The paper derives a 2-Dimensional spectrum estimator from some recent results on the statistical properties of wavelet packet coefficients of random processes. It provides an analysis of the bias of this estimator with respect to the wavelet order. The paper also discusses the performance of this wavelet based estimator, in comparison with the conventional 2-D Fourier-based spectrum estimator o...

In measuring the power spectrum of the distribution of large numbers of dark matter particles in simulations, or galaxies in observations, one has to use Fast Fourier Transforms (FFT) for calculational efficiency. However, because of the required mass assignment onto grid points in this method, the measured power spectrum 〈|δf (k)|2〉 obtained with an FFT is not the true power spectrum P (k) but...

Howard E. Michel Abdul Ahad S. Awwal, MEMBER SPIE Wright State University Computer Science and Engineering Department Dayton, Ohio 45435 E-mail: [email protected] Abstract. A new implementation of the joint Fourier transform correlation (JFTC) utilizing the phase information in the Fourier plane is proposed. When a phase-based thresholding scheme is used on the joint Fourier spectrum, the co...

A new design of laser warning system is proposed. This novel system is composed of an optical antenna based on fiber bundle and a spatially modulated stationary Michelson interferometer as Fourier transform device. The interferometer has no moving parts, which can distinguish laser from background noise and from other non-coherent radiation such as flares, sunlight, and lighting. Based on Fouri...

one of the most fundamental reservoir characteristics is the thickness. the analysis of thin bed tuning on seismic reflectivity has been studied extensively by wides (1973) and neidel and pogiaggliomi (1977), who discussed the limits of seismic resolution. during the past decade, the industry has developed a plethora of new attributes in studying thin beds by employing spectral decomposition (p...

We present a new signal processing method that extracts the reference spectrum information from an acquired optical coherence tomography (OCT) image without a separate calibration step of reference spectrum measurement. The reference spectrum is used to remove the fixed-pattern noise that is a characteristic artifact of Fourier-domain OCT schemes. It was found that the conventional approach bas...

We show that a stationary signal concept such as the Fourier transform (FT) can be linked to a time-varying (TV) concept such as linear TV filtering. In particular, we give a continuous-time and discrete-time linear TV filter interpretation to continuous-time FT and discrete Fourier transform (DFT), respectively. As a consequence, important variants such as warped DFT, DCT, DST also can be view...

A technique for calculation of variability coherence at different timescales performed directly in the time domain is introduced. Simulations are made to compare the coherence spectrum derived by the time domain technique with the coherence function by Fourier analysis. The results indicate that in comparison with the Fourier analysis the time domain technique is more powerful for revealing sig...

Ramanujan sums are exponential sums with exponent defined over the irreducible fractions. Until now, they have been used to provide converging expansions to some arithmetical functions appearing in the context of number theory. In this paper, we provide an application of Ramanujan sum expansions to periodic, quasiperiodic and complex time series, as a vital alternative to the Fourier transform....

The fractional Fourier transform is a mathematical operation that generalizes the well-known Fourier transform. This operation has been shown to have physical and optical fundamental meanings, and it has been experimentally implemented by relatively simple optical setups. Based on the fractional Fourier-transform operation, a new space-frequency chart definition is introduced. By the applicatio...