# Determining Analytically the DTFT of Sequences

Having difficulty with determining analytically the DTFT of sequences. I have attached a word document with problems that require answering

Determine analytically the DTFT of each of the following sequences. See attachment for details

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#### Solution Preview

Determine analytically the DTFT of each of the following sequences.

DTFT of y(k) = Y{e^(jw)} = Sigma(from k = -~ to k = +~) [ y(k)*e^-(jwk) ]

(where Sigma is the summation, "~" is infinity, and "^" is the exponent (power) operator)

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1. y(k) = 3(0.9)^k u(k)

Y{e^(jw)} = Sigma(from k = -~ to k = +~) [ 3(0.9)^k u(k)*e^-(jwk) ]

= 3* Sigma(from k = 0 to k = +~) ...

#### Solution Summary

Step by step calculations of DTFT of sequences are included. Geometric series theory, time shift theorem, and Euler's theorem are applied in the solution.