$(10$ points$)$ Answer the following questions using the Nyquist bit

rate. Note that $lo{g}_{2}2=1,lo{g}_{2}4=2,lo{g}_{2}8=3$ and $lo{g}_{2}16=4.$

a$.$ According to Nyquist, what is the bit rate we can send data

through a noiseless channel with a bandwidth of $8000Hz$ if we

use a signal with $8$ different levels?

b$.$ What is the bit rate if use $16$ different levels?

$(10$ points$)$ Answer the following questions using the Shannon

capacity. Note that $lo{g}_{2}2=1,lo{g}_{2}4=2,lo{g}_{2}8=3$ and $lo{g}_{2}16=4.$

a$.$ What is the bit rate we can send data through a noisy channel

with a bandwidth of $8000Hz$ and SNR of $7?$

b$.$ According to Shannon, if we want to double the bit rate, how

many times we need to increase the bandwidth $($without

changing SNR$)?$