Sampling and reconstruction

Week 3

Sampling maps a continuous signal to a sequence. If the signal contains no energy above f_max, sampling at f_s > 2 f_max preserves everything; below that, components above f_s/2 fold into the band and cannot be separated afterwards.

Reconstruction is an interpolation: ideal low-pass filtering, zero-order hold, linear interpolation. The three differ in what they do between samples, not at the samples themselves.

Exercise

A signal is band-limited to 3 kHz and sampled at 8 kHz. How much does the spectrum change if the sample rate is reduced to 5 kHz? Sketch both spectra before answering.