Frequency estimation using warped discrete Fourier transform

Franz, Stefan; Mitra, S.K.; Doblinger, Gerhard

doi:10.1016/s0165-1684(03)00079-3

Cited by 38 publications

(30 citation statements)

References 8 publications

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“…The Cramer-Rao bound is included for reference as in [3] and the reciprocal value of the variance in dB is also shown. For the calculations the values L = 24, N = 64 are adopted.…”

Section: Frequency Estimationmentioning

confidence: 99%

“…A better es- timation of the positions of the spectra peaks can be obtained using large zero padding, thus leading to very large FFT lengths. In [3] a warped discrete Fourier transform is used and its performance is compared with several other procedures, namely: Dichotomous-search, Tretter's linear regression, Kay's phase difference and chirp Z-transform methods. Further readings and applications of this technique can be found in [2,4,5,[8][9][10].…”

Section: Introductionmentioning

confidence: 99%

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A new zoom algorithm and its use in frequency estimation

Ortigueira¹,

Serralheiro²,

Machado³

2015

Waves, Wavelets and Fractals

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This paper presents a novel zoom transform algorithm for a more reliable frequency estimation. In fact, in many signal processing problems exact determination of the frequency of a signal is of paramount importance. Some techniques derived from the Fast Fourier Transform (FFT), just pad the signal with enough zeros in order to better sample its Discrete-Time Fourier Transform. The proposed algorithm is based on the FFT and avoids the problems observed in the standard heuristic approaches. The analytic formulation of the novel approach is presented and illustrated by means of simulations over short-time based signals. The presented examples demonstrate that the method gives rise to precise and deterministic results.

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“…The Cramer-Rao bound is included for reference as in [3] and the reciprocal value of the variance in dB is also shown. For the calculations the values L = 24, N = 64 are adopted.…”

Section: Frequency Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A new zoom algorithm and its use in frequency estimation

Ortigueira¹,

Serralheiro²,

Machado³

2015

Waves, Wavelets and Fractals

View full text Add to dashboard Cite

show abstract

“…Other approaches to the problem are based on multiple signal classification (MUSIC) algorithms, least mean-square (LMS) estimators, and DFT derivatives such as Goertzel algorithm (Evans, 1996). The approach taken in this paper is to explore the use of another DFT derivative called the warped discrete Fourier transform or WDFT (Makur et al, 2001;Franz et al, 2003).…”

Section: Introductionmentioning

confidence: 99%

Efficient Detection of Multi-Narrowband Using the Warped Discrete Fourier Transform

Kwon¹

2018

JCSIT

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This paper presents a multi-narrowband signal processing paradigm that is based on the use of the warped discrete Fourier transform (WDFT). The WDFT evaluates a discrete-time signal in the context of a nonuniform frequency spectrum, a process called warping. Compared to a conventional DFT or FFT, which produces a spectrum having uniform frequency resolution across the entire baseband, the WDFT's frequency resolution is both non-uniform and programmable. This feature is exploited for use in analyzing multinarrowband signals which are problematic to the DFT/FFT. The paper focuses on optimizing frequency discrimination by determining the best warping strategy and control by using the intelligent search algorithms and criteria of optimization, or cost functional. The system developed and tested focuses on maximizing the WDFT frequency resolution over those frequencies that exhibit a localized concentration of spectral energy and, implicitly, diminishing the importance of other frequency ranges. The paper demonstrates that by externally controlling the frequency resolution of the WDFT in an intelligent manner, multi-narrowband signals can be more readily detected and classified. Furthermore, the WDFT can be built upon an FFT enabled framework, insuring high efficiency and bandwidths.

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“…Determining the frequencies, i.e., the locations of local maxima of the spectrum, is the most difficult problem in these methods. For this purpose, iterative algorithms have been applied [6][7][8][9][10], the nonparametric spectrum interpolation methods [11][12] are applicable (zero padding technique [13], chirped-Z transform [14][15][16][17], warped DFT [18][19][20] and interpolation by decimation [11]) and the methods of interpolated DFTs have been developed . Nonparametric spectrum interpolation methods make it possible to zoom in on the frequency domain but do not decrease the errors caused by long-range spectral leakage (i.e., by sidelobes of spectrum lines of neighbor components in the spectrum), which are defined by the frequency characteristic of the data window applied [47].…”

Section: Introduction: Spectral Analysis and The Unit Circle Approximmentioning

confidence: 99%

Minimization of Maximum Errors in Universal Approximation of the Unit Circle by a Polygon

Borkowski¹

2011

Metrology and Measurement Systems

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This paper presents a universal approximation of the unit circle by a polygon that can be used in signal processing algorithms. Optimal choice of the values of three parameters of this approximation allows one to obtain a high accuracy of approximation. The approximation described in the paper has a universal character and can be used in many signal processing algorithms, such as DFT, that use the mathematical form of the unit circle. One of the applications of the described approximation is the DFT linear interpolation method (LIDFT). Applying the results of the presented paper to improve the LIDFT method allows one to significantly decrease the errors in estimating the amplitudes and frequencies of multifrequency signal components. The paper presents the derived formulas, an analysis of the approximation accuracy and the region of best values for the approximation parameters.

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Frequency estimation using warped discrete Fourier transform

Cited by 38 publications

References 8 publications

A new zoom algorithm and its use in frequency estimation

A new zoom algorithm and its use in frequency estimation

Efficient Detection of Multi-Narrowband Using the Warped Discrete Fourier Transform

Minimization of Maximum Errors in Universal Approximation of the Unit Circle by a Polygon

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