Various transforms are employed for signal processing to obtain useful information, which is not explicitly available when the signal is in the time domain. Most of the real time signals such as speech, biomedical signals, etc., are non-stationary signals. The Fourier transform (FT), used for most of the signal processing applications, determines the frequency components present in the signal b...

Certain solutions to Harper’s equation are discrete analogues of (and approximations to) the Hermite–Gaussian functions. They are the energy eigenfunctions of a discrete algebraic analogue of the harmonic oscillator, and they lead to a definition of a discrete fractional Fourier transform (FT). The discrete fractional FT is essentially the time-evolution operator of the discrete harmonic oscill...

Integrable equations with second order Lax pair like KdV and CamassaHolm (CH) exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants (Schwarz form). These properties for the CH hierarchy are discussed in this contribution. The squared eigenfunctions of the spectral problem, associated to the Camassa-Holm equation represent a complete basis of ...

Wave-front reconstruction with the use of the fast Fourier transform (FFT) and spatial filtering is shown to be computationally tractable and sufficiently accurate for use in large Shack-Hartmann-based adaptive optics systems (up to at least 10,000 actuators). This method is significantly faster than, and can have noise propagation comparable with that of, traditional vector-matrix-multiply rec...

In this article, recent measurements made with LIFTIRS, the Livermore Imaging Fourier Transform InfraRed Spectrometer, are presented. The experience gained with this instrument has produced a variety of insights into the tradeoffs between signal to noise ratio (SNR), spectral resolution and temporal resolution for time multiplexed Fourier transform imaging spectrometers. This experience has als...

Quantum image recognition is a technology by using quantum algorithm to process the image information. It can obtain better effect than classical algorithm. In this paper, four different quantum algorithms are used in the three stages of palmprint recognition. First, quantum adaptive median filtering algorithm is presented in palmprint filtering processing. Quantum filtering algorithm can get a...

This paper addresses the features of Hough Transform (HT) butterflies suitable for image-based segment detection and measurement. The full segment parameters such as the position, slope, width, length, continuity, and uniformity are related to the features of the HT butterflies. Mathematical analysis and experimental data are presented in order to demonstrate and build the relationship between ...

Motivated by a recently proposed biologically inspired face recognition approach, we investigated the relation between human behavior and a computational model based on Fourier-Bessel (FB) spatial patterns. We measured human recognition performance of FB filtered face images using an 8-alternative forced-choice method. Test stimuli were generated by converting the images from the spatial to the...

A method is presented for using a Fourier transform spectrometer (FTS) to calibrate the metrology of a second FTS. This technique is particularly useful when the second FTS is inside a cryostat or otherwise inaccessible.

Elliptical Fourier functions (EFF) were generated for the boundary outline of the mandibular form in 24 non-orthodontic growth study subjects at 9, 11, 13, and 15 years of age. The mean residual fit (observed versus predicted points) of the mandibular form was 0.11 mm, with a range from 0.09 to 0.14 mm, suggesting an accurate fit. The mean plot for each of the four age groups was area standardi...