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That paper includes an example of frequency aliasing dating back to 1922. The first published use of the term "aliasing" in this context is due to Blackman and Tukey in 1958. [ 5 ] In their preface to the Dover reprint [ 6 ] of this paper, they point out that the idea of aliasing had been illustrated graphically by Stumpf [ 7 ] ten years prior.
In this example, f s is the sampling rate, and 0.5 cycle/sample × f s is the corresponding Nyquist frequency. The black dot plotted at 0.6 f s represents the amplitude and frequency of a sinusoidal function whose frequency is 60% of the sample rate. The other three dots indicate the frequencies and amplitudes of three other sinusoids that ...
When the signal is sampled at a higher sample rate (see § Critical frequency), the resulting discrete-time sequence is said to be free of the distortion known as aliasing. Conversely, for a given sample rate the corresponding Nyquist frequency is one-half the sample rate. Note that the Nyquist rate is a property of a continuous-time signal ...
The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate required to avoid a type of distortion called aliasing. The theorem states that the sample rate must be at least twice the bandwidth of the signal to avoid aliasing.
Aliasing is an automatic and unavoidable result of observing such a fraction. [3] [4] The aliasing properties of a design are often summarized by giving its resolution. This measures the degree to which the design avoids aliasing between main effects and important interactions. [5]
A common example is the conversion of a sound wave to a sequence of "samples". A sample is a value of the signal at a point in time and/or space; this definition differs from the term's usage in statistics, which refers to a set of such values. [A] A sampler is a subsystem or operation that extracts samples from a continuous signal.