Design the following Butterworth IIR filters. Let Fs=8000Hz. Determine H(s) of the analog Butterworth prototype based on a normalized sampling frequency Fs=1Hz (to simplify the computations). NOTE: If a digital filter with fc=800Hz is to be designed with Fs=8000Hz, an equivalent filter with normalized frequencies fc=0.1Hz and Fs=1Hz can be designed instead. The normalized frequencies are computed by dividing all the original frequencies with the original Fs.
Design the following Butterworth IIR filters. Let Fs=8000Hz. Determine H(s) of the analog Butterworth prototype based on a normalized sampling
frequency Fs=1Hz (to simplify the computations).
NOTE: If a digital filter with fc=800Hz is to be designed with Fs=8000Hz, an equivalent filter with normalized frequencies fc=0.1Hz and Fs=1Hz can be designed instead. The normalized frequencies are computed by dividing all the original frequencies with the original Fs.
Determine H(z) and the difference equation of the Butterworth IIR filter using Bilinear
transformation with pre-warping.
(a) 2nd-order Lowpass
fc=800Hz
Note: The normalized frequencies are fc=0.1Hz and Fs=1Hz.
Answer: H(s)= 0.4223/(s^2+0.919s+0.4223)
y[n]=0.0675x[n]+0.1349x[n-1]+0.0675x[n-2]+1.143y[n-1]-0.4128y[n-2]
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