleDOI
TL;DR: The notion of optimal phase-only filters (OPOFs) that yield improved signal to noise ratios (SNRs) with the help of several analytical examples and simulation results are introduced.
Abstract: We introduce the notion of optimal phase-only filters (OPOFs) that yield improved signal to noise ratios (SNRs). We illustrate the improvement in SNR resulting from the use of OPOFs with the help of several analytical examples and simulation results.

114 citations


Patent
Frederick J. Barr1
25 Aug 1989
TL;DR: In this article, a scale factor is applied to the output of a pressure transducer and a particle velocity transducers positioned substantially adjacent one another in the water to reduce coherent noise in a marine reflection prospecting system.
Abstract: A marine seismic reflection prospecting system reduces coherent noise by applying a scale factor to the output of a pressure transducer and a particle velocity transducer positioned substantially adjacent one another in the water. The transducers can be positioned at a point in the water above the bottom and, thereby, eliminate downgoing components of reverberation, or they can be positioned on the water's bottom and, thereby, eliminate both upgoing and downgoing components of the reverberation. The scale factor, which derives from the acoustical impedance of the water or water-bottom material, can be determined both deterministically and statistically. The former involves measuring and comparing the responses of the pressure and velocity transducers to a pressure wave induced in the water. The latter involves comparing the magnitude of the pressure signal autocorrelation to the pressure and velocity signal crosscorrelation at selected lag values or, alternatively, comparing the magnitude of the pressure signal autocorrelation to the velocity signal autocorrelation at selected lag values.

110 citations


Patent
21 Apr 1989
TL;DR: In this paper, a section of a drill string was used to cancel upward moving acoustical noise and precondition the data in recognition of the comb filter characteristics of the drill string.
Abstract: Acoustical signals are transmitted through a section of drill string (30) by cancelling upward moving acoustical noise and by preconditioning the data in recognition of the comb filter characteristics of the drill string. Spaced sensors (52, 54) provide a delayed signal to summer (46) which is combined with a signal from suitable circuitry (28) and then applied to sensors (42, 44) for transmitting an uphole signal having no downward moving noise.

103 citations


Journal ArticleDOI
TL;DR: A concise review of the theory of adaptive modeling, identification, and control of dynamic structural systems based on discrete‐time recordings is presented and guidelines for model selection and model validation and the computational aspects of the method are discussed.
Abstract: A concise review of the fheory of adaptive modeling, identification, and control of dynamic structural systems based on discrete‐time recordings is presented. Adaptive methods have four major advantages over the classical methods: (1) Removal of the noise from the signal is done over the whole frequency band; (2) time‐varying characteristics of systems can be tracked; (3) systems with unknown characteristics can be controlled; and (4) a small segment of the data is needed during the computations. Included in the paper are the discrete‐time representation of single‐input single‐output (SISO) systems, models for SISO systems with noise, the concept of stochastic approximation, recursive prediction error method (RPEM) for system identification, and the adaptive control. Guidelines for model selection and model validation and the computational aspects of the method are also discussed in the paper. The present paper is the first of two companion papers. The theory given in the paper is limited to that which is...

102 citations


Journal ArticleDOI
TL;DR: The Ll- Filters are introduced to generate the order statistic filters (L-filters) and the nonrecursive linear, or finite-duration impulse-response (FIR), filters.
Abstract: The Ll-filters are introduced to generate the order statistic filters (L-filters) and the nonrecursive linear, or finite-duration impulse-response (FIR), filters. Such estimators are particularly effective filtering signals that do not necessarily follow Gaussian distributions. They can be designed to restore one-dimensional or multidimensional signals corrupted by noise of impulsive type. Such filters are appealing since they are suitable for being made robust against the presence of spurious outliers in the data. >

Proceedings ArticleDOI
23 May 1989
TL;DR: Signal-selective direction-finding algorithms that overcome many of the limitations of existing techniques are presented and makes it possible to resolve a number of desired signals not exceeding the number of sensors in the presence of arbitrary noise and a virtually unlimited number of unknown interferers.
Abstract: Signal-selective direction-finding algorithms that overcome many of the limitations of existing techniques are presented. The algorithms automatically classify signals as desired or undesired on the basis of their known spectral correlation properties and estimate only the desired signals' directions of arrival. The signal-selective nature of the techniques eliminates the need for knowledge of the characteristics of the noise or interference in the environment and makes it possible to resolve a number of desired signals not exceeding the number of sensors in the presence of arbitrary noise and a virtually unlimited number of unknown interferers. For example, the interferers can exhibit an arbitrarily high degree of correlation among themselves and can arrive from directions arbitrarily close to those of the desired signals. >

