Showing papers on "Spectral density estimation published in 1991"
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TL;DR: In this article, a constant Q transform with a constant ratio of center frequency to resolution has been proposed to obtain a constant pattern in the frequency domain for sounds with harmonic frequency components.
Abstract: The frequencies that have been chosen to make up the scale of Western music are geometrically spaced. Thus the discrete Fourier transform (DFT), although extremely efficient in the fast Fourier transform implementation, yields components which do not map efficiently to musical frequencies. This is because the frequency components calculated with the DFT are separated by a constant frequency difference and with a constant resolution. A calculation similar to a discrete Fourier transform but with a constant ratio of center frequency to resolution has been made; this is a constant Q transform and is equivalent to a 1/24‐oct filter bank. Thus there are two frequency components for each musical note so that two adjacent notes in the musical scale played simultaneously can be resolved anywhere in the musical frequency range. This transform against log (frequency) to obtain a constant pattern in the frequency domain for sounds with harmonic frequency components has been plotted. This is compared to the conventio...
890 citations
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TL;DR: This is the third in a series of four tutorial papers on biomedical signal processing and concerns the estimation of the power spectrum (PS) and coherence function (CF) od biomedical data.
Abstract: This is the third in a series of four tutorial papers on biomedical signal processing and concerns the estimation of the power spectrum (PS) and coherence function (CF) od biomedical data. The PS is introduced and its estimation by means of the discrete Fourier transform is considered in terms of the problem of resolution in the frequency domain. The periodogram is introduced and its variance, bias and the effects of windowing and smoothing are considered. The use of the autocovariance function as a stage in power spectral estimation is described and the effects of windows in the autocorrelation domain are compared with the related effects of windows in the original time domain. The concept of coherence is introduced and the many ways in which coherence functions might be estimated are considered.
200 citations
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23 Jan 1991TL;DR: Introduction and Terminology of Fourier Analysis, Random Signal Modeling and Modern Spectral Estimation, and Theory and Application of Cross Correlation and Coherence.
Abstract: Introduction and Terminology. Empirical Modeling and Approximation. Fourier Analysis. Probability Concepts and Signal Characteristics. Introduction to Random Processes and Signal Correlation. Random Signals, Linear Systems, and Power Spectra. Spectral Analysis for Random Signals: Classical Estimation. Random Signal Modeling and Modern Spectral Estimation. Theory and Application of Cross Correlation and Coherence.
191 citations
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TL;DR: An algorithm is developed to define, from the data samples themselves, a frequency-weighted norm to use in minimum- Weighted-norm extrapolation, which usually converges in less than 10 iterations to an extrapolation which is characterized as a nonparametric frequency-stationary extension of the data.
Abstract: An algorithm is developed to define, from the data samples themselves, a frequency-weighted norm to use in minimum-weighted-norm extrapolation. The iterative procedure developed consists of using a periodogram spectrum estimate obtained from some samples of the signal estimate/extrapolation found at one iteration to define the weight that is used to estimate at the next iteration. This algorithm usually converges in less than 10 iterations to an extrapolation which is characterized as a nonparametric frequency-stationary extension of the data. The frequency resolution and extrapolation length are controlled by the length of a time-domain window used to obtain smooth spectral estimates between iterations. Examples are provided to illustrate the use of the algorithm for interpolation/extrapolation. The examples give comparable results to nonadaptive extrapolation methods without the need for a priori knowledge. For a certain spectral estimation example, the algorithm provides comparable resolution to the parametric methods with more accurate values of the relative strengths of the narrowband components. >
115 citations
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TL;DR: The modern spectral analysis techniques were shown to be superior to Fourier techniques in most circumstances, provided the model order was chosen appropriately, and robustness considerations tended to recommend the maximum likelihood method for both velocity and spectral estimation.
Abstract: Four spectral analysis techniques were applied to pulsed Doppler ultrasonic quadrature signals to compare the relative merits of each technique for estimation of flow velocity and Doppler spectra. The four techniques were (1) the fast Fourier transform method, (2) the maximum likelihood method, (3) the Burg autoregressive algorithm, and (4) the modified covariance approach to autoregressive modeling. Both simulated signals and signals obtained from an in vitro flow system were studied. Optimal parameter values (e.g. model orders) were determined for each method, and the effects of signal-to-noise ratio and signal bandwidth were investigated. The modern spectral analysis techniques were shown to be superior to Fourier techniques in most circumstances, provided the model order was chosen appropriately. Robustness considerations tended to recommend the maximum likelihood method for both velocity and spectral estimation. Despite the restrictions of steady laminar flow, the results provide important basic information concerning the applicability of modern spectral analysis techniques to Doppler ultrasonic evaluation of arterial disease. >
84 citations
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TL;DR: A data segment length giving maximum spectral resolution is shown to exist for each window type and rate of frequency change, and the effect of mean frequency variation during the data segment has been investigated for different windows and rates of change ofmean frequency.
