For a sixth-order Butterworth high pass filter with cutoff frequency 3 rad/s, compute the following: a. The locations of the poles.
b. The transfer function H(s).
c. The corresponding LCCDE description.

Solution :

Given :

A six order Butterworth high pass filter.

∴ n = 6,

a). The location at poles :

  ∴

Therefore, it has 6 repeated poles at s = 1.

b). The transfer function H(S) :

    Transfer function H(S)

  ∴    H(S)

   H(S)

c). The corresponding LCCDE description :

By taking inverse Laplace transformation on BS

  Hence solved.

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