High efficiency digital filter using sequential multiply and add operations

In a digital filter for filtering an input signal “x” to produce an output signal “y”, wherein filtering occurs by taking n+1 samples of the input signal “x” to extract a number of input signal samples x(0) through x(n), wherein filtering also occurs using digital filter coefficients c(0) through c(n) corresponding to the input signal samples x(0) through x(n), respectively, a computer program product for implementing a method for digitally filtering using sequential multiply and add instructions for increased filtering efficiency for microprocessors that use sequential multiply and add instructions, the computer program product comprising:

• a computer-readable medium having computer-executable instructions which, when executed by a microprocessor, implement the following:
• a step for loading a working value equal to a last input signal sample x(n);
• where “m” is an integer initially equaling “n”, a step for multiplying the working value by a constant c(m)/c(m−1) to thereby alter the working value, wherein the constant c(m)/c(m−1) is equal to the quotient of a digital filter coefficient c(m) corresponding to an input signal sample x(m) divided by a digital filter coefficient c(m−1) corresponding to a previous input signal sample x(m−1);
• a step for adding the working value that resulted from the step for multiplying to the value of the previous input signal sample x(m−1) to thereby alter the working value;
• and
• a step for generating the output signal “y” based at least in part on the working value that resulted from the step for adding.

In a digital filter for filtering an input signal “x” to produce an output signal “y”, wherein filtering occurs by taking n+1 samples of the input signal “x” to extract a number of input signal samples x(0) through x(n), wherein filtering also occurs using digital filter coefficients c(0) through c(n) corresponding to the input signal samples x(0) through x(n), respectively, a method for digitally filtering using sequential multiply and add instructions for increased filtering efficiency for microprocessors that use sequential multiply and add instructions, the method comprising:

• a specific act of a microprocessor loading a working value equal to a last input signal sample x(n);
• where “m” is an integer initially equaling “n”, a specific act of the microprocessor multiplying the working value by a constant c(m)/c(m−1) to thereby alter the working value, wherein the constant c(m)/c(m−1) is equal to the quotient of a digital filter coefficient c(m) corresponding to an input signal sample x(m) divided by a digital filter coefficient c(m−1) corresponding to a previous input signal sample x(m−1);
• a specific act of the microprocessor adding the working value that resulted from the specific act of the microprocessor multiplying to the value of the previous input signal sample x(m−1) to thereby alter the working value;
• and
• a specific act of generating the output signal “y” based at least in part on the working value that resulted from the specific act of the microprocessor adding.

In a digital filter for filtering an input signal “x” to produce an output signal “y”, wherein filtering occurs by taking n+1 samples of the input signal “x” to extract a number of input signal samples x(0) through x(n), wherein filtering also occurs using digital filter coefficients c(0) through c(n) corresponding to the input signal samples x(0) through x(n), respectively, a computer program product for implementing a method for digitally filtering using sequential multiply and add instructions for increased filtering efficiency for microprocessors that use sequential multiply and add instructions, the computer program product comprising:

• a computer-readable medium having computer-executable instructions which, when executed by a microprocessor, implement the following:
• a specific act of a microprocessor loading a working value equal to a last input signal sample x(n);
• where “m” is an integer initially equaling “n”, a specific act of the microprocessor multiplying the working value by a constant c(m)/c(m−1) to thereby alter the working value, wherein the constant c(m)/c(m−1) is equal to the quotient of a digital filter coefficient c(m) corresponding to an input signal sample x(m) divided by a digital filter coefficient c(m−1) corresponding to a previous input signal sample x(m−1);
• a specific act of the microprocessor adding the working value that resulted from the specific act of the microprocessor multiplying to the value of the previous input signal sample x(m−1) to thereby alter the working value;
• and
• a specific act of generating the output signal “y” based at least in part on the working value that resulted from the specific act of the microprocessor adding.