Abstract: Conventional measurement of the spectrum of arterial signals from the pulsed ultrasonic Doppler instrument uses windowed, sequential data segments. The Doppler signal is assumed stationary for the duration of each segment. It is shown here that this assumption is often unreasonable and the effect of mean frequency variation during the data segment has been investigated for different windows and rates of change of mean frequency. A data segment length giving maximum spectral resolution is shown to exist for each window type and rate of frequency change.
74 citations
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TL;DR: In this article, a method for preprocessing noisy speech to minimize the likelihood of error in estimation for use in a recognizer is presented, which is based on the Minimum Mean-Mean-Log-Spectral Distance (MMLSD) estimator.
Abstract: A method is disclosed for use in preprocessing noisy speech to minimize likelihood of error in estimation for use in a recognizer. The computationally-feasible technique, herein called Minimum-Mean-Log-Spectral-Distance (MMLSD) estimation using mixture models and Marlov models, comprises the steps of calculating for each vector of speech in the presence of noise corresponding to a single time frame, an estimate of clean speech, where the basic assumptions of the method of the estimator are that the probability distribution of clean speech can be modeled by a mixture of components each representing a different speech class assuming different frequency channels are uncorrelated within each class and that noise at different frequency channels is uncorrelated. In a further embodiment of the invention, the method comprises the steps of calculating for each sequence of vectors of speech in the presence of noise corresponding to a sequence of time frames, an estimate of clean speech, where the basic assumptions of the method of the estimator are that the probability distribution of clean speech can be modeled by a Markov process assuming different frequency channels are uncorrelated within each state of the Markov process and that noise at different frequency channels is uncorrelated.
72 citations
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TL;DR: In this paper, the effect of weighting on the uncertainty of the discrete time Fourier transform (DTFT) samples of a signal corrupted by additive noise is investigated, and it is shown how the adopted window sequence and the autocovariance function of the noise affect the second-order stochastic moments of the frequency domain data.
Abstract: The effect of weighting on the uncertainty of the discrete time Fourier transform (DTFT) samples of a signal corrupted by additive noise is investigated. Making very weak assumptions, it is shown how the adopted window sequence and the autocovariance function of the noise affect the second-order stochastic moments of the frequency-domain data. The relationship obtained extends the results reported in the literature and is useful in many frequency-domain estimation problems. It is shown how the knowledge of the second-order moments of the transform has allowed the application of the least squares technique for the estimation of the parameters of a multifrequency signal in the frequency-domain. The estimator obtained is very useful when high-accuracy results are required under real-time constraints. The procedure exhibits a better accuracy than similar frequency-domain methods proposed in the literature. >
56 citations
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TL;DR: The robustness of an L p normed solution when estimating the frequency of sinusoids from data contaminated by impulsive noise is demonstrated and insight is gained into the transient and steady behavior of the iterative algorithm.
55 citations
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TL;DR: A method of estimating time-varying spectra of nonstationary signals using recursive least squares (RLS) with variable forgetting factors (VFFs) is described, which has better adaptability than the conventional algorithm with high fixed forgetting factor (FFF) in the non stationary situation, and has lower variance than theventional one with low FFF in the stationary situation.
Abstract: A method of estimating time-varying spectra of nonstationary signals using recursive least squares (RLS) with variable forgetting factors (VFFs) is described. The VFF is adapted to a nonstationary signal by an extended prediction error criterion which accounts for the nonstationarity of the signal. This method has better adaptability than the conventional algorithm with high fixed forgetting factor (FFF) in the nonstationary situation, and has lower variance than the conventional one with low FFF in the stationary situation. The extra computation time for the forgetting adaptation is almost negligible. >
52 citations
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TL;DR: An analysis by synthesis procedure based on the singular value decomposition (SVD) methodology is proposed, using this procedure, a criterion for detecting the number of sinusoidal signals in the presence of noise is defined.
