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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 ...
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.
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.
Plot of sample rates (y axis) versus the upper edge frequency (x axis) for a band of width 1; grays areas are combinations that are "allowed" in the sense that no two frequencies in the band alias to same frequency. The darker gray areas correspond to undersampling with the maximum value of n in the equations of this section.
A signal may be intentionally sampled at a higher rate to reduce the requirements and distortion of the anti-alias filter. For example, compare CD audio with high-resolution audio. CD audio filters the signal to a passband edge of 20 kHz, with a stopband Nyquist frequency of 22.05 kHz and sample rate of 44.1 kHz.
Radial velocity aliasing occurs when reflections arrive from reflectors moving fast enough for the Doppler frequency to exceed the pulse repetition frequency (PRF). Frequency ambiguity resolution is required to obtain the true radial velocity when the measurements is made using a system where the following inequality is true.
Another motive is to reduce the highest frequency, which reduces the minimum rate for alias-free sampling. A frequency shift does not undermine the mathematical tractability of the complex signal representation. So in that sense, the down-converted signal is still analytic. However, restoring the real-valued representation is no longer a simple ...
The frequency axis has units of FFT "bins" when the window of length N is applied to data and a transform of length N is computed. For instance, the value at frequency 1 / 2 "bin" is the response that would be measured in bins k and k + 1 to a sinusoidal signal at frequency k + 1 / 2 . It is relative to the maximum possible ...