Patent
Hans T. Thornander1
17 Nov 1989
TL;DR: In this paper, a noise discrimination circuit is proposed to determine if a given ECG signal pulse exceeds a prescribed threshold level for a prescribed time period, and if the amplitude of the signal pulse remains above the threshold for the duration of the timed window signal, the signal is considered to be a valid signal.
Abstract: A noise discrimination circuit determines if sensed electrocardiographic (ECG) pulsed signals sensed within a pulse generator are valid ECG signals, i.e., valid P-waves or R-waves, or noise. The ECG signal may then be processed. The processed ECG signal is monitored to determine both the amplitude and duration of any signal pulses appearing thereon. If the amplitude of a given ECG signal pulse exceeds a prescribed threshold level for a prescribed time period, the pulse is considered to be a valid ECG signal. The noise discrimination circuit includes: a threshold detector for determining if the amplitude of the ECG signal exceeds the prescribed threshold level; a timer circuit for generating a timed window signal, triggered by the threshold detector whenever the ECG signal amplitude exceeds the prescribed threshold level; and logic circuitry for determining if the amplitude of the ECG signal remains above the threshold level for the duration of the timed window signal. One embodiment allows the prescribed threshold level and duration of the timed window signal to be programmably selected.

PatentDOI
TL;DR: In this article, an adaptive noise cancelling scheme was proposed to overcome the problem that the target signal is degraded, leading to poorer intelligibility, by selectively disabling the adaptive filter from changing its filter values.
Abstract: The invention provides an adaptive noise cancelling apparatus which operates to overcome a problem encountered in conventional noise cancelling circuitry when the signal-to-noise ratio at the sensor array is high--to wit, that the target signal is degraded, leading to poorer intelligibility. An apparatus constructed in accord with the invention selectively inhibits the adaptive filter from changing its filter values in these instances and, thereby, prevents it from generating a noise-approximating signal that will degrade the target component of the output signal.

Journal ArticleDOI
TL;DR: An approach to image analysis and processing, called holospectral imaging, is proposed for dealing with Compton scattering contamination in nuclear medicine imaging, and results indicate a slight increase in the statistical noise but also an increase in contrast and greatly improved ability to quantitate the image.
Abstract: An approach to image analysis and processing, called holospectral imaging, is proposed for dealing with Compton scattering contamination in nuclear medicine imaging. The method requires that energy information be available for all detected photons. A set of frames (typically 16) representing the spatial distribution at different energies is then formed. The relationship between these energy frames is analyzed, and the original data is transformed into a series of eigenimages and eigenvalues. In this space it is possible to distinguish the specific contribution to the image of both primary and scattered photons and, in addition, noise. Under the hypothesis that the contribution of the primary photons dominates the image structure, a filtering process can be performed to reduce the scattered contamination. The proportion of scattered information removed by the filtering process is evaluated for all images and depends on the level of residual quantum noise, which is estimated from the size of the smaller eigenvalues. Results indicate a slight increase in the statistical noise but also an increase in contrast and greatly improved ability to quantitate the image. >

Journal ArticleDOI
TL;DR: It is demonstrated that for almost all schemes of interest in practice, it is quite sufficient for the receiver to implement only four or six linear filters which represent proper reference signals, which makes possible an almost continuous tradeoff between receiver complexity and SNR (signal/noise ratio) losses.
Abstract: By separating the two complexity problems connected with optimum coherent CPM (continuous phase modulation) receivers, namely, the number of linear filters and the number of memory states required, a straightforward procedure for reducing the complexity is proposed and its usefulness is evaluated. A concise analysis of the inherent trellis encoder associated with CPM is given. It is then demonstrated that for almost all schemes of interest in practice, it is quite sufficient for the receiver to implement only four or six linear filters which represent proper reference signals. For a reduction in the number of memory states, decision-feedback sequence estimation together with minimization of the unprocessed intersymbol interference is proposed. Modifications of this procedure allow a state reduction without losses or with only negligible losses because only error events with large distances are affected. Combinations of these methods make possible an almost continuous tradeoff between receiver complexity and SNR (signal/noise ratio) losses. Several examples are considered for which evaluations of minimum Euclidean distances and simulation results are given. >

