$2.$ You are asked to design an analog$-$to$-$digital converter $($ADC$)$ to digitize a biomedical signal acquired via biosensors. The dynamic and frequency range of the biomedical signal given as below:

a$.(9$Pts$)$ If the amplification factor $($A$)$ of your amplifier for the given dynamic range of this signal is determined to be $\backslash (\backslash$mathbf$\{$A $=20\}\backslash ),$ find the dynamic range of this ADC $,$ i$.$e$.,\backslash (\backslash$mathbf$\{$R$\}=\backslash )?$ V

b$.(8$Pts$)$ What is the Nyquist rate for this signal?

c$.(8$Pts$)$ Check aliasing for given sampling frequencies below, and explain briefly:

i$.$ If this signal is sampled at $\backslash ($ f$\_\{$s$\}=300\backslash$mathrm$\{$~Hz$\}\backslash ),$ will aliasing occur?

ii$.$ If this signal is sampled at $\backslash ($ f$\_\{$s$\}=1\mathrm{.}5\backslash$mathrm$\{$kHz$\}\backslash ),$ will aliasing occur?

Note: Please be specific and explain your reasoning.