Get Mathematics of Multidimensional Fourier Transform PDF

By Richard Tolimieri, Myoung An, Chao Lu

ISBN-10: 0387941053

ISBN-13: 9780387941059

ISBN-10: 0387982604

ISBN-13: 9780387982601

The most emphasis of this publication is the advance of algorithms for processing multi-dimensional electronic signs, and especially, algorithms for multi-dimensional Fourier transforms in a kind that's handy for writing hugely effective code on various vector and parallel desktops. The quickly expanding energy of computing chips, the elevated availability of vector and array processors, and the expanding dimension of the knowledge units to be analyzed make writing code that takes the entire algorithmic probabilities into consideration and suits those to the objective structure a tricky job. via emphasizing the unified foundation for some of the ways to multidimensional Fourier transforms, the ebook additionally clarifies tips to make the most the variations in optimizing implementations. This booklet could be of curiosity not just to utilized mathematicians and computing device scientists, but in addition to seismologists, high-energy physicists, crystallographers, electric engineers engaged on photograph processing, and others. themes coated contain: tensor items and the short Fourier rework, one dimensional and multi-dimensional; finite Abelian teams and Fourier transforms; Cooley-Tukey and Good-Thomas algorithms; traces and planes; box algorithms; implementation on RISC and parallel architectures.

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Additional info for Mathematics of Multidimensional Fourier Transform Algorithms, Second edition (Signal Processing and Digital Filtering)

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In diesem Fall muss aber ur alle k ≥ 1 yn = xnn gelten. Dies steht im Widerspruch zu yk = xkk f¨ und somit zur Annahme der Abz¨ ahlbarkeit von (0, 1). Die Annahme ist also falsch und der Satz damit bewiesen. Etwas weniger formal kann man also sagen, dass es viel mehr reelle als rationale Zahlen gibt. Auf den ersten Blick √ mag dies verwundern, ullt haben. Es da wir doch anschaulich nur die L¨ ucken wie 2 aufgef¨ sind eben sehr viele L¨ ucken. Schließlich halten wir noch fest, dass die Unendlichkeiten keine Grenzen kennen.

2 Umkehrbarkeit von Funktionen Oftmals treten Situationen auf, in denen man eine Gleichung der Form f (x) = y nach x aufl¨osen m¨ ochte. Zum Beispiel ist der Preis (y), den man am Monats- oder Jahresende f¨ ur Strom bezahlt, eine Funktion der verbrauchten Menge (x). Umgekehrt kann man sich bei Erhalt der Rechnung, also in Kenntnis des Preises (y), fragen, wie hoch der Verbrauch gewesen ist, der zu der Rechnung gef¨ uhrt hat. Man m¨ochte also eine Gleichung der Form x = g(y) 42 4 Funktionen erhalten.

1 Grundbegriffe 37 d) Ganz wichtig sind auch die Polynome n-ten Grades (n ∈ N) der Form f (x) = an xn + an−1 xn−1 + . . + a1 x + a0 mit Konstanten a0 , . . , an ∈ R. Eine weitere wichtige Funktion ist die Betragsfunktion. 2 (Absolutbetrag). | : R → R, f¨ ur die gilt x→ x −x f¨ ur x ≥ 0 f¨ ur x < 0. Aus der Definition der Betragsfunktion und den Ordnungseigenschaften der reellen Zahllen ergibt sich folgender Satz. 2 (Eigenschaften des Betrags). 5) Beweis. Der Beweis ist nicht schwer, aber eher abstrakt.

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Mathematics of Multidimensional Fourier Transform Algorithms, Second edition (Signal Processing and Digital Filtering) by Richard Tolimieri, Myoung An, Chao Lu

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