$.$ If you use a first$-$order high$-$pass filter, with an in$-$band gain of $1$ and a cut off frequency of $0\mathrm{.}5$ Hz to remove the dc component of the signal after the instrumentation amplifier, what is $|$H$($$)|$ for the high$-$pass filter at $1$ Hz$?$ b$.$ If you sample the signal $($with noise and interference$)$ at $20$ kHz$,$ what input frequencies would cause aliasing? c$.$ If you use a first$-$order low$-$pass filter, with an in$-$band gain of $5$ and a cut off frequency of $80$ Hz$,$ what is the minimum sampling rate that you must use such that the $|$H$($$)|$ for the low$-$pass filter is less than $0\mathrm{.}05$ for any noise or interference that would cause aliasing? d$.$ If the desired ECG signal is $0\mathrm{.}5$ mV at the body, and the $($unwanted$)$ dc signal is $10$ mV$,$ what is the maximum gain you can use in the instrumentation amplifier to prevent clipping $($saturation$)$ of the signal?