$7.(20)$ Seyon and Yonsei found the following device that has a single input and single output port, but they did not know how it worked because they could not see the functional modules inside. Fortunately, they could read the brief specifications of the device written as follows:

$-$ Frequency shaping filter operating in the discrete$-$time domain

$-$ Input signal level: $-1$V $+1$V

$-$ Maximum allowable frequency: $20$ kHz

$($a$)(5)$ Explain the functional role of the 'Frequency shaping filter'.

$($b$)(5)$ Specify various methods to analyze the filter$/$frequency characteristic of the device.

$($c$)(5)$ Guess all the functional modules that might be needed for making the device, and explain the roles and principles of each functional module.

$($d$)(5)$ Explain additional conditions$/$constraints to be considered if you would like to implement it by yourself.