Aliasing from an s-plane perspective

Aliasing phenomena are demonstrated using complex frequency techniques by comparing the s-plane characterization of the continuous signal with the s-plane characterization of the sampled signal. This allows the aliasing phenomena to be described to sophomore- or junior-level students without the vicissitudes of the Fourier transform. Three signals are associated with the sampling operation: the continuous signal to be sampled, the signal representing the sampling operation, and the sampling version of the continuous signal. The sampling operation must be mathematically modeled to be combined with a continuous signal to realize the mathematical version of the sampled signal. The sampling operation can be represented in time as an impulse stream. This pulse stream can be mathematically represented. To avoid confusion when representing the continuous signal and its sampled version in the s-plane. the continuous signal is described in the unsampled s-plane and its sampled form is described in the sampled s-plane. Transforming the sampled signal, the unit step function, sampling a sinusoid, and s-plane characterization are discussed