Question

The oscillatory behavior of the approximation of XN(ω) to the function X(ω) at a point of discontinuity of  X(ω) is known as Gibbs phenomenon.

(a) True

(b) False

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This interesting question is from Frequency Analysis of Discrete Time Signal topic in portion Frequency Analysis of Signals and Systems of Digital Signal Processing

Answer 1

The correct choice is (a) True

Best explanation: We note that there is a significant oscillatory overshoot at ω=ωc, independent of the value of N. As N increases, the oscillations become more rapid, but the size of the ripple remains the same. One can show that as N→∞, the oscillations converge to the point of the discontinuity at ω=ωc. The oscillatory behavior of the approximation of XN(ω) to the function X(ω) at a point of discontinuity of  X(ω) is known as Gibbs phenomenon.