64 lines
1.4 KiB
Plaintext
64 lines
1.4 KiB
Plaintext
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(* Copyright (c) 2011 Stefan Krah. All rights reserved. *)
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The Six Step Transform:
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=======================
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In libmpdec, the six-step transform is the Matrix Fourier Transform (See
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matrix-transform.txt) in disguise. It is called six-step transform after
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a variant that appears in [1]. The algorithm requires that the input
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array can be viewed as an R*C matrix.
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Algorithm six-step (forward transform):
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---------------------------------------
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1a) Transpose the matrix.
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1b) Apply a length R FNT to each row.
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1c) Transpose the matrix.
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2) Multiply each matrix element (addressed by j*C+m) by r**(j*m).
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3) Apply a length C FNT to each row.
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4) Transpose the matrix.
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Note that steps 1a) - 1c) are exactly equivalent to step 1) of the Matrix
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Fourier Transform. For large R, it is faster to transpose twice and do
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a transform on the rows than to perform a column transpose directly.
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Algorithm six-step (inverse transform):
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---------------------------------------
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0) View the matrix as a C*R matrix.
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1) Transpose the matrix, producing an R*C matrix.
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2) Apply a length C FNT to each row.
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3) Multiply each matrix element (addressed by i*C+n) by r**(i*n).
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4a) Transpose the matrix.
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4b) Apply a length R FNT to each row.
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4c) Transpose the matrix.
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Again, steps 4a) - 4c) are equivalent to step 4) of the Matrix Fourier
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Transform.
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--
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[1] David H. Bailey: FFTs in External or Hierarchical Memory
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http://crd.lbl.gov/~dhbailey/dhbpapers/
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