The Art of Signal Sampling and Aliasing:
"What we see is not what it is!"***(Set "Full Screen" view and 1024 X 768 resolution)

Back to interactive experimentation. Review the paper with several sample outputs on this issue. Return to Prof. M. Kostic home page.

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The same simple harmonic, sine-wave signal of 1000 Hz (20 cycles/periods of which are presented in green color in the background) is sampled/measured by different frequency, sequentially increasing in each frame, namely 200, 400, 500, 685, 800, 900, 1000, 1200, 1500, 1900, 2000, 2050, 3000, 5000, and 50 000 Hz. It is striking how the sampled (measured) signal, presented in dark-red color over the green "real" signal, depends on the sampling frequency ("What we see is not what it is!"). For a given signal of 1000 Hz, the critical sampling frequency is 2000 Hz (remember the Nyquist rule!). Around this critical sampling (1900 and 2050) the "beat wave" interference phenomena occur. Below this critical sampling aliasing occurs, reaching the zero value if the sampling is an integer times smaller than or equal to the signal frequency (200, 500, 1000). The higher sampling frequency than the critical, the more realistic is the sampled signal (5000, 50 000). See the links above for more information.

The input and output values and plot are clearly presented in the front panel of the developed virtual instrument, see Front Panel output sample. The arbitrary input values are: signal and sampling frequencies or sampling-to-signal frequency RATIO, number of signal's cycles/periods as well as the magnitude ratio and the phase lag. The output values are: (1) sampling frequency if the sampling to signal frequency ratio is given, (2) the Nyquist frequency, see NOTE for definition, (3) the frequency ratio if the sampling frequency is given, (4) aliasing to signal frequency ratio, (5) the aliasing frequency, (6) total number of sampled points, and (7) number of sampled points per signal period or cycle; the latter should be equal to the sampling to signal frequency ratio.

NOTE: Nyquist frequency may be defined in different ways, namely:

  1. Nyquist frequency defined as maximum signal frequency that could be reliably measured to avoid aliasing, which is solely based on the sampling frequency, i.e. equal to one half of it (used in here). Only signals with smaller than this Nyquist frequency will be sampled reliably, while higher frequency signals will "fold back," i.e. appear as a smaller aliasing frequency signals.
  2. Nyquist frequency defined as minimum required sampling frequency for a given signal frequency to avoid aliasing. It is based on (maximum) signal frequency that could be reliably measured with that minimum sampling frequency. Thus, the sampling frequency has to be larger than this Nyquist frequency. Sometimes half of this value is defined as the Nyquist frequency (to equal the above definition 1) so then the sampling frequency has to be larger than twice this Nyquist frequency.

The above definitions represent the same phenomenon, i.e. the same critical frequency for aliasing, critical sampling twice the signal frequency, but are based on two different references: (1) the sampling frequency (so the Nyquist frequency is maximum signal frequency to be measured without aliasing, i.e. a half of the sampling frequency), and (2) based on a signal frequency (so the Nyquist frequency is the minimum sampling frequency required to avoid aliasing), thus the latter being twice the former.

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