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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.
The starred transform is similar to the Z transform, with a simple change of variables, where the starred transform is explicitly declared in terms of the sampling period (T), while the Z transform is performed on a discrete signal and is independent of the sampling period.
An anti-aliasing filter (AAF) is a filter used before a signal sampler to restrict the bandwidth of a signal to satisfy the Nyquist–Shannon sampling theorem over the band of interest. Since the theorem states that unambiguous reconstruction of the signal from its samples is possible when the power of frequencies above the Nyquist frequency is ...
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A simple illustration of aliasing can be obtained by studying low-resolution images. A gray-scale image can be interpreted as a function in two-dimensional space. An example of aliasing is shown in the images of brick patterns in Figure 5. The image shows the effects of aliasing when the sampling theorem's condition is not satisfied.
Nonuniform sampling is based on Lagrange interpolation and the relationship between itself and the (uniform) sampling theorem. Nonuniform sampling is a generalisation of the Whittaker–Shannon–Kotelnikov (WSK) sampling theorem. The sampling theory of Shannon can be generalized for the case of nonuniform samples, that is, samples not taken ...
Between samples no measurement of the signal is made; the sampling theorem guarantees non-ambiguous representation and recovery of the signal only if it has no energy at frequency f s /2 or higher (one half the sampling frequency, known as the Nyquist frequency); higher frequencies will not be correctly represented or recovered and add aliasing ...
Signal sampling representation. The continuous signal S(t) is represented with a green colored line while the discrete samples are indicated by the blue vertical lines. In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a