Chris@42: (*
Chris@42:  * Copyright (c) 1997-1999 Massachusetts Institute of Technology
Chris@42:  * Copyright (c) 2003, 2007-14 Matteo Frigo
Chris@42:  * Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology
Chris@42:  *
Chris@42:  * This program is free software; you can redistribute it and/or modify
Chris@42:  * it under the terms of the GNU General Public License as published by
Chris@42:  * the Free Software Foundation; either version 2 of the License, or
Chris@42:  * (at your option) any later version.
Chris@42:  *
Chris@42:  * This program is distributed in the hope that it will be useful,
Chris@42:  * but WITHOUT ANY WARRANTY; without even the implied warranty of
Chris@42:  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
Chris@42:  * GNU General Public License for more details.
Chris@42:  *
Chris@42:  * You should have received a copy of the GNU General Public License
Chris@42:  * along with this program; if not, write to the Free Software
Chris@42:  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
Chris@42:  *
Chris@42:  *)
Chris@42: 
Chris@42: (* trigonometric transforms *)
Chris@42: open Util
Chris@42: 
Chris@42: (* DFT of real input *)
Chris@42: let rdft sign n input =
Chris@42:   Fft.dft sign n (Complex.real @@ input)
Chris@42: 
Chris@42: (* DFT of hermitian input *)
Chris@42: let hdft sign n input =
Chris@42:   Fft.dft sign n (Complex.hermitian n input)
Chris@42: 
Chris@42: (* DFT real transform of vectors of two real numbers,
Chris@42:    multiplication by (NaN I), and summation *)
Chris@42: let dft_via_rdft sign n input =
Chris@42:   let f = rdft sign n input
Chris@42:   in fun i -> 
Chris@42:     Complex.plus
Chris@42:       [Complex.real (f i); 
Chris@42:        Complex.times (Complex.nan Expr.I) (Complex.imag (f i))]
Chris@42: 
Chris@42: (* Discrete Hartley Transform *)
Chris@42: let dht sign n input =
Chris@42:   let f = Fft.dft sign n (Complex.real @@ input) in
Chris@42:   (fun i ->
Chris@42:     Complex.plus [Complex.real (f i); Complex.imag (f i)])
Chris@42: 
Chris@42: let trigI n input = 
Chris@42:   let twon = 2 * n in
Chris@42:   let input' = Complex.hermitian twon input
Chris@42:   in
Chris@42:   Fft.dft 1 twon input'
Chris@42: 
Chris@42: let interleave_zero input = fun i -> 
Chris@42:   if (i mod 2) == 0
Chris@42:       then Complex.zero
Chris@42:   else
Chris@42:     input ((i - 1) / 2)
Chris@42: 
Chris@42: let trigII n input =
Chris@42:   let fourn = 4 * n in
Chris@42:   let input' = Complex.hermitian fourn (interleave_zero input)
Chris@42:   in
Chris@42:   Fft.dft 1 fourn input'
Chris@42: 
Chris@42: let trigIII n input =
Chris@42:   let fourn = 4 * n in
Chris@42:   let twon = 2 * n in
Chris@42:   let input' = Complex.hermitian fourn
Chris@42:       (fun i -> 
Chris@42: 	if (i == 0) then
Chris@42: 	  Complex.real (input 0)
Chris@42: 	else if (i == twon) then
Chris@42: 	  Complex.uminus (Complex.real (input 0))
Chris@42: 	else
Chris@42: 	  Complex.antihermitian twon input i)
Chris@42:   in
Chris@42:   let dft = Fft.dft 1 fourn input'
Chris@42:   in fun k -> dft (2 * k + 1)
Chris@42: 
Chris@42: let zero_extend n input = fun i ->
Chris@42:   if (i >= 0 && i < n)
Chris@42:   then input i
Chris@42:   else Complex.zero
Chris@42: 
Chris@42: let trigIV n input =
Chris@42:   let fourn = 4 * n
Chris@42:   and eightn = 8 * n in
Chris@42:   let input' = Complex.hermitian eightn 
Chris@42:       (zero_extend fourn (Complex.antihermitian fourn 
Chris@42: 			 (interleave_zero input)))
Chris@42:   in
Chris@42:   let dft = Fft.dft 1 eightn input'
Chris@42:   in fun k -> dft (2 * k + 1)
Chris@42: 
Chris@42: let make_dct scale nshift trig =
Chris@42:   fun n input ->
Chris@42:     trig (n - nshift) (Complex.real @@ (Complex.times scale) @@ 
Chris@42: 		       (zero_extend n input))
Chris@42: (*
Chris@42:  * DCT-I:  y[k] = sum x[j] cos(pi * j * k / n)
Chris@42:  *)
Chris@42: let dctI = make_dct Complex.one 1 trigI
Chris@42: 
Chris@42: (*
Chris@42:  * DCT-II:  y[k] = sum x[j] cos(pi * (j + 1/2) * k / n)
Chris@42:  *)
Chris@42: let dctII = make_dct Complex.one 0 trigII
Chris@42: 
Chris@42: (*
Chris@42:  * DCT-III:  y[k] = sum x[j] cos(pi * j * (k + 1/2) / n)
Chris@42:  *)
Chris@42: let dctIII = make_dct Complex.half 0 trigIII
Chris@42: 
Chris@42: (*
Chris@42:  * DCT-IV  y[k] = sum x[j] cos(pi * (j + 1/2) * (k + 1/2) / n)
Chris@42:  *)
Chris@42: let dctIV = make_dct Complex.half 0 trigIV
Chris@42: 
Chris@42: let shift s input = fun i -> input (i - s)
Chris@42: 
Chris@42: (* DST-x input := TRIG-x (input / i) *)
Chris@42: let make_dst scale nshift kshift jshift trig =
Chris@42:   fun n input ->
Chris@42:     Complex.real @@ 
Chris@42:     (shift (- jshift)
Chris@42:        (trig (n + nshift) (Complex.uminus @@
Chris@42: 			   (Complex.times Complex.i) @@
Chris@42: 			   (Complex.times scale) @@ 
Chris@42: 			   Complex.real @@ 
Chris@42: 			   (shift kshift (zero_extend n input)))))
Chris@42: 
Chris@42: (*
Chris@42:  * DST-I:  y[k] = sum x[j] sin(pi * j * k / n)
Chris@42:  *)
Chris@42: let dstI = make_dst Complex.one 1 1 1 trigI
Chris@42: 
Chris@42: (*
Chris@42:  * DST-II:  y[k] = sum x[j] sin(pi * (j + 1/2) * k / n)
Chris@42:  *)
Chris@42: let dstII = make_dst Complex.one 0 0 1 trigII
Chris@42: 
Chris@42: (*
Chris@42:  * DST-III:  y[k] = sum x[j] sin(pi * j * (k + 1/2) / n)
Chris@42:  *)
Chris@42: let dstIII = make_dst Complex.half 0 1 0 trigIII
Chris@42: 
Chris@42: (*
Chris@42:  * DST-IV  y[k] = sum x[j] sin(pi * (j + 1/2) * (k + 1/2) / n)
Chris@42:  *)
Chris@42: let dstIV = make_dst Complex.half 0 0 0 trigIV
Chris@42: