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The sequence x(n)=\(\frac{sin⁡ ω_c n}{πn}\) does not have both z-transform and Fourier transform.

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The sequence x(n)=\(\frac{sin⁡ ω_c n}{πn}\) does not have both z-transform and Fourier transform.

(a) True

(b) False

The question was posed to me in homework.

Asked question is from Frequency Analysis of Discrete Time Signal topic in chapter Frequency Analysis of Signals and Systems of Digital Signal Processing

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The correct choice is (b) False

For explanation I would say: The given x(n) do not have Z-transform. But the sequence have finite energy. So, the given sequence x(n) has a Fourier transform.

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