Journal ArticleDOI
TL;DR: The authors study the effect of correlated noise on the performance of a distributed detection system and consider a suboptimal scheme by assuming that the local sensors have the same operating point, and that the distribution of the sensor observation is symmetric.
Abstract: The authors study the effect of correlated noise on the performance of a distributed detection system. They consider a suboptimal scheme by assuming that the local sensors have the same operating point, and that the distribution of the sensor observation is symmetric. This implies that the joint distribution of the sensor decisions, and therefore the fusion rule, are symmetric functions of the sensor decisions. The detection of a known signal in additive Gaussian noise and in Laplacian noise are considered. In both cases, system performance deteriorates when the correlation between the sensor noises is positive and increasing, whereas the performance improves considerably when the correlation is negative and increasing in magnitude. >

Journal ArticleDOI
TL;DR: It is shown that one can obtain a continuous assessment of the upper limit of magnitudes of seismic events in the target region that would go undetected by such a network, and the problem of using a network to continously monitor the seismic noise field is addressed.
Abstract: This paper presents an approach to multi-channel processing of data recorded by a network of stations which represents an extension of the delay-and-sum beamforming traditionally applied in array processing. A number of geographical beam-steering points are defined, and for each beam a set of time-aligned traces derived from the network stations are processed together so as to extract, for each step in time, a set of features corresponding to that particular beam. Applying this approach to the network of the three regional arrays, NORESS, ARCESS, and FINESA, in Fennoscandia, we demonstrate its usefulness for associating regional phases detected at individual arrays and originating from the same event. We also address the problem of using a network to continously monitor the seismic noise field. The purpose here is to determine to what extent interfering events affect the monitoring of events within a target region. In this regard, we show that one can obtain, at a given confidence level, a continuous assessment of the upper limit of magnitudes of seismic events in the target region that would go undetected by such a network.

Journal ArticleDOI
Hideto Hidaka1, Kazuyasu Fujishima1, Yoshio Matsuda1, Mikio Asakura1, T. Yoshihara1 
TL;DR: Twisted bit-line architectures to reduce or eliminate the noise are proposed and demonstrated by the soft-error rate improvement of a 1-Mb DRAM, and they are shown to be promising candidates for overcoming the scaling problems of DRAMs.
Abstract: As the memory cell array of DRAM has been scaled down, inter-bit-line coupling noise has emerged as a serious problem. The signal loss due to this noise is estimated at about 40% of the signal amplitude in a polycide-bit-line 16-Mb DRAM with a technologically attainable scaling scheme. Twisted bit-line architectures to reduce or eliminate the noise are proposed and demonstrated by the soft-error rate improvement of a 1-Mb DRAM. The effective critical charge is improved by 35%, which is attributed not only to the improvement of the signal amplitude but also to the elimination of large coupling noise during the sensing operation. The impact of these twisted bit-line architectures from a scaling viewpoint is also examined, and they are shown to be promising candidates for overcoming the scaling problems of DRAMs. >

Proceedings ArticleDOI
23 May 1989
TL;DR: An analysis of the four-layer, feedforward, noise-reduction neural network proposed by S. Tamura author and A. Waibel is described, showing that the linear part of the transformation performs linear noise reduction as well as linear speech/noise-characteristic extraction.
Abstract: An analysis of the four-layer, feedforward, noise-reduction neural network proposed by S. Tamura author and A. Waibel (Int. Conf. Acoust., Speech and Signal Proc., p.553-6, 1988) is described. Each layer has 60 units and is fully interconnected with the next higher layer. The input of the network is given by a 60-point-long (at 12-kHz sampling rate) noisy waveform, and the output is a 60-point-long noise-free waveform. The network was trained using the back-propagation learning algorithm. The network is divided into three subelements for the analysis. Each element stands for a transformation from a layer output to the next higher layer output. First, the transformation from the input layer to the first hidden layer is analyzed, showing that the linear part of the transformation performs linear noise reduction as well as linear speech/noise-characteristic extraction. It is also shown that the transformation from the first hidden layer to the second hidden layer greatly compresses the noise region of the first hidden layer by sigmoid nonlinearities, while preserving its speech region, and the transformation from the second hidden layer to the output layer linearly suppresses the noise components. The spectra of basis vectors spanning an output waveform space show poor higher formant structures. >

