A q-version of the Fourier transformation and some of its properties are discussed. INTRODUCTION Models of q-harmonic oscillators are being developed in connection with quantum groups and their various applications (see, for example, Refs. [M], [Bi], [AS1], and [AS2]). For a complete correspondence with the quantum-mechanical oscillator problem, these models need an analog of the Fourier transf...

i I affirm, that I have created this diploma thesis on my own, with the exclusive usage of the refer-enced literature. Contents Introduction 1 1 Mathematical background 3 1. A Test images 77 iii iv CONTENTS Introduction The discrete wavelet transformation (see section 1.1 for details) has become a very popular tool to preprocess images to improve the performance of many tasks in the field of an...

The measurement algorithms applied in power quality measurement systems are based on Fast Fourier Transformation. That one-dimension frequency analysis is sufficient in many cases. However, to illustrate the character of the signal in a more comprehensive manner, it is crucial to represent the investigated signal on time-frequency plane. There are a lot of time-frequency representations (TFR) f...

Dispersive Fourier transformation is a powerful technique in which the spectrum of an optical pulse is mapped into a time-domain waveform using chromatic dispersion. It replaces a diffraction grating and detector array with a dispersive fiber and single photodetector. This simplifies the system and, more importantly, enables fast real-time measurements. Here we describe a novel ultrafast barcod...

i I affirm, that I have created this diploma thesis on my own, with the exclusive usage of the refer-enced literature. Contents Introduction 1 1 Mathematical background 3 1. A Test images 77 iii iv CONTENTS Introduction The discrete wavelet transformation (see section 1.1 for details) has become a very popular tool to preprocess images to improve the performance of many tasks in the field of an...

INTRODUCTION Postural instability is one of the most disabling features of Parkinson's disease. OBJECTIVE To evaluate postural balance in Parkinson's disease. METHODS Thirty patients with Parkinson's disease were compared with controls using Tetrax™ interactive balance system posturography. RESULTS For different positions, patients with Parkinson's disease showed a significantly higher we...

A family of orthonormal mode sets arises when Hermite-Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an orthosymplectic ray transformation matrix. Essentially new orthonormal mode sets can be obtained by lett...

In this paper we present the results of applying data compression to a three-dimensional object recognition technique based on phase-shift digital holography. Industry-standard lossless data compression algorithms were rst applied. Next, lossy techniques based on subsampling, discrete cosine transformation, and discrete Fourier transformation were examined. We used normalized cross-correlation ...

We use dispersive Fourier transformation to measure shot-to-shot spectral instabilities in femtosecond supercontinuum generation. We study both the onset phase of supercontinuum generation with distinct dispersive wave generation, as well as a highly-unstable supercontinuum regime spanning an octave in bandwidth. Wavelength correlation maps allow interactions between separated spectral componen...

Landscape structure is a main determinant of ecological landscape potentials. The basic differentiation of relief into depressions and elevations at deliberately chosen scales can be managed comfortably by the Fourier transformation. The automated extraction of these structures from an elevation map using Fourier transformation or singular value decomposition can help to overcome complicated an...