What type of filter is the one shown in the Figure belowRULES

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gadgets $($mobile phones, tablets, etc.$)$ are prohibited for any reason whatsoever and require

disciplinary actions. Cheating is considered an academic violation according to Qatar University's

rules and regulations, and may result in immediate expulsion from the University. Students must

not engage in any form of cheating or other activities that violate the student code of conduct.

Write your answers neatly $($in English$)$ in the space provided for them. You must show all

your work for credit.

$(25$ pts$,5$ pts each$)$ Multiple Choice Questions

a$)$ If the discrete time Fourier transform output is discrete, then the input is

A$)$ Aperiodic

B$)$ Periodic

C$)$ Depends on the frequency

D$)$ Cannot be determined

b$)$ If $x[n]$ is finite duration, the region of convergence for the $z-$transform is $...$

A$)$ Cannot be determined from given information. More information is required.

B$)$ ROC is entire $z-$plane with the possible exception of $z=0$ or $z=$ infinity

C$)|z|>1$

D$)|z|<1$

c$)$ Which algorithmic paradigm does Fast Fourier Transform benefit from?

A$)$ Divide and Conquer

B$)$ Greedy Algorithm

C$)$ Dynammic Programming

D$)$ None

d$)$ Let $x[n]$ and $h[n]$ denote two finite length sequences, both of length $6.$ What is the smallest value of $N$ for which an $N-$point circular convolution of $x[n]$ with $h[n]$ will be identical to the linear

convolution?

A$)5$

B$)6$

C$)10$

D$)11$

e$)$ The complexity of N$-$Point Fast Fourier Transform is directly proportional with:

A$)$ N

B$)$ NLOGN

D$)N^3$

A$)N$