Journal ArticleDOI
TL;DR: This study presents a performance evaluation of non-linear filters derived from the robust point estimation theory by classification of various approaches to nonlinear filtering into three types of estimators according to the process of the filter.
Abstract: Nonlinear filters are used in many applications, including speech and image processing, owing to their ability to suppress noise and preserve signal features such as edges. This study presents a performance evaluation of non-linear filters derived from the robust point estimation theory. The first part of the work is a classification of various approaches to nonlinear filtering into three types of estimators according to the process of the filter. The second part is a computer implementation and evaluation of all of the filters discussed. Finally, a summary of experimental results is presented.

Patent
30 Jan 1989
TL;DR: In this paper, a laser beam is reflected from the surface of the body and detected along with the Planck radiation along with a signal correlation technique to generate an output signal proportional to the Johnson noise introduced into the reflected laser beam as a direct measure of the absolute temperature.
Abstract: Method and device for direct, non-contact temperature measure of a body. A laser beam is reflected from the surface of the body and detected along with the Planck radiation. The detected signal is analyzed using signal correlation technique to generate an output signal proportional to the Johnson noise introduced into the reflected laser beam as a direct measure of the absolute temperature of the body.

Journal ArticleDOI
Rainer Tonn1
TL;DR: In this paper, seven methods for the evaluation of the seismic quality factor Q have been investigated: wavelet modeling, spectral modelling, spectral ratio method, spectral matching technique, amplitude decay method, risetime method, and the determination of Q using the analytical signal.

Journal ArticleDOI
TL;DR: In this paper, the results of field deployments demonstrate that, with signal conditioning and ensemble averaging, signal-to-noise ratios can be achieved that allow turbulent variation in concentration to be measured.
Abstract: For ultrasonic backscatter devices to be of aid in studies of turbulent sediment transport dynamics, the procedures for converting signal to concentration estimates should be as accurate as possible, and the space and time resolution should be as high as possible. Signal conversion for the 3‐MHz system considered here takes into account nearfield beam pattern effects on propagation and attenuation. Enhancing resolution involves explicit consideration of various sources of noise and interference. The results of field deployments demonstrate that, with signal conditioning and ensemble averaging, signal‐to‐noise ratios can be achieved that allow turbulent variation in concentration to be measured. Two possible sources of error in the conversion procedure are: (1) attenuation due to scatters is not measured in situ, but must be estimated from the data, and (2) with a single‐frequency beam, the effects on scattering response of concentration variation and particle‐size variation cannot be uncoupled.

Journal ArticleDOI
TL;DR: It was shown that information-theoretic criteria for detection of the number of signals under an additive model with white noise when the noise variance is known or unknown are strongly consistent even when the underlying distribution is not necessarily Gaussian.
Abstract: L.C. Zhao et al. (1986) proposed certain information-theoretic criteria for detection of the number of signals under an additive model with white noise when the noise variance is known or unknown. It was shown that these criteria are strongly consistent even when the underlying distribution is not necessarily Gaussian. Upper bounds on the probabilities of error detection are obtained here. >

Journal ArticleDOI
TL;DR: In this paper, the authors extended their work to include cases in which the amplification or scattering parameters are themselves stochastic variables, and derived expressions for the noise power spectrum and the quantum efficiency for stationary, photon-limited inputs.
Abstract: The utility of multivariate moment-generating functions for analyzing the influence of stochastic amplifying and scattering mechanisms on the transfer of signal and noise through multistage imaging systems was shown in a previous study [ J. Opt. Soc. Am. A4, 895 ( 1987)]. Here we extend that study to include cases in which the amplification or scattering parameters are themselves stochastic variables. Each of these cases is illustrated by a physical example drawn from the study of radiographic screen–film imaging. For stationary, photon-limited inputs, expressions for the noise power spectrum and the detective quantum efficiency are derived for each case.

