, which is the frequency domain dual of the Nyquist–Shannon sampling theorem.
Whittaker in 1935, and in the formulation of the Nyquist–Shannon sampling theorem by Claude Shannon in 1949.
This can be thought as one consequence of Nyquist–Shannon sampling theorem, the lattice points being viewed as the "sampling points" of a continuous wave.
However, such low frequencies by definition (Nyquist–Shannon sampling theorem) are very low bandwidth, so this type of communication is not widely used.
From a signal processing point of view, ignoring the point spread function and approximating the integral of radiance with a single, central sample (through a ray with no thickness) can lead to strong aliasing because the "projected geometric signal" has very high frequencies exceeding the Nyquist-Shannon maximal frequency that can be represented using the uniform pixel sampling rate.
This leads to a natural formulation of the Nyquist–Shannon sampling theorem.
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.
The Nyquist–Shannon sampling theorem observes that the minimum sampling frequency required to record a signal successfully must be greater than twice the bandwidth of the signal.
Per the Nyquist–Shannon sampling theorem, the sampling frequency (8 kHz) must be at least twice the highest component of the voice frequency via appropriate filtering prior to sampling at discrete times (4 kHz) for effective reconstruction of the voice signal.
The Nyquist–Shannon sampling theorem implies that a faithful reproduction of the original signal is only possible if the sampling rate is higher than twice the highest frequency of the signal.
The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals and discrete-time signals.
In a properly matched analog-to-digital converter (ADC) and digital-to-analog converter (DAC) pair the analog signal is accurately reconstructed per the constraints of the Nyquist–Shannon sampling theorem dependent on the sampling rate and quantization error dependent on the audio or video bit depth.
This fact that the dimensions have to agree is related to the Nyquist–Shannon sampling theorem.
A phenomenon occurs as the spatial frequency is increased past the whole pixel Nyquist limit from the Nyquist–Shannon sampling theorem; Chromatic aliasing (color fringes) may appear with higher spatial frequencies in a given orientation on the color subpixel arrangement.
In particular, Nyquist determined that the number of independent pulses that could be put through a telegraph channel per unit time is limited to twice the bandwidth of the channel, and published his results in the papers "Certain factors affecting telegraph speed" (1924) and "Certain topics in Telegraph Transmission Theory" (1928).
This minimum sampling rate is called the Nyquist rate.
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