153 lines
4 KiB
OCaml
153 lines
4 KiB
OCaml
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(*
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* Copyright (c) 1997-1999 Massachusetts Institute of Technology
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* Copyright (c) 2003, 2007-14 Matteo Frigo
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* Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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*
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*)
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(* trigonometric transforms *)
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open Util
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(* DFT of real input *)
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let rdft sign n input =
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Fft.dft sign n (Complex.real @@ input)
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(* DFT of hermitian input *)
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let hdft sign n input =
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Fft.dft sign n (Complex.hermitian n input)
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(* DFT real transform of vectors of two real numbers,
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multiplication by (NaN I), and summation *)
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let dft_via_rdft sign n input =
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let f = rdft sign n input
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in fun i ->
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Complex.plus
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[Complex.real (f i);
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Complex.times (Complex.nan Expr.I) (Complex.imag (f i))]
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(* Discrete Hartley Transform *)
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let dht sign n input =
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let f = Fft.dft sign n (Complex.real @@ input) in
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(fun i ->
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Complex.plus [Complex.real (f i); Complex.imag (f i)])
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let trigI n input =
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let twon = 2 * n in
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let input' = Complex.hermitian twon input
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in
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Fft.dft 1 twon input'
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let interleave_zero input = fun i ->
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if (i mod 2) == 0
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then Complex.zero
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else
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input ((i - 1) / 2)
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let trigII n input =
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let fourn = 4 * n in
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let input' = Complex.hermitian fourn (interleave_zero input)
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in
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Fft.dft 1 fourn input'
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let trigIII n input =
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let fourn = 4 * n in
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let twon = 2 * n in
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let input' = Complex.hermitian fourn
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(fun i ->
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if (i == 0) then
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Complex.real (input 0)
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else if (i == twon) then
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Complex.uminus (Complex.real (input 0))
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else
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Complex.antihermitian twon input i)
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in
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let dft = Fft.dft 1 fourn input'
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in fun k -> dft (2 * k + 1)
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let zero_extend n input = fun i ->
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if (i >= 0 && i < n)
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then input i
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else Complex.zero
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let trigIV n input =
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let fourn = 4 * n
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and eightn = 8 * n in
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let input' = Complex.hermitian eightn
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(zero_extend fourn (Complex.antihermitian fourn
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(interleave_zero input)))
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in
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let dft = Fft.dft 1 eightn input'
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in fun k -> dft (2 * k + 1)
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let make_dct scale nshift trig =
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fun n input ->
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trig (n - nshift) (Complex.real @@ (Complex.times scale) @@
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(zero_extend n input))
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(*
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* DCT-I: y[k] = sum x[j] cos(pi * j * k / n)
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*)
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let dctI = make_dct Complex.one 1 trigI
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(*
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* DCT-II: y[k] = sum x[j] cos(pi * (j + 1/2) * k / n)
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*)
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let dctII = make_dct Complex.one 0 trigII
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(*
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* DCT-III: y[k] = sum x[j] cos(pi * j * (k + 1/2) / n)
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*)
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let dctIII = make_dct Complex.half 0 trigIII
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(*
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* DCT-IV y[k] = sum x[j] cos(pi * (j + 1/2) * (k + 1/2) / n)
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*)
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let dctIV = make_dct Complex.half 0 trigIV
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let shift s input = fun i -> input (i - s)
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(* DST-x input := TRIG-x (input / i) *)
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let make_dst scale nshift kshift jshift trig =
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fun n input ->
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Complex.real @@
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(shift (- jshift)
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(trig (n + nshift) (Complex.uminus @@
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(Complex.times Complex.i) @@
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(Complex.times scale) @@
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Complex.real @@
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(shift kshift (zero_extend n input)))))
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(*
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* DST-I: y[k] = sum x[j] sin(pi * j * k / n)
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*)
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let dstI = make_dst Complex.one 1 1 1 trigI
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(*
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* DST-II: y[k] = sum x[j] sin(pi * (j + 1/2) * k / n)
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*)
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let dstII = make_dst Complex.one 0 0 1 trigII
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(*
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* DST-III: y[k] = sum x[j] sin(pi * j * (k + 1/2) / n)
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*)
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let dstIII = make_dst Complex.half 0 1 0 trigIII
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(*
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* DST-IV y[k] = sum x[j] sin(pi * (j + 1/2) * (k + 1/2) / n)
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*)
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let dstIV = make_dst Complex.half 0 0 0 trigIV
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