Generating filter coefficients for a multi-channel notch rejection filter

A system for generating coefficient values, comprising:

• a series of accumulator circuits comprising a leading accumulator circuit and a last accumulator circuit, wherein each accumulator circuit of the series of accumulator circuits comprises a data input and a data output, wherein the data output of each accumulator circuit, except the last accumulator circuit, is coupled to the data input of a successive adjacent accumulator circuit in the series of accumulator circuits;
• a base function generator configured to:
• store a plurality of different base functions, wherein each base function of the plurality of different base functions is a respective specified order derivative of a corresponding respective filter function;
• select a base function from the plurality of different base functions according to a filter select input;
• and
• sequentially output a series of data values to the data input of the leading accumulator circuit, wherein the series of data values corresponds to the selected base function wherein each accumulator circuit is configured to:
• (a) add a data value currently at the data input of the accumulator circuit to a currently stored data value in the accumulator circuit to produce an updated data value, wherein the updated data value corresponds to a respective value of a specified order integral of the base function;
• (b) store the updated data value in the accumulator circuit;
• and
• (c) output the updated data value at the data output of the accumulator circuit;
• and
• a coefficient output configured to output a sequence of filter coefficient values corresponding to a specified order integral of the selected base function;
• and
• selection circuitry coupled to the data output of each of the plurality of accumulator circuits and configured to selectively couple the data output of one of the plurality of accumulator circuits to the coefficient output according to the respective specified order of the derivative of the respective filter function corresponding to the selected base function;
• wherein each filter coefficient value of the sequence of filter coefficient values corresponds to a current data value at the data output of the one of the plurality of accumulator circuits selectively coupled to the coefficient output.