Methodology One common method for designing FIR filters is the Parks-McClellan filter design algorithm, based on the Remez exchange algorithm. Here the user specifies a desired frequency response, a weighting function for errors from this response, and a filter order N. The algorithm then finds the set of N coefficients that minimize the maximum deviation from the ideal. Intuitively, this finds the filter that is as close as you can get to the desired response given that you can use only N coefficients. This method is particularly easy in practice and at least one textRabiner, Lawrence R., and Gold, Bernard, 1975: Theory and Application of Digital Signal Processing (Englewood Cliffs, New Jersey: Prentice-Hall, Inc.) includes a program that takes the desired filter and N and returns the optimum coefficients. One possible drawback to filters designed this way is that they contain many small ripples in the passband(s), since such a filter minimizes the peak error.
Methodology One common method for designing FIR filters is the Parks-McClellan filter design algorithm based on the Remez exchange algorithm Here the user specifies a desired frequency response a weighting function for errors from this response and a filter order N The algorithm then finds the set of N coefficients that minimize the maximum deviation from the ideal Intuitively this finds the filter that is as close as you can get to the desired response given that you can use only N coefficients This method is particularly easy in practice and at least one textRabiner Lawrence R and Gold Bernard 1975 Theory and Application of Digital Signal Processing (Englewood Cliffs New Jersey Prentice-Hall Inc) includes a program that takes the desired filter and N and returns the optimum coefficients One possible drawback to filters designed this way is that they contain many small ripples in the passband(s) since such a filter minimizes the peak error