1. Lowpass Butterworth Transfer Function

Design a 6th-order lowpass Butterworth filter with a cutoff frequency of 300Hz, which for data sampled at 1000Hz, corresponds to 0.6 rad/sample.

2. Bandstop Butterworth FilterDesign a 6th-order Butterworth bandstop filter with normalized edge frequencies of 0.2 and 0.6 rad/sample.

3. Highpass Butterworth FilterDesign a 9th-order highpass Butterworth filter. Specify a cutoff frequency of 300Hz, which for data sampled at 1000Hz, corresponds to 0.6 rad/sample.

4. Bandpass Butterworth Filter

Design a 20th-order Butterworth bandpass filter with a lower cutoff frequency of 500Hz and a higher cutoff frequency of 560Hz. Specify a sample rate of 1500Hz.