As technology increases, more and more devices are becoming digital. The typical purpose of a digital filter is to detect unwanted signals and noise and remove them by filtering. The infinite impulse response (IIR) filter is also called a recursive filter because of the feedback necessary during implementation. A filter can be expressed as a cascade of second-order sections (SOS). For N sections, there are (N!) ways to pair the poles and zeros. There are also (N!) ways to order the resulting second-order sections, for a total of (N!)2 different filter configurations for implementation. In this thesis, for a 6th order filter with three second-order sections, there are (3!)2 or 36 different ordering and pairings.;Jackson's proposed a few rules for the pairing of the poles and zeros and the ordering of the second-order sections. These rules were investigated using MATLAB for Butterworth, Chebyshev, and elliptic filter type. Three cutoff frequencies were used to represent the low, mid, and high cutoff frequencies. The value of the low cutoff frequency is .2pi. The value of the mid cutoff frequency is .5pi. The value of the high cutoff frequency is .8pi. The filters were also implemented for both DF1 and DF2.;A broad new "rule" was not created but a few detailed "rules" were suggested depending on the filter type and direct-form implementation.
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