The clean ECG signal described in Q14 is corrupted by the periodic noise n(t) shown in Figure. The period P=1/30 s (ω 0 =30 Hz) and amplitude A=1.                           a.       Sample the noise...

The clean ECG signal described in Q14 is corrupted by the periodic noise n(t) shown in Figure. The period P=1/30 s (ω₀=30 Hz) and amplitude A=1.

a.       Sample the noise at the frequency ω_s=250 Hz (T_s=0.004 s), and add it to the clean ECG signal. Denote the corrupted signal by u(t_k), where t_k=kT_s, k=0, 1, 2, 3, ….

b.      Expand the noise in a Fourier series expansion,

c.       Design and implement a multinotch filter to remove all the frequency components (except DC) below the Nyquist frequency ω_nyq=0.5ω_s=125 Hz.

d.      Graph the filter input u(t_k) and its output y(t_k) below it.

e.      Compare the clean ECG signal s(t_k) and the filter output y(t_k).

Exercise-5