Optimal factoring of FIR filters

A method of determining factors of an FIR filter, suitable for building the FIR filter as a cascade of factors, the method comprising:

• factoring, using a processing device, the filter's transfer function into 1st order and 2nd order factors based on its natural zero-pairings;
• creating, using the processing device, a collection of N angle values (θk), where k=1, . . . , N, wherein each angle value corresponds to a 2nd order factor of the filter's transfer function;
• organizing, using the processing device, the pairings of N angle values into pairing candidates by creating a table with N rows and N columns, one row for each angle value (θk), and one column for each angle value (θk);
• entering, using the processing device, an estimated quantization cost for each pairing candidate in the corresponding row/column position of the table;
• reorganizing, using the processing device, the entries in each row of the table to have an increasing estimated quantization cost to produce a reorganized table, and entering in each row/column position of the reorganized table an identifier of the column that the estimated quantization cost came from in the table;
• defining a threshold to indicate a number of columns of the reorganized table of estimated quantization costs to employ in the determination of the factors of the filter;
• generating, using the processing device, a matrix based on a total number of pairing candidates found in each row of the reorganized table and each column of the reorganized table as defined by the threshold;
• determining, using the processing device, a subset of pairing candidates in the matrix that provides a lowest predicted total quantization cost between all pairing candidates represented within the matrix;
• using the subset of pairing candidates to determine, using the processing device, coefficients of the filter factors;
• and
• building the FIR filter having factors with the determined coefficients.