Design proceure for low-pass digital Butterworth IIR filter

    The low-pass digital Butterworth filter is designed as per the following steps:

step 1:Choose the type of transformation either bilinear or impulse invariant

step 2:Calculate the ratio of analog frequencies

step 3:Decide the order of filter N such that

step 4:Calculate the analog cutoff frequency

step 5:Determine the transfer function of analog filter.

   If N id odd, then H(s) is given by

When the order N is odd,

where the coefficient bk is given by,

step 6:Convert the analog transfer function into digital one usinng the choen transformation

EXAMPLE 1:

          Design a buttterworth digital filter using the bilinear transformation. The specifications of the desired low pass filter are:

with T=1 sec