cannam@127: (*
cannam@127:  * Copyright (c) 1997-1999 Massachusetts Institute of Technology
cannam@127:  * Copyright (c) 2003, 2007-14 Matteo Frigo
cannam@127:  * Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology
cannam@127:  *
cannam@127:  * This program is free software; you can redistribute it and/or modify
cannam@127:  * it under the terms of the GNU General Public License as published by
cannam@127:  * the Free Software Foundation; either version 2 of the License, or
cannam@127:  * (at your option) any later version.
cannam@127:  *
cannam@127:  * This program is distributed in the hope that it will be useful,
cannam@127:  * but WITHOUT ANY WARRANTY; without even the implied warranty of
cannam@127:  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
cannam@127:  * GNU General Public License for more details.
cannam@127:  *
cannam@127:  * You should have received a copy of the GNU General Public License
cannam@127:  * along with this program; if not, write to the Free Software
cannam@127:  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
cannam@127:  *
cannam@127:  *)
cannam@127: 
cannam@127: (* trigonometric transforms *)
cannam@127: open Util
cannam@127: 
cannam@127: (* DFT of real input *)
cannam@127: let rdft sign n input =
cannam@127:   Fft.dft sign n (Complex.real @@ input)
cannam@127: 
cannam@127: (* DFT of hermitian input *)
cannam@127: let hdft sign n input =
cannam@127:   Fft.dft sign n (Complex.hermitian n input)
cannam@127: 
cannam@127: (* DFT real transform of vectors of two real numbers,
cannam@127:    multiplication by (NaN I), and summation *)
cannam@127: let dft_via_rdft sign n input =
cannam@127:   let f = rdft sign n input
cannam@127:   in fun i -> 
cannam@127:     Complex.plus
cannam@127:       [Complex.real (f i); 
cannam@127:        Complex.times (Complex.nan Expr.I) (Complex.imag (f i))]
cannam@127: 
cannam@127: (* Discrete Hartley Transform *)
cannam@127: let dht sign n input =
cannam@127:   let f = Fft.dft sign n (Complex.real @@ input) in
cannam@127:   (fun i ->
cannam@127:     Complex.plus [Complex.real (f i); Complex.imag (f i)])
cannam@127: 
cannam@127: let trigI n input = 
cannam@127:   let twon = 2 * n in
cannam@127:   let input' = Complex.hermitian twon input
cannam@127:   in
cannam@127:   Fft.dft 1 twon input'
cannam@127: 
cannam@127: let interleave_zero input = fun i -> 
cannam@127:   if (i mod 2) == 0
cannam@127:       then Complex.zero
cannam@127:   else
cannam@127:     input ((i - 1) / 2)
cannam@127: 
cannam@127: let trigII n input =
cannam@127:   let fourn = 4 * n in
cannam@127:   let input' = Complex.hermitian fourn (interleave_zero input)
cannam@127:   in
cannam@127:   Fft.dft 1 fourn input'
cannam@127: 
cannam@127: let trigIII n input =
cannam@127:   let fourn = 4 * n in
cannam@127:   let twon = 2 * n in
cannam@127:   let input' = Complex.hermitian fourn
cannam@127:       (fun i -> 
cannam@127: 	if (i == 0) then
cannam@127: 	  Complex.real (input 0)
cannam@127: 	else if (i == twon) then
cannam@127: 	  Complex.uminus (Complex.real (input 0))
cannam@127: 	else
cannam@127: 	  Complex.antihermitian twon input i)
cannam@127:   in
cannam@127:   let dft = Fft.dft 1 fourn input'
cannam@127:   in fun k -> dft (2 * k + 1)
cannam@127: 
cannam@127: let zero_extend n input = fun i ->
cannam@127:   if (i >= 0 && i < n)
cannam@127:   then input i
cannam@127:   else Complex.zero
cannam@127: 
cannam@127: let trigIV n input =
cannam@127:   let fourn = 4 * n
cannam@127:   and eightn = 8 * n in
cannam@127:   let input' = Complex.hermitian eightn 
cannam@127:       (zero_extend fourn (Complex.antihermitian fourn 
cannam@127: 			 (interleave_zero input)))
cannam@127:   in
cannam@127:   let dft = Fft.dft 1 eightn input'
cannam@127:   in fun k -> dft (2 * k + 1)
cannam@127: 
cannam@127: let make_dct scale nshift trig =
cannam@127:   fun n input ->
cannam@127:     trig (n - nshift) (Complex.real @@ (Complex.times scale) @@ 
cannam@127: 		       (zero_extend n input))
cannam@127: (*
cannam@127:  * DCT-I:  y[k] = sum x[j] cos(pi * j * k / n)
cannam@127:  *)
cannam@127: let dctI = make_dct Complex.one 1 trigI
cannam@127: 
cannam@127: (*
cannam@127:  * DCT-II:  y[k] = sum x[j] cos(pi * (j + 1/2) * k / n)
cannam@127:  *)
cannam@127: let dctII = make_dct Complex.one 0 trigII
cannam@127: 
cannam@127: (*
cannam@127:  * DCT-III:  y[k] = sum x[j] cos(pi * j * (k + 1/2) / n)
cannam@127:  *)
cannam@127: let dctIII = make_dct Complex.half 0 trigIII
cannam@127: 
cannam@127: (*
cannam@127:  * DCT-IV  y[k] = sum x[j] cos(pi * (j + 1/2) * (k + 1/2) / n)
cannam@127:  *)
cannam@127: let dctIV = make_dct Complex.half 0 trigIV
cannam@127: 
cannam@127: let shift s input = fun i -> input (i - s)
cannam@127: 
cannam@127: (* DST-x input := TRIG-x (input / i) *)
cannam@127: let make_dst scale nshift kshift jshift trig =
cannam@127:   fun n input ->
cannam@127:     Complex.real @@ 
cannam@127:     (shift (- jshift)
cannam@127:        (trig (n + nshift) (Complex.uminus @@
cannam@127: 			   (Complex.times Complex.i) @@
cannam@127: 			   (Complex.times scale) @@ 
cannam@127: 			   Complex.real @@ 
cannam@127: 			   (shift kshift (zero_extend n input)))))
cannam@127: 
cannam@127: (*
cannam@127:  * DST-I:  y[k] = sum x[j] sin(pi * j * k / n)
cannam@127:  *)
cannam@127: let dstI = make_dst Complex.one 1 1 1 trigI
cannam@127: 
cannam@127: (*
cannam@127:  * DST-II:  y[k] = sum x[j] sin(pi * (j + 1/2) * k / n)
cannam@127:  *)
cannam@127: let dstII = make_dst Complex.one 0 0 1 trigII
cannam@127: 
cannam@127: (*
cannam@127:  * DST-III:  y[k] = sum x[j] sin(pi * j * (k + 1/2) / n)
cannam@127:  *)
cannam@127: let dstIII = make_dst Complex.half 0 1 0 trigIII
cannam@127: 
cannam@127: (*
cannam@127:  * DST-IV  y[k] = sum x[j] sin(pi * (j + 1/2) * (k + 1/2) / n)
cannam@127:  *)
cannam@127: let dstIV = make_dst Complex.half 0 0 0 trigIV
cannam@127: