Sub-Nyquist Distortions in Sampled One- and Two-Dimensional Signals Studied

Hardware testing frequently involves the acquisition of waveform and instrumentation signals, which are often recorded on waveform recorders, oscillographs, and video recorders. Years ago, the waveforms were viewed as analog records, as drawn by a paper strip chart pen or electron beam on a cathode ray tube screen. One of the problems in the past was that the analog electronics may not have been able to accurately display the full amplitude of a signal if the real-time signals exceeded the frequency response bandwidth of the recording device. The advent of digital oscilloscopes, waveform recorders, and video frame-grabbers solved many of the frequency response problems, though not all. A restriction on digital waveform acquisition is well known by people in the instrumentation field. Put simply, the sampling frequency must be at least twice the frequency of any signal to be sampled, or vice versa; the signals must be filtered so that none of the signal frequencies are higher than one-half the sample rate (the Nyquist Limit). Then, per Shannon's Sampling Theorem (1949, ref. 1), any sampled signal can be reconstructed for viewing on a display device. If any signals exceed the Nyquist frequency limit, error signals called aliases occur in the output display