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I am not seeing a direct pair of DTFT transform of the unit step.

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The DTFT of the unit step sequence is the topic of this question. However, you don't need it to solve the problem you were given. The sequence you're supposed to transform is just a finite length sequence with values $1$ in the interval $2\le n\le 7$ and zero otherwise. So computing the transform using the formula for the DTFT should be straightforward, and there's definitely no need for Dirac delta impulses.

Matt L.
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