## Computational Frameworks for the Fast Fourier TransformThe most comprehensive treatment of FFTs to date. Van Loan captures the interplay between mathematics and the design of effective numerical algorithms--a critical connection as more advanced machines become available. A stylized Matlab notation, which is familiar to those engaged in high-performance computing, is used. The Fast Fourier Transform (FFT) family of algorithms has revolutionized many areas of scientific computation. The FFT is one of the most widely used algorithms in science and engineering, with applications in almost every discipline. This volume is essential for professionals interested in linear algebra as well as those working with numerical methods. The FFT is also a great vehicle for teaching key aspects of scientific computing. |

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Acoust applied array assume autosort bit reversal block matrix butterfly C.S. Burrus cache column complex conjugate-even convolution Cooley–Tukey framework defined develop DFT matrix DFT problem Discrete Fourier Transform Discrete Sine Transform discussed DST-II end end end equation external memory Fast Fourier Transform FFT Algorithm following algorithm computes following algorithm overwrites Fºr IEEE IEEE Trans implementation in-place in-place algorithm integer intermediate DFTs inverse involves Kron Kronecker product Lemma length loop m.id main memory Mixed Radix mixed-radix multiple DFT multirow DFT node notation Notes and References obtain the following Parallel Comput Pease perfect shuffle prime factor Proc(u procedure processor Proof r(kL Radix radix-2 recursive References for Section shared-memory Speech Signal Process split-radix Suppose Temperton Theorem transposed Stockham twiddle-factor two-dimensional unit stride update workspace Xice y(jr z(kL zloe