Apparatus, methods, and computer program products for determining the coefficients of a function with decreased latency

A method for determining the coefficients of a function representative of an input signal based on a predetermined plurality of samples of the input signal, wherein said method comprises the steps of:

• receiving samples of the signal;
• and
• incorporating the data into the coefficients in natural order as each sample is received to thereby remove the need to store the samples for processing,
• wherein each coefficient is comprised of at least one term that is at least partially based upon a combination of a sample and a mathematical function, wherein said method further comprises the step of determining a respective term of each coefficient by combining each sample upon receipt with the mathematical function associated with the sample and the coefficient.

An apparatus for determining the coefficients of a function representative of an input signal based on a predetermined plurality of samples of the input signal, wherein each coefficient is at least partially based upon a combination of the sample and a mathematical function, wherein said apparatus comprises:

• a first memory device for storing a value representing the mathematical function associated with the sample and each coefficient;
• and
• a coefficient generator in electrical communication with said memory device, wherein said coefficient generator receives the sample of the input signal and for each coefficient accesses said first memory device and combines the stored value with the sample and the coefficient to produce an updated coefficient value,
• wherein said first memory device includes an array having a plurality of cells, wherein each cell of the array stores a value representing the mathematical function associated with the respective sample and each coefficient, wherein each cell of said array has a unique address, which is designated by the respective coefficient and sample, and wherein, for the sample and each coefficient, said coefficient generator accesses the cell of said first memory device using the address associated with the sample and coefficient, multiplies the sample by the stored value to thereby define a term.

A method for determining the coefficients of a function representative of an input signal based on a predetermined plurality of samples of the input signal, wherein each coefficient is at least partially based upon a combination of the sample and a mathematical function, wherein said method comprises:

• storing a value representing the mathematical function associated with the sample and each coefficient in a first memory device;
• receiving the sample of the input signal;
• determining a respective value by accessing the necessary stored value;
• and
• combining the stored value with the sample and the incomplete coefficient to produce an updated coefficient value,
• wherein the first memory device includes an array having a plurality of cells, wherein said storing step stores a value representing the mathematical function associated with the sample and a respective coefficient in each cell of the array, wherein each cell of the array has a unique address, which is designated by the respective coefficient and sample, and wherein, for the sample and each coefficient, said determining step accesses the cell of the first memory device using the address associated with the sample and coefficient and multiplies the sample by the stored value to thereby define a term.

A computer program product for determining the coefficients of a function representative of an input signal based on a predetermined plurality of samples of the input signal, wherein the computer program product comprises:

• a computer readable storage medium having computer readable program code means embodied in said medium, said computer-readable program code means comprising:
• first computer instruction means for receiving samples of the signal;
• and
• second computer instruction means for incorporating the data from each sample into the coefficients in natural order as each sample is received thus removing the need to store the samples for processing,
• wherein each coefficient is comprised of at least one term that is at least partially based upon a combination of a sample and a mathematical function, said computer-readable program code means further comprising third computer instruction means for determining a respective term of each coefficient by combining each sample upon receipt with the mathematical function associated with the sample and the coefficient.

A computer program product for determining the coefficients of a function for a given input signal based on a sample of the input signal, wherein each coefficient is comprised of at least one term that is at least partially based upon a combination of the sample and a mathematical function, wherein the computer program product comprises:

• a computer readable storage medium having computer readable program code means embodied in said medium, said computer-readable program code means comprising:
• first computer instruction means for storing a value representing the mathematical function associated with the sample and each coefficient in a first memory device;
• second computer instruction means for receiving the sample of the input signal;
• third computer instruction means for determining a respective term of each coefficient by accessing the first memory device, multiplying the sample by the value representing the mathematical function associated with the sample and coefficient to thereby define a term;
• and
• fourth computer instruction means for updating each coefficient by adding the respective term to the previous value of the coefficient,
• wherein the first memory device includes an array having a plurality of cells, wherein said first computer instruction means stores a value representing the mathematical function associated with the sample and a respective coefficient in each cell of the array, wherein each cell of the array has a unique address, which is designated by the respective coefficient and sample, and wherein, for the sample and each coefficient, said third computer instruction means accesses the cell of the first memory device using the address associated with the sample and coefficient and multiplies the sample by the stored value to thereby define a term, and thereafter said fourth computer instruction means updates the coefficient by adding the term to the previous value of the coefficient.

An apparatus for generating coefficients of a function representative of an input set of data, said apparatus comprising a processing element that:

• receives clock signals,
• receives samples at certain clock times,
• generates coefficients calculated using the sample values based on a sample number associated with the sample and a coefficient number associated with the coefficient, wherein each coefficient contains components of each sample value, and
• provides each coefficient,
• wherein each coefficient is comprised of at least one term that is at least partially based upon a combination of a sample and a mathematical function, wherein said processing element generates a respective term of each coefficient by combining each sample upon receipt with the mathematical function associated with the sample and the coefficient.

An apparatus for generating coefficients of a function representative of an input set of data, said apparatus comprising a processing element that:

• receives clock signals,
• receives samples at certain clock times,
• generates coefficients calculated using the sample values based on a sample number associated with the sample and a coefficient number associated with the coefficient, wherein each coefficient contains components of each sample value, and
• provides each coefficient,
• wherein said interface logic allows selection of at least one of the following modes:
• reset, forward/inverse function, multiple channels and data registers.

A method of generating coefficients of a function representative of an input set of data, the method comprising the steps of:

• receiving clock signals;
• receiving samples at certain clock times;
• generating coefficients calculated using the sample values based on a sample number associated with the sample and a coefficient number associated with the coefficient, wherein each coefficient contains components of each sample value;
• and
• providing each coefficient,
• wherein each coefficient is comprised of at least one term that is at least partially based upon a combination of a sample and a mathematical function, wherein said generating step generates a respective term of each coefficient by combining each sample upon receipt with the mathematical function associated with the sample and the coefficient.

HDL code that when compiled is a computer program product for determining the coefficients of a function representative of an input signal based on a predetermined plurality of samples of the input signal, wherein the HDL code when compiled comprises:

• a computer readable storage medium having computer readable program code means embodied in said medium, said computer-readable program code means comprising:
• first computer instruction means for receiving samples of the signal;
• and
• second computer instruction means for incorporating the data from each sample into the coefficients in natural order as each sample is received thus removing the need to store the samples for processing,
• wherein each coefficient is comprised of at least one term that is at least partially based upon a combination of a sample and a mathematical function, said computer-readable program code means further comprising third computer instruction means for determining a respective term of each coefficient by combining each sample upon receipt with the mathematical function associated with the sample and the coefficient.