Topic
Spectral density estimation
About: Spectral density estimation is a research topic. Over the lifetime, 5391 publications have been published within this topic receiving 123105 citations.
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Papers
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TL;DR: By employing the sparse signal reconstruction algorithms, ideal time-frequency representations are obtained and the presented theory is illustrated on several examples dealing with different auto-correlation functions and corresponding TFDs.
Abstract: The estimation of time-varying instantaneous frequency (IF) for monocomponent signals with an incomplete set of samples is considered. A suitable time-frequency distribution (TFD) reduces the non-stationary signal into a local sinusoid over the lag variable prior to the Fourier transform. Accordingly, the observed spectral content becomes sparse and suitable for compressive sensing reconstruction in the case of missing samples. Although the local bilinear or higher order auto-correlation functions will increase the number of the missing samples, the analysis shows that an accurate IF estimation can be achieved even if we deal with only few samples, as long as the auto-correlation function is properly chosen to coincide with the signals phase non-linearity. In addition, by employing the sparse signal reconstruction algorithms, ideal time-frequency representations are obtained. The presented theory is illustrated on several examples dealing with different auto-correlation functions and corresponding TFDs.
42 citations
03 May 2010
TL;DR: This paper proposes a fast interpolation method, independent of the window type and order, based on suitable lookup tables, proving that the method provides results as good as those obtained with other methods, without requiring the same high computation burden.
Abstract: The evaluation of the spectral components of a signal by means of discrete Fourier transform or fast Fourier transform algorithms is subject to leakage errors whenever the sampling frequency is not coherent with the signal frequency. Smoothing windows are used to mitigate these errors, and interpolation methods are applied in the frequency domain to reduce them further on. However, if cosine windows are employed, closed-form formulas for the evaluation of harmonic frequencies can be used only with the Rife-Vincent class I windows, while approximated formulas have to be used in other cases. In both cases, a high computation burden is required. This paper proposes a fast interpolation method, independent of the window type and order, based on suitable lookup tables. Experimental results are reported, and the accuracy is discussed, proving that the method provides results as good as those obtained with other methods, without requiring the same high computation burden.
42 citations
TL;DR: In this paper, the Fourier transform method of interference pattern analysis is used for phase measurements of 3D surfaces, free from errors caused by highfrequency disturbances and the variation of background intensity.
Abstract: A Fourier transform method of interference pattern analysis is a powerful tool for automatic phase measurements. The technique is free from errors caused by high-frequency disturbances and the variation of background intensity. The method is particularly useful for waviness and roughness profile reconstruction of 3D surfaces.
42 citations
TL;DR: In this paper, it was shown that extended zero-filling (e.g., a "zoom" transform) actually reduces the accuracy with which the spectral peak position can be determined, and that the results can be more accurate when the FFT processor operates with floating-point (preferably double-precision) rather than fixed-point arithmetic.
Abstract: A frequency-domain Lorentzian spectrum can be derived from the Fourier transform of a time-domain exponentially damped sinusoid of infinite duration. Remarkably, it has been shown that even when such a noiseless time-domain signal is truncated to zero amplitude after a finite observation period, one can determine the correct frequency of its corresponding magnitude-mode spectral peak maximum by fitting as few as three spectral data points to a magnitude-mode Lorentzian spectrum. In this paper, we show how the accuracy of such a procedure depends upon the ratio of time-domain acquisition period to exponential damping time constant, number of time-domain data points, computer word length, and number of time-domain zero-fillings. In particular, we show that extended zero-filling (e.g., a "zoom" transform) actually reduces the accuracy with which the spectral peak position can be determined. We also examine the effects of frequency-domain random noise and round-off errors in the fast Fourier transformation (FFT) of time-domain data of limited discrete data word length (e.g., 20 bit/word at single and double precision). Our main conclusions are: (1) even in the presence of noise, a three-point fit of a magnitude-mode spectrum to a magnitude-mode Lorentzian line shape can offer an accurate estimate of peak position in Fourier transform spectroscopy; (2) the results can be more accurate (by a factor of up to 10) when the FFT processor operates with floating-point (preferably double-precision) rather than fixed-point arithmetic; and (3) FFT roundoff errors can be made negligible by use of sufficiently large (> 16 K) data sets.
42 citations
TL;DR: In this paper, Levinson's algorithm is developed in the context of mean-square estimation and is applied to a variety of topics related to Wiener filtering and spectral estimation, including prediction theory, Wold's decomposition, lattice filters, autoregressive processes, the method of maximum entropy, and the general class of extrapolating spectra.
Abstract: Levinson’s algorithm is developed in the context of mean-square estimation and is applied to a variety of topics related to Wiener filtering and spectral estimation. The study includes the innovations approach to prediction theory, Wold’s decomposition, lattice filters, autoregressive processes, the method of maximum entropy, and the general class of extrapolating spectra.
42 citations