Write your OWN Matlab algorithm $($without using any built$-$in Fourier Transform

algorithm of any software$)$ to determine and plot the DFT$,$ specifically the amplitude

spectrum in the range $0<=<=$

$2,$ where $$ is the sampling frequency, for the following

cases:

$($a$)1$ cycle of $()=47(2200)$ with $20$ zeros padded and $=2$kHz;

$($b$)1$ cycle of $()=47(2200)$ with $200$ zeros padded and $=2$kHz;

$($c$)100$ cycles of $()=47(2200)$ with $200$ zeros padded and $=2$kHz;

$($d$)()=50[(2200)(2200)+(2200)(2200)]+$

$50[(2200)(2200)(2200)(2200)]$ in the range $0<=<=1$s$,$

with $4000$ zeros padded and $=2$kHz;

$($e$)()=47(2300)+50(2400)+74(21500)+5(21600)$ in

the range $0<=<=0\mathrm{.}5$s$,$ with $8000$ zeros padded and $=4$kHz;

$($f$)()=47(2300)+50(2400)+74(21500)+5(21600)$ in

the range $0<=<=0\mathrm{.}5$s$,$ with $8000$ zeros padded and $=1\mathrm{.}2$kHz$.$

Test of Knowledge

Observe the results you have obtained in Part $($d$),($e$)$ and $($f$)$ carefully in particular the

location of the peak and the amplitude. Are the results as expected? Why? Explain your

reasoning in detail for all three cases.

To receive full credit, you must submit the following two documents on webcourses:

$1.$ Your computer code in the $.$m file format;

$2.$ A pdf document that includes all your plots as well as your responses to the questions

in Test of Knowledge.

For this project, you can work individually or in a group of up to two members. Each group

is required to upload only one submission. The deadline will be strictly enforced, and no

late submissions will be accepted once the submission window is closed on webcourses.