You have been assigned to help with a study that investigates the brain wave patterns of people with depression. Assume a sampling frequency of $128$ Hz is used. Design the following filters to extract frequencies of $1$ Hz to $40$ Hz $.$

i$.7$ point FIR filter $($provide the $\backslash (\backslash$mathrm$\{$h$\}[\backslash$mathrm$\{$n$\}]\backslash )$ and magnitude spectrum$)$

ii$.$ IIR filter $($provide the transfer function $\backslash (\backslash$mathrm$\{$H$\}(\backslash$mathrm$\{$z$\})\backslash )$ and magnitude spectrum$)$

You do not need to draw the signal flow graph. Comment and suggest an improvement for each filter you have designed.$|$

$($b$)$ Design an IIR filter that approximates the following analog low pass filter by providing the $\backslash ($ H$($z$)\backslash ).$ You do not need to draw the signal flow graph.

$\backslash [$

H$($s$)=\backslash$frac$\{1\}\{$s$^\{2\}+1\mathrm{.}414$ s$+1\}$

$\backslash ]$