Updates

fftw-3.3.10/genfft/trig.ml

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