The oscillatory behavior of the approximation of XN(ω) to the function X(ω) at a point of discontinuity ofX(ω) is known as Gibbs phenomenon.(a) True(b) FalseI have been asked this question during an interview.This interesting question is from Frequency Analysis of Discrete Time Signal topic in portion Frequency Analysis of Signals and Systems of Digital Signal Processing

The oscillatory behavior of the approximation of XN(ω) to the functio

1.	The oscillatory behavior of the approximation of XN(ω) to the function X(ω) at a point of discontinuity ofX(ω) is known as Gibbs phenomenon.(a) True(b) FalseI have been asked this question during an interview.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» 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 ofX(ω) is known as Gibbs phenomenon.

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