scispace - formally typeset
Search or ask a question
Journal ArticleDOI

A fast spectral estimation algorithm based on the FFT

01 Jun 1994-IEEE Transactions on Signal Processing (IEEE)-Vol. 42, Iss: 6, pp 1317-1322
TL;DR: A simple FFT-based algorithm for spectrum estimation using a single pass through the FFT is presented and is certainly better than the single pass FFT in separating closely spaced sinusoids.
Abstract: A simple FFT-based algorithm for spectrum estimation is presented. The major difference between this and spectrum estimation using a single pass through the FFT is that the proposed algorithm is iterative and the FFT is used many times in a systematic may to search for individual spectral lines. Using simulated data, the proposed algorithm is able to detect mulitple sinusoids in additive noise. The algorithm is certainly better than the single pass FFT in separating closely spaced sinusoids. Finally the algorithm is applied to some experimental measurements to illustrate its properties. >
Citations
More filters
Journal ArticleDOI
TL;DR: A decoupled parameter estimation (DPE) algorithm for estimating sinusoidal parameters from both one-dimensional and two-dimensional data sequences corrupted by AR noise, which provides excellent estimation performance under the model assumptions and is robust to mismodeling errors.
Abstract: We present a decoupled parameter estimation (DPE) algorithm for estimating sinusoidal parameters from both 1-D and 2-D data sequences corrupted by autoregressive (AR) noise. In the first step of the DPE algorithm, we use a relaxation (RELAX) algorithm that requires simple fast Fourier transforms (FFTs) to obtain the estimates of the sinusoidal parameters. We describe how the RELAX algorithm may be used to extract radar target features from both 1-D and 2-D data sequences. In the second step of the DPE algorithm, a linear least-squares approach is used to estimate the AR noise parameters. The DPE algorithm is both conceptually and computationally simple. The algorithm not only provides excellent estimation performance under the model assumptions, in which case the estimates obtained with the DPE algorithm are asymptotically statistically efficient, but is also robust to mismodeling errors.

528 citations


Cites methods from "A fast spectral estimation algorith..."

  • ...If we redetermine all of the sinusoidal parameters once in each step of the RELAX algorithm, then RELAX becomes the complex version of the algorithm proposed in [ 6 ] for real data sequences....

    [...]

  • ...We remark, however, that similarly to the method in [ 6 ], the FFT-based RELAX does not exploit the structure in (26) and, hence, is an approximate approach....

    [...]

  • ...We shall explain how the RELAX algorithm is related to the CLEAN algorithm [5] and its improved version [ 6 ], which have been shown to provide good performance with both numerical and experimental data [5]-[7]....

    [...]

Journal ArticleDOI
TL;DR: A two-fold benchmarking scheme for evaluating existing SAR-ATR systems and motivating new system designs is proposed, and a taxonomization methodology for surveying the numerous methods published in the open literature is proposed.
Abstract: The purpose of this paper is to survey and assess the state-of-the-art in automatic target recognition for synthetic aperture radar imagery (SAR-ATR). The aim is not to develop an exhaustive survey of the voluminous literature, but rather to capture in one place the various approaches for implementing the SAR-ATR system. This paper is meant to be as self-contained as possible, and it approaches the SAR-ATR problem from a holistic end-to-end perspective. A brief overview for the breadth of the SAR-ATR challenges is conducted. This is couched in terms of a single-channel SAR, and it is extendable to multi-channel SAR systems. Stages pertinent to the basic SAR-ATR system structure are defined, and the motivations of the requirements and constraints on the system constituents are addressed. For each stage in the SAR-ATR processing chain, a taxonomization methodology for surveying the numerous methods published in the open literature is proposed. Carefully selected works from the literature are presented under the taxa proposed. Novel comparisons, discussions, and comments are pinpointed throughout this paper. A two-fold benchmarking scheme for evaluating existing SAR-ATR systems and motivating new system designs is proposed. The scheme is applied to the works surveyed in this paper. Finally, a discussion is presented in which various interrelated issues, such as standard operating conditions, extended operating conditions, and target-model design, are addressed. This paper is a contribution toward fulfilling an objective of end-to-end SAR-ATR system design.

269 citations


Cites methods from "A fast spectral estimation algorith..."

  • ...Some popular methods include the relaxation algorithm (RELAX) [154], [158], [159], CLEAN [160]–[162], Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT), and Decoupled Least Squares (DLS) [163]....

    [...]

  • ...Indeed, the CLEAN algorithm and its variants [162] are instances of the RELAX algorithm....

    [...]

  • ...The CLEAN algorithm [160]–[162] was first introduced in radio astronomy [161], and later utilized for radar imaging [160]....

    [...]

