Which is the frequency required by the sampling theorem?

Which is the frequency required by the sampling theorem?

The sampling frequency required by the sampling theorem is called the Nyquist frequency. The transformation of signals into the frequency domain ( Fig. 2.5) is performed by the Fourier transformation, which essentially reformulates the signal into a cosine function space.

How is the sampling theorem related to artifacts?

The sampling theorem essentially says that a signal has to be sampled at least with twice the frequency of the original signal. Since signals and their respective speed can be easier expressed by frequencies, most explanations of artifacts are based on their representation in the frequency domain.

How is sampling of the original signal described?

In the frequency domain, sampling of the original signal is described as the convolution of the original signal with a comb function (with peaks repeating at the sampling frequency). Due to the periodicity of the comb function (we take samples at regular positions), the convolved signal also exposes a replicating pattern.

Who is the founder of the sampling theorem?

Therefore in mathematics and engineering literature sometimes it is also called WKS sampling theorem after Whittaker, Kotel’nikov and Shannon. The main basis in signal theory is the sampling theorem that is credited to Nyquist [1924] —who first formulated the theorem in 1928.

Which is the result of the Shannon sampling theorem?

Shannon Sampling Theorem. : A continuous-time signal with frequencies no higher than can be reconstructed exactly from its samples , if the samples are taken at a sampling frequency , that is, at a sampling frequency greater than . The frequency is known as the Nyquist frequency.

What is the Nyquist criterion for the sampling theorem?

The sampling theorem gives a criterion for recovery of v (t) from v * ( t ). If ω s is not larger than twice the highest frequency in V (ω), then the frequency-shifted bands of V (ω) overlap ( Fig. 12.42) and cannot be separated by filtering. The Nyquist criterion for recoverability of the original continuous signal is FIG. 12.42.