Assume the sampling rate is 1000 Hz. Design a digital low-pass Butterworth filter with MATLAB with a cutoff frequency of 50 Hz. Assume a sampling rate of 100 Hz. Filter the signal given by xðtÞ ¼ 1 þ...

Assume the sampling rate is 1000 Hz. Design a digital low-pass Butterworth filter

with MATLAB with a cutoff frequency of 50 Hz.

Assume a sampling rate of 100 Hz. Filter the signal given by

xðtÞ ¼ 1 þ sinð0:125ptÞ þ 0:5 sinð0:25ptÞ þ 0:25 sinð0:5ptÞ þ :125 sinðptÞ

by filters of progressively lower cutoff frequencies of 50, 5, 0.5, and 0.05 Hz.