New PDF release: Algorithms for Discrete Fourier Transform and Convolution,

By Richard Tolimieri, Myoung An, Chao Lu

ISBN-10: 0387982612

ISBN-13: 9780387982618

This graduate-level textual content offers a language for figuring out, unifying, and imposing a large choice of algorithms for electronic sign processing - specifically, to supply principles and methods which can simplify or perhaps automate the duty of writing code for the most recent parallel and vector machines. It therefore bridges the distance among electronic sign processing algorithms and their implementation on various computing systems. The mathematical thought of tensor product is a habitual topic during the ebook, considering those formulations spotlight the information stream, that is in particular very important on supercomputers. due to their value in lots of purposes, a lot of the dialogue centres on algorithms with regards to the finite Fourier rework and to multiplicative FFT algorithms.

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Additional resources for Algorithms for Discrete Fourier Transform and Convolution, Second edition (Signal Processing and Digital Filtering)

Sample text

Usually we choose 5- 1 mod 7 to be the smallest positive integer among them. 16 2. 3) where for i = 1,2, ... , n, mi are positive integers and bi are integers. We call it a set of simultaneous linear Diophantine equations. Are these simultaneous linear Diophantine equations solvable and how can we solve them? Now let us consider a special case when mi (i = 1,2, ... , n) are pairwise relatively prime. Theorem 5 (Chinese Remainder Theorem (CRT» Assume that mi (i = 1,2, ... , n) are positive integers and pairwise relatively prime.

3) where for i = 1,2, ... , n, mi are positive integers and bi are integers. We call it a set of simultaneous linear Diophantine equations. Are these simultaneous linear Diophantine equations solvable and how can we solve them? Now let us consider a special case when mi (i = 1,2, ... , n) are pairwise relatively prime. Theorem 5 (Chinese Remainder Theorem (CRT» Assume that mi (i = 1,2, ... , n) are positive integers and pairwise relatively prime. 4) where M = mlm2··· m n , M i 1,2, ... , n). Proof.

Theorem 13 is essential, but it is difficult to use it for constructing a PT. Now we consider the next theorem. 28 2. 12) where GCD means the greatest common divisor. With some knowledge of the number theory, this theorem can be proven (see [4]). Using this theorem, we can derive two types of PTs, which are particularly useful for constructing fast algorithms. Theorem 15 (M(z),G(z),pl) is aPT ifp is a prime number, l is a positive integer, G(z) is a nonzero polynomial and I GP (z) - 1 M(z) = GPI-l() z-1 .

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Algorithms for Discrete Fourier Transform and Convolution, Second edition (Signal Processing and Digital Filtering) by Richard Tolimieri, Myoung An, Chao Lu


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