Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation

Note 43. Bessel Filters

Bessel filters are designed to have maximally flat group-delay characteristics. Consequently, there are no oscillations in the step response, thus making Bessel filters attractive for applications that call for low levels of pulse distortion. The transfer function of an nth-order lowpass Bessel filter is given by

43.1

where q_n(s) is the polynomial of degree n given by

The polynomial q_n(s) can be obtained from q_n–1(s) and q_n–2(s) using the recursion

q_n(s) = (2n – 1)q_{n – 1} + s²q_{n – 2}

Table 43.1 lists q_n(s) for n = 2 through ...