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 using a low-pass filter to interpolate between the sampled values. If the signal is truly band-limited and you sample fast enough (at least twice the highest frequency), an ideal low-pass filter with a brick-wall cutoff at half the sampling rate would reconstruct the original waveform exactly. But that ideal filter isn’t something you can realize in practice: its impulse response is infinitely long and non-causal, so it cannot be implemented physically. Moreover, any frequency components of the original signal above the Nyquist limit aren’t captured by the samples in the first place, so they cannot be recovered no matter what filter you use. So there is no realizable ideal low-pass filter that can perfectly reconstruct all frequency components; perfect reconstruction is possible only for the portion of the spectrum within the Nyquist limit, and even that relies on an ideal filter that cannot be built.