Proceedings ArticleDOI
01 Jan 1989
TL;DR: The methods is based on a stochastic signal model and uses optimal signal parameter estimes obtained from the measurements via maximum likelihood estimation or weighted subspace fitting to derive an optimal estimator of all the signal waveforms.
Abstract: The problem of estimating the waveform of narrowband signals impinging on a sensor array is of importance in many engineering applications. A known look-direction for a signal-of-interest (SOI) is usually assumed and a particular performance measure is optimized. To achieve optimality, these methods require the SOI to be uncorrelated with the other signals as well as the additive noise. Herein, the signal parameters (directions) are assumed to be unknown and an optimal estimator of all the signal waveforms is derived. The signal waveforms can be correlated or even coherent. The methods is based on a stochastic signal model and uses optimal signal parameter estimes obtained from the measurements via maximum likelihood estimation or weighted subspace fitting. Based on these estimates, the emitter signal covariance is estimated and a structured maximum a posteriori estimate of the signal waveforms is obtained. Simulations are presented comparing this estimator to the deterministic maximum likelihood estimator and the unstructured stochastic estimator.

Patent
TL;DR: In this article, a signal detector and signal detection methodology is provided to monitor oscillatory signals such as sound signals, to produce detector output in response to the presence of target signals having a frequency within a selected frequency range, such as ultrasonic sound signals.
Abstract: A signal detector and signal detection methodology is provided to monitor oscillatory signals, such as sound signals, to produce detector output in response to the presence of target signals having a frequency within a selected frequency range, such as ultrasonic sound signals. The detector has input processing circuitry that receives the oscillatory signals and filters out those which do not fall within the selected frequency range to produce an input signal. The input signal is split into two components, a primary input component and a control component. The primary input component is amplified proportionally to the amplitude of the control component. Preferably, the primary input component is processed to produce a clean, stable intermediate signal. Here, the signal detector provides processing circuitry that passes primary input components that have amplitudes exceeding a threshold, to eliminate low level noise; the primary input components are variably amplified inversely to the amplitude thereof to produce an initial intermediate signal having a substantially uniform amplitude at the frequency of the input signal. This initial intermediate signal is processed by a Schmitt-Trigger to create a square-wave signal. The processing circuit includes a scaler sub-circuit to divide the square-wave signal by an integer, and an integrating sub-circuit integrates the resulting scaled signal to produce the intermediate signal. An amplification circuit has variable gain controlled by averaging the amplitude of the input signal by way of the control component so that the intermediate signal is amplified according to the original amplitude to produce a scaled replica of the filtered input signal. Sensitivity adjustment and visual and audible displays are used for the detector output.

Journal ArticleDOI
TL;DR: An adaptive noise cancelling structure suitable for situations where the noise reference transducer is closely spaced relative to the primary transducers, based on two LMS delay line cancellers with cross-coupled feedback is described.

Patent
23 Jun 1989
TL;DR: In this paper, the signal emitted from a spin excited by a series of pulse sequences is detected by a coil and amplified to perform phase sensitive detection to form a detection signal, a smoothing means 8 for detecting protruding noise, clip detection for detecting the clip state of a signal and the smoothing of the signal by moving averaging with respect to the detection signal is provided.
Abstract: PURPOSE:To form an image stably and accurately, by removing noise, DC level shift and timing shift by providing a smoothing means, a DC correcting means and a phase correcting means. CONSTITUTION:The signal emitted from a spin excited by a series of pulse sequences is detected by a coil and amplified to perform phase sensitive detection to form a detection signal. A smoothing means 8 for performing the spike detection for detecting protruding noise, clip detection for detecting the clip state of a signal and the smoothing of the signal by moving averaging with respect to said detection signal, a DC correcting means 9 for detecting the DC level of the signal to correct the same and a phase correcting means 10 for calculating the unnecessary phase difference component of the signal and removing the phase difference calculated from the phase quantity of the whole are provided. Since the noise of a resonance signal derived from various factors of the system is removed and the signal is further smoothed and DC correction and phase correction are performed, the noise or artifact of a formed image is reduced and the stability of the system can be enhanced.