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Increasing the temporal resolution of transients

Apply a one-level Haar transform (or Hadamard) on each short MDCT
to nearly double the time-domain resolution.

--- a/libcelt/bands.c

+++ b/libcelt/bands.c

@@ -452,6 +452,19 @@

    RESTORE_STACK;

 }

+static void haar1(celt_norm *X, int N0, int stride)

+{

+   int i, j;

+   N0 >>= 1;

+   for (i=0;i<stride;i++)

+      for (j=0;j<N0;j++)

+      {

+         celt_norm tmp = X[stride*2*j+i];

+         X[stride*2*j+i] = MULT16_16_Q15(QCONST16(.7070678f,15), X[stride*2*j+i] + X[stride*(2*j+1)+i]);

+         X[stride*(2*j+1)+i] = MULT16_16_Q15(QCONST16(.7070678f,15), tmp - X[stride*(2*j+1)+i]);

+      }

+}

+

 /* This function is responsible for encoding and decoding a band for both

    the mono and stereo case. Even in the mono case, it can split the band

    in two and transmit the energy difference with the two half-bands. It

@@ -466,19 +479,33 @@

    int imid=0, iside=0;

    int N0=N;

    int N_B=N;

+   int N_B0;

    int spread0=spread;

+   int do_haar = 0;

    if (spread)

       N_B /= spread;

+   N_B0 = N_B;

    split = stereo = Y != NULL;

    if (!stereo && spread>1 && level==0)

    {

+      if ((N_B&1) == 0)

+      {

+         spread <<= 1;

+         N_B >>= 1;

+         do_haar = 1;

+         if (encode)

+            haar1(X, N_B0, spread0);

+         if (lowband)

+            haar1(lowband, N_B0, spread0);

+         spread0 = spread;

+      }

       if (encode)

-         deinterleave_vector(X, N_B, spread);

+         deinterleave_vector(X, N_B, spread0);

       if (lowband)

-         deinterleave_vector(lowband, N_B, spread);

+         deinterleave_vector(lowband, N_B, spread0);

    }

    /* If we need more than 32 bits, try splitting the band in two. */

@@ -752,6 +779,12 @@

          interleave_vector(X, N_B, spread0);

          if (lowband)

             interleave_vector(lowband, N_B, spread0);

+         if (do_haar)

+         {

+            haar1(X, N_B0, spread0>>1);

+            if (lowband)

+               haar1(lowband, N_B0, spread0>>1);

+         }

       }

       if (lowband_out && !stereo)