A Short Survey on Arithmetic Transforms and the Arithmetic Hartley Transform
Copyright policy )A Short Survey on Arithmetic Transforms and the Arithmetic Hartley Transform
La complexité arithmétique a un rôle principal dans la performance des algorithmes d'évaluation du spectre. La théorie des transformées arithmétiques offre une méthode de calcul des transformées trigonométriques avec un nombre minimal de multiplications. Dans cet article, les algorithmes proposés pour la transformée de Fourier arithmétique sont étudiés. Une nouvelle transformée arithmétique pour calculer la transformée de Hartley discrète est introduite : la transformée de Hartley arithmétique. Le processus d'interpolation s'avère être l'élément clé de la théorie de la transformation arithmétique.
La complejidad aritmética tiene un papel principal en el rendimiento de los algoritmos para la evaluación del espectro. La teoría de transformadas aritméticas ofrece un método para calcular transformadas trigonométricas con un número mínimo de multiplicaciones. En este trabajo se estudian los algoritmos propuestos para la transformada aritmética de Fourier. Se introduce una nueva transformada aritmética para calcular la transformada discreta de Hartley: la transformada aritmética de Hartley. El proceso de interpolación se muestra como el elemento clave de la teoría de la transformación aritmética.
Arithmetic complexity has a main role in the performance of algorithms for spectrum evaluation. Arithmetic transform theory offers a method for computing trigonometrical transforms with minimal number of multiplications. In this paper, the proposed algorithms for the arithmetic Fourier transform are surveyed. A new arithmetic transform for computing the discrete Hartley transform is introduced: the Arithmetic Hartley transform. The interpolation process is shown to be the key element of the arithmetic transform theory.
يلعب التعقيد الحسابي دورًا رئيسيًا في أداء الخوارزميات لتقييم الطيف الترددي. تقدم نظرية التحويل الحسابي طريقة لحساب التحويلات المثلثية بأقل عدد من الضربات. في هذه الورقة، يتم مسح الخوارزميات المقترحة لتحويل فورييه الحسابي. تم تقديم تحويل حسابي جديد لحساب تحويل هارتلي المنفصل: تحويل هارتلي الحسابي. تبين أن عملية الاستيفاء هي العنصر الرئيسي في نظرية التحويل الحسابي.
- UNIVERSIDADE DE SAO PAULO Brazil
- Universidade Federal de Pernambuco Brazil
Arbitrary-precision arithmetic, Mathematical analysis, Engineering, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Hartley transform, Mathematics - Numerical Analysis, Floating-Point Arithmetic in Scientific Computation, Advanced Techniques in Digital Signal Processing, Discrete Fourier transform (general), Interval Analysis, Algebra over a field, Arithmetic, 42Bxx, 65Txx, Pure mathematics, Numerical Analysis (math.NA), System Identification Techniques, Affine arithmetic, Affine transformation, Fourier analysis, Fractional Fourier transform, Algorithm, Computational Theory and Mathematics, Discrete Hartley transform, Saturation arithmetic, Mathematics - Classical Analysis and ODEs, Control and Systems Engineering, Signal Processing, Computer Science, Physical Sciences, Fourier transform, Mathematics
Arbitrary-precision arithmetic, Mathematical analysis, Engineering, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Hartley transform, Mathematics - Numerical Analysis, Floating-Point Arithmetic in Scientific Computation, Advanced Techniques in Digital Signal Processing, Discrete Fourier transform (general), Interval Analysis, Algebra over a field, Arithmetic, 42Bxx, 65Txx, Pure mathematics, Numerical Analysis (math.NA), System Identification Techniques, Affine arithmetic, Affine transformation, Fourier analysis, Fractional Fourier transform, Algorithm, Computational Theory and Mathematics, Discrete Hartley transform, Saturation arithmetic, Mathematics - Classical Analysis and ODEs, Control and Systems Engineering, Signal Processing, Computer Science, Physical Sciences, Fourier transform, Mathematics
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