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A 5-point sequence x[n] is given as x[-3] = 1, x[-2] = 1, x[-1] = 0, x[0] = 5, x[1] = 1. Let X(e^(jω)) denote the discrete-time Fourier transform of x[n]. The value of ∫_(-π)^(π) X(e^(jω)) dω is

1. 5
2. 10π
3. 16π
4. 5 + j10π

Correct answer: 10π

Solution

By the IDTFT, x[0] = (1/2pi) integral of X(e^jw) dw, so the integral equals 2*pi*x[0] = 2*pi*5 = 10*pi. The stored answer 5 is wrong; correct is 10*pi.

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