One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as linearity, of being stationary, and of satisfjmg the Dirichlet conditions. A recent development at the National Aeronautics an...

This paper presents a class of random orthogonal sequences associated with the number theoretic Hilbert transform. We present a constructive procedure for finding the random sequences for different modulus values. These random sequences have autocorrelation function that is zero everywhere excepting at the origin. These sequences may be used as keys and in other cryptography applications.

Computing the Fourier transform and its inverse is important in many applications of mathematics, such as frequency analysis, signal modulation, and filtering. Two methods will be derived for numerically computing the inverse Fourier transforms, and they will be compared to the standard inverse discrete Fourier transform (IDFT) method. The first computes the inverse Fourier transform through di...

We propose a new band-extrapolation method using an iterative Hilbert-transform procedure, which is applicable for band-limited complex-frequency data obtained from a Fourier-transform phase-modulation fluorometer (FT-PMF). Without the band limitation, the real and the imaginary parts of the complex-frequency data obtained from the FT-PMF form a Hilbert-transform pair because of causality. Howe...

In this paper we address the parallel beam 2D computer tomography reconstruction. The proposed method belongs to the field of analytic reconstruction methods and is compared to several methods known in the field, among other the two-step Hilbert-transform method. In contrast to the latter, the derivative data is multiplied with an orientation vector and the Hilbert transform is replaced with th...