Which statement about low-pass filtering in signal reconstruction is true?

Which statement about low-pass filtering in signal reconstruction is true?

• A. An ideal low-pass filter exists that can perfectly reconstruct all frequency components.
• B. There is no ideal low-pass filter that can perfectly reconstruct all frequency components.
• C. A low-pass filter is irrelevant for reconstruction from samples.
• D. Any low-pass filter with a cutoff above the highest frequency component will suffice.

Answer: (B)

Reconstruction from samples relies on replacing the discrete sequence with a continuous-time signal using a low-pass reconstruction filter. Perfect reconstruction is only guaranteed if the original signal is strictly bandlimited to below half the sampling rate. If any energy lies above that limit, aliasing occurs during sampling, and no filter can undo those aliased components to recover the original spectrum. In theory, an ideal reconstruction filter (a perfect sinc filter) could exactly reconstruct a bandlimited signal from its samples, but that filter has infinite duration and is non-causal, so it cannot be realized in practice. Because not all signals are bandlimited and a universal, realizable filter cannot perfectly recover every possible spectrum, there is no ideal low-pass filter that can perfectly reconstruct all frequency components. In practice we approximate with realizable filters and hope the signal is close to bandlimited so reconstruction is accurate.

Reconstruction from samples relies on replacing the discrete sequence with a continuous-time signal using a low-pass reconstruction filter. Perfect reconstruction is only guaranteed if the original signal is strictly bandlimited to below half the sampling rate. If any energy lies above that limit, aliasing occurs during sampling, and no filter can undo those aliased components to recover the original spectrum. In theory, an ideal reconstruction filter (a perfect sinc filter) could exactly reconstruct a bandlimited signal from its samples, but that filter has infinite duration and is non-causal, so it cannot be realized in practice. Because not all signals are bandlimited and a universal, realizable filter cannot perfectly recover every possible spectrum, there is no ideal low-pass filter that can perfectly reconstruct all frequency components. In practice we approximate with realizable filters and hope the signal is close to bandlimited so reconstruction is accurate.