Abstract: An analysis by synthesis procedure based on the singular value decomposition (SVD) methodology is proposed. Using this procedure, a criterion for detecting the number of sinusoidal signals in the presence of noise is defined. Consecutive reconstructions are performed, and the resulting error power is compared to the noise variance in order to get the best approximation of the original noncorrupted signal. The number of the singular values corresponding to a reconstruction error power as close as possible to the noise variance gives the parsimonious order. The existence of such a criterion is important for both high-quality reconstruction and spectral analysis. Various spectral estimation techniques used on a reconstructed signal make it possible to retrieve harmonics in a highly noisy environment with very short data lengths. >
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14 Nov 1991
TL;DR: In this article, a signal processing apparatus and method for iteratively determining the inverse Arithmetic Fourier Transform (AFT) of an input signal by converting the input signal, which represents Fourier coefficients of a function that varies in relation to time, space, or other independent variable, into a set of output signals representing the values of a Fourier series associated with the input signals.
Abstract: A signal processing apparatus and method for iteratively determining the inverse Arithmetic Fourier Transform (AFT) of an input signal by converting the input signal, which represents Fourier coefficients of a function that varies in relation to time, space, or other independent variable, into a set of output signals representing the values of a Fourier series associated with the input signal. The signal processing apparatus and method utilize a process in which a data set of samples is used to iteratively compute a set of frequency samples, wherein each computational iteration utilizes error information which is calculated between the initial data and data synthesized using the AFT. The iterative computations converge and provide AFT values at the Farey-fraction arguments which are consistent with values given by a zero-padded Discrete Fourier Transform (DFT), thus obtaining dense frequency domain samples without interpolation or zero-padding.
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TL;DR: In this article, a new interpolation procedure is introduced which accounts for variable peak width and is adaptive, to avoid the usual periodicities inherent to this interpolation problem, and the new estimators are compared with other commonly used methods using simulated LDA signals.
Abstract: The discrete Fourier transform (DFT) finds widespread use in laser anemometry for the estimation of frequency, phase and signal-to-noise ratio (SNR) of individual Doppler signals. Peak interpolation is a common method for increasing the accuracy of these estimates without significantly adding to the computational load. Many methods for peak interpolation do not account for large variations in the peak width due to signal length variations, and thus often result in biased SNR estimates and/or frequency estimates. A new interpolation procedure is introduced which accounts for variable peak width and is adaptive, to avoid the usual periodicities inherent to this interpolation problem. Estimators of frequency and SNR based on this interpolation are compared with other commonly used methods using simulated LDA signals. The new estimators are shown to be more accurate and robust.
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TL;DR: The accuracy of the output of the Fast Fourier Transform is studied by estimating the expectedvalue and the variance of the accompanying linear forms in terms of the expected value and variance ofThe relative roundoff errors for the elementary operations of addition and multiplication.
Abstract: We study the accuracy of the output of the Fast Fourier Transform by estimating the expected value and the variance of the accompanying linear forms in terms of the expected value and variance of the relative roundoff errors for the elementary operations of addition and multiplication. We compare the results with the corresponding ones for the direct algorithm for the Discrete Fourier Transform, and we give indications of the relative performances when different rounding schemes are used. We also present the results of numerical experiments run to test the theoretical bounds and discuss their significance.
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TL;DR: The singular value decomposition (SVD) autoregressive moving average, (ARMA) procedure is applied to computer-generated synthetic Doppler signals as well as in-vivo Dopplers data recorded in the carotid artery, and it is found that no single set of model orders was capable of producing consistent spectral estimates throughout the cardiac cycle.
Abstract: The singular value decomposition (SVD) autoregressive moving average, (ARMA) procedure is applied to computer-generated synthetic Doppler signals as well as in-vivo Doppler data recorded in the carotid artery. Two essential algorithmic parameters (the initially proposed model order and the number of overdetermined equations used) prove difficult to choose. The resulting spectra are very dependent on these two parameters. For the simulated data models orders of (3, 3) provide good results. However, when applying the SVD-ARMA algorithm to in-vivo Doppler signals no single set of model orders was capable of producing consistent spectral estimates throughout the cardiac cycle. Altering the model orders also necessitates the selection of new algorithmic parameters. Hence, the SVD-ARMA approach cannot be considered suitable as a spectral estimation technique, for real-time Doppler ultrasound systems. >
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TL;DR: The algorithm uses discrete, parametric signal models in z-space, whose parameters are determined by a two step identification algorithm to develop a method for the supervision and fault diagnosis of dynamic systems.
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TL;DR: This algorithm is a two-step approach: first, the AR parameters are estimated by solving a version of the 2-D modified Yule-Walker equation, for which some existing efficient algorithms are available; then the MA spectrum parameters are obtained by simple computations.
