Add variable alpha and size of half window for Kaiser-Bessel Derived window

generation. Hard code Bessel I0 approximation iterations to 50.

See thread for discussion:
[FFmpeg-devel] [PATCH] Move Kaiser-Bessel Derived window to mdct.c
Started on the 2008/01/10

Originally committed as revision 11520 to svn://svn.ffmpeg.org/ffmpeg/trunk

libavcodec/ac3dec.c

@@ -277,7 +277,7 @@ static int ac3_decode_init(AVCodecContext *avctx)
     ac3_tables_init();
     ff_mdct_init(&s->imdct_256, 8, 1);
     ff_mdct_init(&s->imdct_512, 9, 1);
-    ff_kbd_window_init(s->window);
+    ff_kbd_window_init(s->window, 5.0, 256);
     dsputil_init(&s->dsp, avctx);
     av_init_random(0, &s->dith_state);
 

libavcodec/dsputil.h

@@ -648,8 +648,10 @@ typedef struct MDCTContext {
 /**
  * Generate a Kaiser-Bessel Derived Window.
  * @param   window  pointer to half window
+ * @param   alpha   determines window shape
+ * @param   n       size of half window
  */
-void ff_kbd_window_init(float *window);
+void ff_kbd_window_init(float *window, float alpha, int n);
 
 int ff_mdct_init(MDCTContext *s, int nbits, int inverse);
 void ff_imdct_calc(MDCTContext *s, FFTSample *output,

libavcodec/mdct.c

@@ -26,24 +26,25 @@
  */
 
 // Generate a Kaiser-Bessel Derived Window.
-void ff_kbd_window_init(float *window)
+#define BESSEL_I0_ITER 50 // default: 50 iterations of Bessel I0 approximation
+void ff_kbd_window_init(float *window, float alpha, int n)
 {
    int i, j;
    double sum = 0.0, bessel, tmp;
-   double local_window[256];
-   double alpha2 = (5.0 * M_PI / 256.0) * (5.0 * M_PI / 256.0);
+   double local_window[n];
+   double alpha2 = (alpha * M_PI / n) * (alpha * M_PI / n);
 
-   for (i = 0; i < 256; i++) {
-       tmp = i * (256 - i) * alpha2;
+   for (i = 0; i < n; i++) {
+       tmp = i * (n - i) * alpha2;
        bessel = 1.0;
-       for (j = 100; j > 0; j--) /* default to 100 iterations */
+       for (j = BESSEL_I0_ITER; j > 0; j--)
            bessel = bessel * tmp / (j * j) + 1;
        sum += bessel;
        local_window[i] = sum;
    }
 
    sum++;
-   for (i = 0; i < 256; i++)
+   for (i = 0; i < n; i++)
        window[i] = sqrt(local_window[i] / sum);
 }