Search results for "Discrete Fourier Transform"
showing 10 items of 22 documents
Discrete wavelet transform implementation in Fourier domain for multidimensional signal
2002
Wavelet transforms are often calculated by using the Mallat algorithm. In this algorithm, a signal is decomposed by a cascade of filtering and downsampling operations. Computing time can be important but the filtering operations can be speeded up by using fast Fourier transform (FFT)-based convolutions. Since it is necessary to work in the Fourier domain when large filters are used, we present some results of Fourier-based optimization of the sampling operations. Acceleration can be obtained by expressing the samplings in the Fourier domain. The general equations of the down- and upsampling of digital multidimensional signals are given. It is shown that for special cases such as the separab…
A Robust Wrap Reduction Algorithm for Fringe Projection Profilometry and Applications in Magnetic Resonance Imaging.
2017
In this paper, we present an effective algorithm to reduce the number of wraps in a 2D phase signal provided as input. The technique is based on an accurate estimate of the fundamental frequency of a 2D complex signal with the phase given by the input, and the removal of a dependent additive term from the phase map. Unlike existing methods based on the discrete Fourier transform (DFT), the frequency is computed by using noise-robust estimates that are not restricted to integer values. Then, to deal with the problem of a non-integer shift in the frequency domain, an equivalent operation is carried out on the original phase signal. This consists of the subtraction of a tilted plane whose slop…
Optical illustration of a varied fractional Fourier-transform order and the Radon-Wigner display.
2010
Based on an all-optical system, a display of a fractional Fourier transform with many fractional orders is proposed. Because digital image-processing terminology is used, this display is known as the Radon–Wigner transform. It enables new aspects for signal analysis that are related to time- and spatial-frequency analyses. The given approach for producing this display starts with a one-dimensional input signal although the output signal contains two dimensions. The optical setup for obtaining the fractional Fourier transform was adapted to include only fixed free-space propagation distances and variable lenses. With a set of two multifacet composite holograms, the Radon–Wigner display has b…
Introduction: Signals and Transforms
2015
In this chapter we outline some well known facts about periodic signals and transforms, which are needed throughout the book. For details we refer to the classical textbook Oppenheim and Schafer [2].
Electric quantum walks in two dimensions
2015
We study electric quantum walks in two dimensions considering Grover, Alternate, Hadamard, and DFT quantum walks. In the Grover walk the behaviour under an electric field is easy to summarize: when the field direction coincides with the x or y axes, it produces a transient trapping of the probability distribution along the direction of the field, while when it is directed along the diagonals, a perfect 2D trapping is frustrated. The analysis of the alternate walk helps to understand the behaviour of the Grover walk as both walks are partially equivalent; in particular, it helps to understand the role played by the existence of conical intersections in the dispersion relations, as we show th…
Teaching Fourier optics through ray matrices
2005
In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics prov…
White-light optical implementation of the fractional fourier transform with adjustable order control.
2000
An optical implementation of the fractional Fourier transform (FRT) with broadband illumination is proposed by use of a single imaging element, namely, a blazed diffractive lens. The setup displays an achromatized version of the FRT of order P of any two-dimensional input function. This fractional order can be tuned continuously by shifting of the input along the optical axis. Our compact and flexible configuration is tested with a chirplike input signal, and the good experimental results obtained support the theory.
Aiding phase unwrapping by increasing the number of residues in two-dimensional wrapped-phase distributions.
2015
In phase unwrapping residues are points of locally inconsistent phase that occur within a wrapped-phase map, which are usually regarded as being problematic for phase-unwrapping algorithms. Real phase maps typically contain a number of residues that are approximately proportional to the subsequent difficulty in unwrapping the phase distribution. This paper suggests the radical use of the discrete Fourier transform to actually increase the number of residues in 2D phase-wrapped images that contain discontinuities. Many of the additional residues that are artificially generated by this method are located on these discontinuities. For example, in fringe projection systems, such phase discontin…
Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm.
1996
A method for the calculation of the fractional Fourier transform (FRT) by means of the fast Fourier transform (FFT) algorithm is presented. The process involves mainly two FFT’s in cascade; thus the process has the same complexity as this algorithm. The method is valid for fractional orders varying from −1 to 1. Scaling factors for the FRT and Fresnel diffraction when calculated through the FFT are discussed.
Jauni ieskati kvantu automātu stāvokļu skaita efektivitātē
2022
Kvantu galīgi automāti var sasniegt eksponenciālu stāvokļu skaitu efektivitāti, salīdzinot ar determinētiem galīgiem automātiem. Viena problēma, kurā ir zināms, ka kvantu galīgiem automātiem ir eksponenciālas priekšrocības, ir MODn problēma, taču nav zināma metode, kā uzkonstruēt tādu kvantu automātu. Šajā darbā eksponenciāli efektīvie MODn algoritmi tiek vispārināti jaunā algoritmā, kas samazina vajadzīgo stāvokļu skaitu. Jaunā algoritma saaistības ar esošiem virzieniem literatūrā tiek aprakstītas, un tiek piedāvātas divas jaunas skaitļu virknes, kuras varētu izmantot, lai uzkonstruētu tādus kvantu automātus.