Abstract: The authors present a practical algorithm for estimating the power spectrum of a 2-D homogeneous random field based on 2-D autoregressive moving average (ARMA) modeling. This algorithm is a two-step approach: first, the AR parameters are estimated by solving a version of the 2-D modified Yule-Walker equation, for which some existing efficient algorithms are available; then the MA spectrum parameters are obtained by simple computations. The potential capability and the high-resolution performance of the algorithm are demonstrated by using some numerical examples. >
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TL;DR: The sensitivity to the spectral estimate of the original image of linear minimum mean-square error (LMMSE) color image restoration methods is determined and full-correlation Wiener restoration may be outperformed by the independent-channel restoration depending on the prototype image used in spectral estimation.
Abstract: The sensitivity to the spectral estimate of the original image of linear minimum mean-square error (LMMSE) color image restoration methods is determined. It is concluded that (i) sensitivity of the full-correlation Wiener restoration to the spectral estimate is higher than that of the independent-channel Wiener restoration, and the full-correlation restoration is extremely sensitive to windowing, (ii) among independent-channel restorations, the ones based on autoregressive spectral estimates are the least sensitive, and (iii) full-correlation Wiener restoration may be outperformed by the independent-channel restoration depending on the prototype image used in spectral estimation. >
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TL;DR: Signal subspace spectral estimation algorithms of the MUSIC type [l-3] are particularly effective for estimating the direction of arrival (DOA) of incoming plane wave signals arising from point emission sources in the far field of spatial phased arrays.
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TL;DR: The problem of estimating the parameters of a real-valued, stationary, nondeterministic, autoregressive process of order p from a time series of finite length is discussed and a new approach is proposed to sequentially estimate the reflection coefficients in pairs.
Abstract: The problem of estimating the parameters of a real-valued, stationary, nondeterministic, autoregressive process of order p from a time series of finite length is discussed Burg's algorithm estimates these parameters indirectly by sequentially estimating one reflection coefficient at a time The proposed approach is to sequentially estimate the reflection coefficients in pairs The new algorithm has the same order of computational complexity as Burg's It is guaranteed to generate parameter estimates that correspond to a stationary process (as does Burg's), and it produces estimates of the power spectral density that do not appear to suffer from spectral line splitting, in contrast to Burg's algorithm >
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01 Jun 1991TL;DR: Several novel performance criteria are proposed and analyzed for parameter estimation of the system parameters given only the output measurements (image pixels) and are sensitive to the magnitude as well as phase of the underlying stochastic image model.
Abstract: Finite-dimensional linear parametric models for multidimensional random signals have been found useful in many applications such as image coding, enhancement, restoration, synthesis, classification,a nd spectral estimation. A vast majority of this work is based upon exploitation of only the second-order statistics of the data either explicitly or implicitly. A consequence of this is that either the underlying models should be quarter-plane (or, half plane) causal and minimum phase, or the impulse response of the underlying parametric model must possess certain symmetry (such as 'symmetric noncausality'), in order to achieve parameter identifiability. I consider a general (possibly asymmetric noncausal and/or nonminimum phase) 2D autoregressive moving average random field model driven by an independent and identically distributed 2D non-Gaussian sequence. Several novel performance criteria are proposed and analyzed for parameter estimation of the system parameters given only the output measurements (image pixels). The proposed criteria exploit the higher order cumulant statistics of the data and are sensitive to the magnitude as well as phase of the underlying stochastic image model.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
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14 Apr 1991TL;DR: For signal processing applications, discrete time and frequency WHOS distributions are introduced and shown to be implemented with two fast-Fourier-transform-based algorithms.
Abstract: The Wigner higher-order spectra (WHOS) are defined as extensions of the Wigner distribution (WD) to higher-order statistics domains. A general class of time-frequency higher-order spectra is also defined in terms of arbitrary higher-order moments of the signal as generalizations of the Cohen's general class of time-frequency representations. For signal processing applications, discrete time and frequency WHOS distributions are introduced and shown to be implemented with two fast-Fourier-transform-based algorithms. One application in which the Wigner bispectrum is applied for the detection of transient signals embedded in noise is presented. The Wigner bispectrum is compared with the WD and simulation results are given. >
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TL;DR: A theoretical analysis of the variance for the time delay estimate between two EEG signals, obtained via the phase spectrum method, and indicates that the formulae can be used even with non-gaussian and relatively narrow-band EEG-like data.
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27 Jun 1991TL;DR: In this paper, a composite electrical signal generated by a light detector is digitized and a processor produces a discrete Fourier transform based on the digitized electrical signal, which includes two peak frequencies corresponding to the two velocity components.
Abstract: A laser doppler velocimeter uses frequency shifting of a laser beam to provide signal information for each velocity component. A composite electrical signal generated by a light detector is digitized and a processor produces a discrete Fourier transform based on the digitized electrical signal. The transform includes two peak frequencies corresponding to the two velocity components.
