Efficient real-time computation of FIR filter coefficients

An FIR filter comprising:

• a plurality of sample and hold circuits operative to sample an input signal and to provide a plurality of input samples;
• a real-time coefficient determinator to compute a plurality of coefficients corresponding to the plurality of input samples according to a desired cutoff frequency;
• a plurality of multipliers operative to multiply the plurality of input samples with the corresponding plurality of coefficients;
• and
• an accumulator operative to accumulate results from the plurality of multipliers and to provide a filtered signal.

An FIR filter comprising:

• means for determining coefficients in real-time;
• means for sampling an input signal to obtain samples;
• means for multiplying the samples with the coefficients;
• and
• means for accumulating products of the samples and the coefficients.

A coefficient determinator comprising:

• means for computing a sine of an input value;
• means for computing an inverse of the input value;
• means for computing a sinc of the input value;
• and
• means for forming a coefficient from the sinc of the input value.

A method of computing a filter coefficient, the method comprising:

• providing an input value;
• computing a sine of the input value utilizing a first lookup table;
• computing an inverse of the input value utilizing a second lookup table;
• and
• computing a sinc of the input value as a product of the sine of the input value and the inverse of the input value.

A method of computing a sine function comprising:

• providing an input value;
• referencing a lookup table to find a closest tabled value to the input value;
• retrieving a sine/cosine pair corresponding to the closest tabled value;
• and
• computing a sine of the input value as a function of the retrieved sine/cosine pair.

A method of computing an inverse function comprising:

• providing an input value;
• computing a most significant digit of the input value;
• computing an order variable value;
• forming an index utilizing the most significant digit;
• referencing a memory table with the index and retrieving a reference value;
• forming a remainder;
• and
• computing an inverse of the input value as a function of the remainder, the reference value and the order variable value.

A method of computing an inverse function comprising:

• providing an input value;
• computing a most significant digit of the input value;
• subtracting a number from the most significant digit to compute an order variable value;
• forming an index utilizing the most significant digit;
• referencing a memory table with the index and retrieving a reference value, wherein the memory table includes reference values in the range from 1/(512*513) to 1/(1023*1024);
• forming a remainder;
• and
• computing an inverse of the input value as a function of the remainder, the reference value and the order variable value.

A method of computing an inverse function comprising:

• providing an input value;
• computing a most significant digit;
• computing an order variable value as a function of the most significant digit and an index size;
• referencing a memory table to retrieve a reference value;
• and
• computing an inverse of the input value as a function of the reference value and the order variable value.

A method of operating an FIR filter comprising:

• providing an input signal;
• sampling the input signal to obtain a sample corresponding to a TAP;
• providing an input value corresponding to the TAP;
• computing a sine of the input value utilizing a first lookup table;
• computing an inverse of the input value utilizing a second lookup table;
• computing a sinc of the input value as a product of the sine of the input value and the inverse of the input value;
• forming a coefficient from the sine of the input value;
• and
• multiplying the coefficient and the sample.