For simple signals it is possible to obtain some information on their DTFTs without computing it. Let

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For simple signals it is possible  to obtain some information on their DTFTs without computing it. Let

x[n] = δ[n] + 2δ[n ˆ’ 1] + 3δ[n ˆ’ 2] + 2δ[n ˆ’ 3] + δ[n ˆ’ 4].

(a) Find X(ej0) and X(ejÏ€) without computing the DTFT X(ejω).

(b) Find

|X(e®)*dw

(c) Find the phase of X(ejω). Is it linear?

Use MATLAB to verify your results.

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