Journal ArticleDOI
TL;DR: New computationally efficient algorithms for estimating the parameters (frequency, amplitude, and phase) of one or more real tones (sinusoids) or complex tones (cisoids) in noise from a block of N uniformly spaced samples are presented.
Abstract: This paper presents new computationally efficient algorithms for estimating the parameters (frequency, amplitude, and phase) of one or more real tones (sinusoids) or complex tones (cisoids) in noise from a block of N uniformly spaced samples. The first algorithm is an interpolator that uses the peak sample in the discrete Fourier spectrum (DFS) of the data and its two neighbors. We derive Cramer-Rao bounds (CRBs) for such interpolators and show that they are very close to the CRB's for the maximum likelihood (ML) estimator. The new algorithm almost reaches these bounds. A second algorithm uses the five DFS samples centered on the peak to produce estimates even closer to ML. Enhancements are presented that maintain nearly ML performance for small values of N. For multiple complex tones with frequency separations of at least 4/spl pi//N rad/sample, unbiased estimates are obtained by incorporating the new single-tone estimators into an iterative "cyclic descent" algorithm, which is a computationally cheap nonlinear optimization. Single or multiple real tones are handled in the same way. The new algorithms are immune to nonzero mean signals and (provided N is large) remain near-optimal in colored and non-Gaussian noise.

263 citations


Cites methods from "A fast spectral estimation algorith..."

  • ...Alternatively, the unbiased ML estimates can be found using a computationally simple “cyclic descent” optimization algorithm [9], [20]....

    [...]

Journal ArticleDOI
TL;DR: Synchronized and unsynchronized experimental results validated with a sub-millimeter accurate optical tracking system are presented with a detailed discussion of various system errors.
Abstract: There are many challenges in building an ultra-wideband (UWB) indoor local positioning system for high-accuracy applications. These challenges include reduced accuracy due to multipath interference, sampling rate limitations, tag synchronization, and antenna phase-center variation. Each of these factors must be addressed to achieve millimeter or sub-millimeter accuracy. The developed system architecture is presented where a 300-ps Gaussian pulse modulates an 8-GHz carrier signal and is transmitted through an omni-directional UWB antenna. Receiver-side peak detection, a low-cost subsequential-sampling mixer utilizing a direct digital synthesizer, high fidelity 10-MHz crystals, and Vivaldi phase-center calibration are utilized to mitigate these challenging problems. Synchronized and unsynchronized experimental results validated with a sub-millimeter accurate optical tracking system are presented with a detailed discussion of various system errors.

204 citations

Journal ArticleDOI
TL;DR: It is found that, in situations with a moderate or high level of spectral interference, the IWPA method outperforms the IFFT and is even competitive with ESPRIT, which has the lowest computational cost.

76 citations


Cites background from "A fast spectral estimation algorith..."

  • ...In [13] this disadvantage is alleviated by applying zero padding....

    [...]

  • ...Recently, a simple iterative algorithm has been proposed in [13] to reduce the long-range spectral leakage....

    [...]

References
More filters
Journal ArticleDOI
01 Nov 1981
TL;DR: In this paper, a summary of many of the new techniques developed in the last two decades for spectrum analysis of discrete time series is presented, including classical periodogram, classical Blackman-Tukey, autoregressive (maximum entropy), moving average, autotegressive-moving average, maximum likelihood, Prony, and Pisarenko methods.
Abstract: A summary of many of the new techniques developed in the last two decades for spectrum analysis of discrete time series is presented in this tutorial. An examination of the underlying time series model assumed by each technique serves as the common basis for understanding the differences among the various spectrum analysis approaches. Techniques discussed include the classical periodogram, classical Blackman-Tukey, autoregressive (maximum entropy), moving average, autotegressive-moving average, maximum likelihood, Prony, and Pisarenko methods. A summary table in the text provides a concise overview for all methods, including key references and appropriate equations for computation of each spectral estimate.

2,941 citations

Journal ArticleDOI
01 Sep 1982
TL;DR: In this paper, the frequency estimation performance of the forward-backward linear prediction (FBLP) method was improved for short data records and low signal-to-noise ratio (SNR) by using information about the rank M of the signal correlation matrix.
Abstract: The frequency-estimation performance of the forward-backward linear prediction (FBLP) method of Nuttall/Uhych and Clayton, is significantly improved for short data records and low signal-to-noise ratio (SNR) by using information about the rank M of the signal correlation matrix. A source for the improvement is an implied replacement of the usual estimated correlation matrix by a least squares approximation matrix having the lower rank M. A second, related cause for the improvement is an increase in the order of the prediction filter beyond conventional limits. Computationally, the recommended signal processing is the same as for the FBLP method, except that the vector of prediction coefficients is formed from a linear combination of the M principal eigenvectors of the estimated correlation matrix. Alternatively, singular value decomposition can be used in the implementation. In one special case, which we call the Kumaresan-Prony (KP) case, the new prediction coefficients can be calculated in a very simple way. Philosophically, the improvement can be considered to result from a preliminary estimation of the explainable, predictable components of the data, rather than attempting to explain all of the observed data by linear prediction.

1,072 citations