Problem$-1\mathrm{.}1$

Let the sequence be

Generate and plot each of the following sequences using the stem function. For signal generation use the functions described in Section $2\mathrm{.}2$ of the textbook.

$($a$)$

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$($b$)$

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$($c$)$

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Problem$-1\mathrm{.}2$

The sinusoidal sequence is periodic if the normalized frequency is a rational number; that is$,,$ where and are integers.

$($a$)$ Prove the above result.

Proof:

$($b$)$ Generate and plot its values using the stem function.

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Is this sequence periodic? If it is$,$ what is its fundamental period? From the examination of the plot what interpretation can you give to the integers and above?

Answer:

$($c$)$ Generate and plot $.$

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Is this sequence periodic? What do you conclude from the plot? If necessary examine values of the sequence in the workspace to arrive at your answer.

Answer: