Optimal factoring of FIR filters
A method and system for the design and implementation of an optimally factored filter is presented. Pairs of angle values are organized in pairing candidates and a threshold is defined to indicate an upper bound on the number of pairing candidates. A first pairing candidate is exchanged above the threshold with a second pairing candidate below the threshold and a matrix is generated based on the pairing candidates below the threshold. A lowest predicted total quantization cost between all pairing candidates represented within the matrix is determined and the pairing candidates that result in the lowest predicted total quantization cost are used to determine the coefficients of the filter.
1. A method, performed by a processing device, for determining a sequence of a plurality of stages of a filter, the method comprising:
determining a sum of squared coefficient values for each stage of the plurality of stages of the filter;
arranging the plurality of stages of the filter in cascade such that:
a first stage position in the cascade includes a stage having a lowest sum of squared coefficient values among each stage of the plurality of stages, and
a subsequent stage position includes another stage of the plurality of stages, such that a partial filter comprising the another stage and each previous stage in the cascade has a lowest sum of squared coefficient values among the possible stages to choose for the another stage.
2. The method of claim 1 , further comprising:
identifying one or more stages in the arranged cascade having the highest sum of squared coefficient values among all of the stages in the arranged cascade; and
distributing the one or more stages having the highest sum of squared coefficient values among the other stages in the arranged cascade.
3. The method of claim 2 , wherein the distributing comprises distributing such that the one more stages having the highest sum of squared coefficients are substantially spaced equally apart from one another in the cascade.
4. The method of claim 1 , wherein more than half of the stages of the plurality of stages each has an order of four or greater.
5. The method of claim 1 , wherein a subset of the plurality of stages each has an order of four or greater, and the total order of the subset of the plurality of stages is greater than a total order of a remainder of the stages in the plurality of stages.