5 research outputs found
Two Families of Radix-2 FFT Algorithms With Ordered Input and Output Data
Two radix-2 families of fast Fourier transform (FFT)
algorithms that have the property that both inputs and outputs
are addressed in natural order are derived in this letter. The algorithms
obtained have the same complexity that Cooley鈥揟ukey
radix-2 algorithms but avoid the bit-reversal ordering applied to
the input. These algorithms can be thought as a variation of the
radix-2 Cooley鈥揟ukey ones
Detector de contorns basat en el domini transformat
RESUM
En aquest document es presenta un detector de contorns d鈥檌matges basat en el domini transformat. A partir de la
interpretaci贸 de la transformada de Fourier de la imatge i la seva formulaci贸 matricial en termes dels diferents modes,
es realitza una selecci贸 de les components passa baixes a partir de les quals es reconstrueix la component de baixa
freq眉猫ncia que es resta de la imatge original per tal d鈥檕btenir el detector. Aquest detector de contorns no 茅s esbiaixat.
L鈥檃lgorisme pot ser aplicat utilitzant diferents mides del bloc de processament, que pot anar de la imatge sencera a
blocs de redu茂des dimensions: 36X36, 16x16 o 8x8, per fer un seguiment de les propietats locals de la imatge quan
aquesta 茅s presenta caracter铆stiques espacials poc uniformes.En este documento se presenta un detector de contornos de im谩genes basado en el dominio transformado. A partir de
la interpretaci贸n de la transformada de Fourier de la imagen y su formulaci贸n matricial en t茅rminos de los diferentes
modos, se realiza una selecci贸n de las componentes paso-bajas a partir de las cuales se reconstruye la componente
de baja frecuencia que se restar谩 a la imagen original pora obtener el detector. Este detector de contornos no es
sesgado. El algoritmo puede ser aplicado utilizando diferentes medidas del bloque de procesado, que puede ir de la
imagen entera a bloques de reducidas dimensiones: 36x36, 16x16 o 8x8, que permiten hacer un seguimiento de las
propiedades locales de la imagen cuando 茅sta presenta caracter铆sticas sectoriales muy diversas.In this document an image contour detector based on the transformed domain is presented. Following the interpretation
of the image Fourier transform and its matrix formulation in terms of its different modes, we select the base-band ones
from which we reconstruct the low frequency image component. This component is subtracted to the original image in
order to obtain the contours. This contour detector is not biased. The algorithm can be implemented using different block
processing sizes, which can range from the entire image to blocks of smaller dimensions: 36x36, 16x16 or 8x8. Small
blocks improve the contour detector performance when the local properties of the image are not uniform
Quantum Fourier transform revisited
The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a particular matrix decomposition of the discrete Fourier transform (DFT) matrix. In this paper, we show that the quantum Fourier transform (QFT) can be derived by further decomposing the diagonal factors of the FFT matrix decomposition into products of matrices with Kronecker product structure. We analyze the implication of this Kronecker product structure on the discrete Fourier transform of rank-1 tensors on a classical computer. We also explain why such a structure can take advantage of an important quantum computer feature that enables the QFT algorithm to attain an exponential speedup on a quantum computer over the FFT algorithm on a classical computer. Further, the connection between the matrix decomposition of the DFT matrix and a quantum circuit is made. We also discuss a natural extension of a radix-2 QFT decomposition to a radix-d QFT decomposition. No prior knowledge of quantum computing is required to understand what is presented in this paper. Yet, we believe this paper may help readers to gain some rudimentary understanding of the nature of quantum computing from a matrix computation point of view
New FFT/IFFT Factorizations with Regular Interconnection Pattern Stage-to-Stage Subblocks
Les factoritzacions de la FFT (Fast Fourier Transform) que presenten un patr贸 d鈥檌nterconnexi贸 regular entre factors o
etapes son conegudes com algorismes paral路lels, o algorismes de Pease, ja que foren originalment proposats per
Pease. En aquesta contribuci贸 s鈥檋an desenvolupat noves factoritzacions amb blocs que presenten el patr贸
d鈥檌nterconnexi贸 regular de Pease. S鈥檋a mostrat com aquests blocs poden ser obtinguts a una escala pr猫viament
seleccionada. Les noves factoritzacions per ambdues FFT i IFFT (Inverse FFT) tenen dues classes de factors: uns pocs
factors del tipus Cooley-Tukey i els nous factors que proporcionen la mateix patr贸 d鈥檌nterconnexi贸 de Pease en blocs.
Per a una factoritzaci贸 donada, els blocs comparteixen dimensions, el patr贸 d鈥檌nterconnexi贸 etapa a etapa i a m茅s cada
un d鈥檈lls pot ser calculat independentment dels altres.FFT (Fast Fourier Transform) factorizations presenting a regular interconnection pattern between factors or stages are
known as parallel algorithms, or Pease algorithms since were first proposed by Pease. In this paper, new FFT/IFFT
(Inverse FFT) factorizations with blocks that exhibit regular Pease interconnection pattern are derived. It is shown these
blocks can be obtained at a previously selected scale. The new factorizations for both the FFT and IFFT have two kinds
of factors: a few Cooley-Tukey type factors and new factors providing the same Pease interconnection pattern property
in blocks. For a given factorization, these blocks share dimensions, the interconnection pattern stage-to-stage, and all of
them can be calculated independently from one another.Las factoritzaciones de la FFT (Fast Fourier Transform) que presentan un patr贸n de interconexiones regular entre
factores o etapas son conocidas como algoritmos paralelos, o algoritmos de Pease, puesto que fueron originalmente
propuestos por Pease. En esta contribuci贸n se han desarrollado nuevas factoritzaciones en subbloques que presentan
el patr贸n de interconexi贸n regular de Pease. Se ha mostrado como estos bloques pueden ser obtenidos a una escalera
previamente seleccionada. Las nuevas factoritzaciones para ambas FFT y IFFT (Inverse FFT) tienen dos clases de
factores: unos pocos factores del tipo Cooley-Tukey y los nuevos factores que proporcionan el mismo patr贸n de
interconexi贸n de Pease en bloques. Para una factoritzaci贸n dada, los bloques comparten dimensiones, patr贸n
d鈥檌nterconexi贸n etapa a etapa y adem谩s cada uno de ellos puede ser calculado independientemente de los otros