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This is an involved topic that can not be adequately described in a few paragraphs. However, the following may give you an intuitive feel for the roll of Q: The denominator of a filter transfer function has roots that are called "poles". In general, these roots are complex, consisting of a real and and imaginary part, e.g .5 +/- j.866. Q is the ratio of the imaginary component to the real component. Poles with high Qs result in a sharper, more "peaky" filter frequency response, and a higher overshoot to a step input. The Q, or equivalently, the damping factor, plus the natural resonant frequency (w0) completely define the response of a 1 or 2 pole filter section. All linear filters can be broken down into 1st and 2nd order filter sections. This discussion applies to "all-pole" filters, i.e., filters that have a constant numberator.