By Arndt J
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Extra info for Algorithms for Programmers
Example text
B {ω} B is the cc. of C {ω2 } C and therefore every B {} B-term is the cc. of the C {} C-term in the same line. Is there a nice and general scheme for real valued convolutions based on the MFA? Read on for the positive answer. 6 s, d lower half plus/minus higher half of x CHAPTER 2. 6 46 Convolution of real valued data using the MFA For row 0 (which is real after the column FFTs) one needs to compute the (usual) cyclic convolution; for row R/2 (also real after the column FFTs) a negacyclic convolution is needed7 , the code for that task is given on page 62.
G. multiplications, additions, load/stores) of the code it emits. Even better if those numbers are compared to the corresponding values found in the compiled assembler code. It is possible to have gcc produce the assembler code with the original source interlaced (which is a great tool with code optimization, cf. the target asm in the FXT makefile). lst As an example the (generated) template
The transposing back at the end of the routine can be avoided if a backtransform will follow9 , the backtransform must then be called with R and C swapped. The generalization to higher dimensions is straight forward. 10 The matrix Fourier algorithm (MFA) The matrix Fourier algorithm10 (MFA) works for (composite) data lengths n = R C. Consider the input array as a R × C-matrix (R rows, C columns). 7 (matrix Fourier algorithm) The matrix Fourier algorithm (MFA) for the FFT: 1. Apply a (length R) FFT on each column.
Algorithms for Programmers by Arndt J
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