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