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The oscillatory behavior near the band edge of the low pass filter is known as Gibbs phenomenon.

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The oscillatory behavior near the band edge of the low pass filter is known as Gibbs phenomenon.

(a) True

(b) False

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The origin of the question is Design of Linear Phase FIR Filters Using Windows in portion Digital Filters Design of Digital Signal Processing

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Right answer is (a) True

For explanation I would say: The multiplication of hd(n) with a rectangular window is identical to truncating the Fourier series representation of the desired filter characteristic Hd(ω). The truncation of Fourier series is known to introduce ripples in the frequency response characteristic H(ω) due to the non-uniform convergence of the Fourier series at a discontinuity. The oscillatory behavior near the band edge of the low pass filter is known as Gibbs phenomenon.

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