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TL;DR: It is concluded that the autoregressive (AR) model provides a more accurate estimate of aortic input impedance than does the Fourier transform when data length is limited.
Abstract: We evaluated the advantages of the autoregressive (AR) model over the conventional Fourier transform in estimating aortic input impedance. In 10 anesthetized open-chest dogs, we digitized aortic pressure and flow at 200 Hz for 51.20 s under random ventricular pacing and subdivided them into five segments. We obtained aortic input impedance over the frequency range of 0.1-20 Hz both by AR model and by Fourier transform for various lengths of data, i.e., from one to four consecutive segments. For any given data length, the impedance spectrum estimated by the AR model was smoother than that obtained by the Fourier transform. To evaluate the accuracy of the estimated impedance, we predicted instantaneous aortic pressure of the fifth segment by convolving corresponding aortic flow with the impulse response of aortic input impedance. The prediction error was less with the AR model than that resulting from Fourier transform as long as the number of the segments was less than four. We conclude that the AR model provides a more accurate estimate of aortic input impedance than does the Fourier transform when data length is limited.
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TL;DR: An autoregressive moving average (ARMA) model is proposed to improve the Doppler spectral width estimates and takes advantage of a priori knowledge of the correlation matrix, which arises in the derivation of the governing equations of the ARMA parameters.
Abstract: The measurement of clear-air turbulence with a Doppler radar is investigated. An autoregressive moving average (ARMA) model is proposed to improve the Doppler spectral width estimates. An iterative algorithm that has its origin in system identification is used for the estimation of the ARMA parameters. By taking advantage of a priori knowledge of the correlation matrix, which arises in the derivation of the governing equations of the ARMA parameters, the ARMA spectral estimate can be improved. This improvement is shown in terms of bias and variance of the spectral width estimate. >
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14 Apr 1991TL;DR: An iterative algorithm for computing a reduced-rank principal component least squares estimate of the adaptive weight vector to be used for spatially nulling interference received in the sidelobes of the formed beams of an array of antenna elements is described.
Abstract: An iterative algorithm for computing a reduced-rank principal component least squares estimate of the adaptive weight vector to be used for spatially nulling interference received in the sidelobes of the formed beams of an array of antenna elements is described. Based on a power/deflation method for extraction estimates of the dominant eigenstructure components, the algorithm is used to approximate the subspace spanned by the sample covariance eigenvectors associated with the directions of arrival of spatially coherent interference. Side information that can aid the discrimination between interference and noise subspaces is also produced. Performance is illustrated by the results of processing signals recorded from the individual elements of a linear antenna array operating in the HF band. >
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TL;DR: The use of digital signal processors (DSPs) that enable continuous estimates of signal frequency components to be incorporated into a broad range of real-time systems is considered and Classical spectral estimation methods are reviewed.
Abstract: The use of digital signal processors (DSPs) that enable continuous estimates of signal frequency components to be incorporated into a broad range of real-time systems is considered. Classical spectral estimation methods are reviewed. Real-time implementation of the methods, all of which use some form of fast Fourier transform method, on DSP chips is discussed. Some applications of these chips are examined. >
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23 Sep 1991TL;DR: The authors describe some time-variant algorithms of autoregressive (AR) identification that result in obtaining a set of AR parameters for each data sample that were applied in the study of the heart rate variability signal in dogs during coronary occlusion and in human subjects during transient ischemic episodes.
Abstract: The authors describe some time-variant algorithms of autoregressive (AR) identification that result in obtaining a set of AR parameters for each data sample. The performances of the algorithms were tested on simulated series to better understand their capability in tracking abrupt or constant-rate changes in the signal. A power spectrum density was obtained at each sample and a compressed spectrum array (CSA) graph is plotted. The algorithms were then applied in the study of the heart rate variability signal in dogs during coronary occlusion and in human subjects during transient ischemic episodes. Spectral parameters were obtained on a beat-to-beat basis, for a better comprehension of the dynamic role of the autonomic nervous system in this pathology. >
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30 Apr 1991
TL;DR: In this paper, the Fourier coefficients of one or more Fourier components of a measuring signal are estimated using a filter to obtain an estimate of the measuring signal at sampling time k-1.
Abstract: A circuit and method for iteratively estimating Fourier coefficients of one or more Fourier components of a measuring signal utilizes a filter to determine the Fourier coefficients for sampling time k-1. The coefficients are utilized to obtain an estimate of the measuring signal at sampling time k. A subtractor circuit subtracts an actual sample of the measuring signal at sampling time k from the estimate of the measuring signal at sampling time k to obtain a difference signal. The difference signal is inputted back into the filter to determine an estimate of the Fourier coefficients at sampling time k.