Q$.4(10)$

A spectrum analyzer generates a spectrogram by computing a $65536-$point FFT of a chunk of the input signal at a time and it can analyze signals with frequency as high as $1$ MHz $.$

a$)(2)$ What should be the minimum sampling frequency $($in kHz $)?$

b$)(2)$ What should be the minimum time duration of the chunk?

The constellation diagram of $16-$QAM is shown below.

c$)(2)$ Write down the FS coefficient for representing symbol $[0111]$ and $[1000].$

An OFDM system uses symbols containing $1024$ subcarriers, each using $64-$QAM instead of $16-$QAM as shown above to transmit bits. The fundamental ordinary frequency of the subcarriers is $12\mathrm{.}5$ kHz $.$

d$)(2)$ How many bits can be transmitted by one symbol with all the subcarriers?

e$)(2)$ This OFDM system is used for wireless communication environment where the largest delay difference among all the paths is $0\mathrm{.}01$ ms $.$ Ignoring overheads $($pilots$,$ synchronization, etc.$)$ and errors, what is the maximum number of bits that can be transmitted per second? Represent the answer in Mbps $($Megabit per second$).$