Signal Reconstruction with Low-Pass Filtering

Signal reconstruction with low-pass filtering helps turn a sampled signal back into a smooth continuous signal. When a continuous signal is sampled with a period T, the sampled version creates replicas of the original spectrum in the frequency domain. These replicas are spaced by the sampling frequency.

Consider a continuous signal and its sampled counterpart with a sampling period T.

Applying a zero-order hold to the sampled signal results in a piecewise constant signal.

Cascading the zero hold with a reconstruction filter gives the reconstructed signal.

An ideal low-pass filter removes all spectrum replicas in the frequen...