Efficient fixed-point approximations of forward and inverse discrete cosine transforms

A device comprising:

• a processor programmed to control,
• a scaling module that scales each coefficient in an 8×8 matrix of encoded coefficients by one of a factor A, a factor B, a factor C, a factor D, a factor E, a factor F, a factor G, a factor H, a factor I, or a factor J in order to produce a matrix of scaled coefficients;
• wherein A=1024, B=1138, C=1730, D=1609, E=1264, F=1922, G=1788, H=2923, I=2718, and J=2528;
• an inverse transform module that uses repeated applications of a fixed-point scaled one-dimensional transform to transform the matrix of scaled coefficients into a matrix of transformed coefficients;
• a right-shift module that right-shifts transformed coefficients in the matrix of transformed coefficients in order to produce a matrix of adjusted coefficients;
• and
• wherein each adjusted coefficient in the matrix of adjusted coefficients approximates a corresponding value in a matrix of values that would be produced by applying an ideal two-dimensional inverse discrete cosine transform (“IDCT”) to the matrix of encoded coefficients;
• an output module that outputs an 8×8 block of pixels, wherein each pixel in the block of pixels includes a pixel component value based on an adjusted coefficient in the matrix of adjusted coefficients.

A device comprising:

• means for scaling coefficients in an 8×8 matrix of encoded coefficients by one of a factor A, a factor B, a factor C, a factor D, a factor E, a factor F, a factor G, a factor H, a factor I, or a factor J in order to produce a matrix of scaled coefficients, wherein A=1024, B=1138, C=1730, D=1609, E=1264, F=1922, G=1788, H=2923, I=2718, and J=2528;
• means for using repeated applications of a fixed-point scaled one-dimensional transform to transform the matrix of scaled coefficients into a matrix of transformed coefficients;
• means for right-shifting transformed coefficients in the matrix of transformed coefficients in order to produce a matrix of adjusted coefficients;
• wherein each adjusted coefficient in the matrix of adjusted coefficients approximates a corresponding value in a matrix of values that would be produced by applying an ideal two-dimensional inverse discrete cosine transform (“IDCT”) to the matrix of encoded coefficients;
• and
• means for outputting an 8×8 block, of pixels, wherein each pixel in the block of pixels includes a pixel component value based on an adjusted coefficient in the matrix of adjusted coefficients.

A non-transitory computer-readable medium comprising instructions, when executed the instructions cause a programmable processor to:

• scale each coefficient in an 8×8 matrix of encoded coefficients by one of a factor A, a factor B, a factor C, a factor D, a factor E, a factor F, a factor G, a factor H, a factor I, or a factor J in order to produce a matrix of scaled coefficients,
• wherein A=1024, B=1138, C=1730, D=1609, E=1264, F=1922, G=1788, H=2923, I=2718, and J=2528;
• use repeated applications a fixed-point scaled one-dimensional transform to transform the matrix of scaled coefficients into a matrix of transformed coefficients,
• right-shift transformed coefficients in the matrix of transformed coefficients in order to produce a matrix of adjusted coefficients;
• wherein each adjusted coefficient in the matrix of adjusted coefficients approximates a corresponding value in a matrix of values that would be produced by applying an ideal two-dimensional inverse discrete cosine transform (“IDCT”) to the matrix of encoded coefficients;
• and
• output signals that cause a display unit to display an 8×8 block of pixels, wherein each pixel in the block of pixels includes a pixel component value based on an adjusted coefficient in the matrix of adjusted coefficients.