/*****************************************************************************
*                                                                            *
*   IDCT2.SPL     Copyright (C) 1998 DSP Development Corporation             *
*                               All Rights Reserved                          *
*                                                                            *
*   Author:      Randy Race                                                  *
*                                                                            *
*   Synopsis:    Calculates the 2D Inverse Discrete Cosine Transform         *
*                                                                            *
*   Revisions:   16 Mar 1998  RRR  Creation                                  *
*                                                                            *
*****************************************************************************/

#include 

#if @HELP_IDCT2

    IDCT2

    Purpose: Calculates the 2D Inverse Discrete Cosine Transform

    Syntax:  IDCT2(s, nr, nc)

              s  - input array
              nr - optional integer, transform length of rows (defaults
                   to row length of input)
              nc - optional integer, transform length of columns (defaults
                   to column  length of input)

    Returns: An array

    Example:
             W1: Ravel(gcos(100, 1/100, 3), 10))
             W2: Dct2(W1)
             W3: Idct2(W2)

             returns the original array (within roundoff error)


    Remarks:
             IDCT2 is often used in conjunction with DCT2 to perform
             image compression.


    See Also
             Dct
             Dct2
             Idct
             Ifft

    For more information, see:

    [1] Jae S. Lim, "Two-dimensional Signal and Image Processing",
        pp. 148-162.  Implements an even-symmetrical DCT.

    [2] Jain, "Fundamentals of Digital Image Processing", pp. 150-153.

    [3] Wallace, "The JPEG Still Picture Compression Standard",
        Communications of the ACM, April 1991.

#endif


/* 2D IDCT */
idct2(a, nr, nc)
{
        local d;

        if (argc < 3)
        {
                nc = numcols(a);
                
                if (argc < 2)
                {
                        nr = numrows(a);
                }
        }

        /* amazingly simple one liner */
        d = transpose(idct(transpose(idct(a, nr)), nc));

        // set correct deltax and deltay
        setdeltay(d, 1 / (2*nc*deltay(a)));
        setdeltax(d, 1 / (2*nr*deltax(a)));

        return(d);
}