Sparse-coefficient functions for reducing computational requirements

A method for reducing computational steps in a digital processor including digital multiplication operations that produce a plurality of multiplication products, wherein the multiplication operations are used to carry out a desired signal processing function, said method comprising:

• specifying the desired signal processing function having an associated set of an initial coefficients for implementing the function;
• determining an initial total number of non-zero bits in the initial coefficients;
• scaling said initial coefficients by a selected scale factor;
• determining a resulting number of non-zero bits of the scaled initial coefficients;
• modifying the selected scale factor and re-determining the resulting number of non-zero bits of the scaled initial coefficients;
• choosing as a final scale factor resulting in a reduced in the number of non-zero bits of the scaled initial coefficients;
• and
• constructing the multiplication function with the initial coefficients scaled by the final scale factor.

A method for reducing computational steps in a digital processor including shift-and-add digital multiplier stages producing a multiplication product, said method comprising:

• specifying a desired function to be implemented in the digital processor, the desired function having respective initial coefficients corresponding to each shift-and-add digital multiplier stage of the function;
• determining an initial total number of non-zero bits of the initial coefficients;
• scaling said initial coefficient by a selected scale factor;
• determining a resulting number of non-zero bits of the scaled initial coefficients;
• modifying the selected scale factor and re-determining the resulting number of non-zero bits of the scaled initial coefficients;
• choosing as a final scale factor the selected scale factor resulting in a reduced number of non-zero bits of the scaled initial coefficients;
• and
• constructing the shift-and-add digital multiplier stages with the initial coefficients scaled by the final scale factor.