Consider the connection between the DTFT and the Z-transform in the  following problems.

(a) Let x[n] = u[n + 2] ˆ’ u[n ˆ’ 3].

i. Can you find the DTFT X(e^jω) of x[n] using the Z-transform? If so, what is it?

ii. Is it true that X(e^j0) = 5? Explain.

(b) For the non-causal signal x[n] = αⁿ u[ ˆ’ n], α > 0, give values of α for which X(e^jω) = X(z)|_{z=e jω}.

(c) Consider the causal and anti-causal signals

show that X₁(z) = X₂(z), and find the regions of convergence.  According to the ROCs, which of the two signals has a DTFT that  can be found from its Z-transform?

Transcribed Image Text:

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