Multimedia signal processing using fixed-point approximations of linear transforms

A multi-media signal processing system comprising:

• means for separating a multi-media signal into block data;
• means for applying a fixed-point approximation of an ideal linear transformation to the block data, the fixed-point approximation structured as a decomposition of the linear transformation into a cascade of simpler transformations comprising one or more primitive operations that can be performed by a multiplication of the input data by a constant fixed-point number, where the value of one or more of the constant fixed-point numbers differs from the closest fixed-point approximation of an ideal constant multiplier value in the simpler transformation in a manner having the effect of increasing the precision of the approximation relative to the ideal linear transformation;
• means for coding the transformed block data into a processed bitstream.

A computer readable storage medium having programming instructions of a multi-media signal processing program stored thereon that is executable on a processor of a signal processing system to process a digital multimedia signal according to a method comprising:

• separating an input multi-media signal into possibly overlapping data blocks;
• and
• applying a fixed-point approximation of an ideal linear transformation to at least some of the blocks, where the fixed-point approximation of the ideal linear transformation is structured as a decomposition of the ideal linear transformation formed by factoring one or more parts of the ideal linear transformation into a cascade of simpler transformations, the simpler transformations comprising one or more primitive operations that can be performed by a multiplication of the input data by a constant fixed-point number, where the value of one or more of the constant fixed-point numbers differs from the closest fixed-point approximation of an ideal constant multiplier value in the simpler transformation in a manner having the effect of increasing the precision of the approximation relative to the ideal linear transformation.