High-pass Butterworth filters have transfer functions of the form HH s ksn Dn s where n is the order of the filter, Dn(s) denotes the nth order polynomial in Table 16.3-2, and k is the pass-band gain. Obtain the transfer function of a third-order Butterworth high-pass filter having a cutoff frequency equal to 100 rad/s and a passband gain equal to 5.

Definitionb 1.1. Given two integers a and d with d non-zero, we say that d divides a (written d | a) if there is an integer c with a = cd. If no such integer exists, so d does not divide a, we write d - a. If d divides a, we say that d is a divisor of a. Proposition 1.2.1: Assume that a, b, and c are integers. If a | b and b | c, then a | c. Proposition 1.3. Assume that a, b, d, x, and y are integers....