We first construct The Nyquist Contour, a contour that encompasses the right-half of the complex plane:

To be able to analyze systems with poles on the imaginary axis, the Nyquist Contour can be modified to avoid passing through the point.

the contour is mapped through the open-loop transfer function, the result is the Nyquist Plot of.

Signaling at the Nyquist rate meant putting as many code pulses through a telegraph channel as its bandwidth would allow.

In the 1920s, it was discovered that the current through an ideal resistor actually has statistical fluctuations, which depend on temperature, even when voltage and resistance are exactly constant ; this fluctuation, now known as Johnson – Nyquist noise, is due to the discrete nature of charge.

Analog signals that have not already been bandlimited must be passed through an anti-aliasing filter before conversion, to prevent the distortion that is caused by audio signals with frequencies higher than the Nyquist frequency, which is half of the system's sampling rate.

In 1927, 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.

:" Nyquist ( 1928 ) pointed out that, if the function is substantially limited to the time interval T, 2BT values are sufficient to specify the function, basing his conclusions on a Fourier series representation of the function over the time interval T ."

No matter what function we choose to change the amplitude vs frequency, the graph will exhibit symmetry between 0 and This symmetry is commonly referred to as folding, and another name for ( the Nyquist frequency ) is folding frequency.

A Nyquist plot is a parametric plot of a transfer function used in automatic control and signal processing.

The Nyquist plot can provide some information about the shape of the transfer function.

* MATLAB function for creating a Nyquist plot of a frequency response of a dynamic system model.

When the continuous function being sampled contains no frequencies equal or higher than the Nyquist frequency, all the aliases caused by sampling occur above the Nyquist frequency.

The stability characteristics of the gain feedback product β A < sub > OL </ sub > are often displayed and investigated on a Nyquist plot ( a polar plot of the gain / phase shift as a parametric function of frequency ).

For example, if a Dirac delta impulse occurs exactly at a sampling point and is ideally lowpass-filtered ( with cutoff at the critical frequency ) per the Nyquist – Shannon sampling theorem, the resulting discrete-time signal will be a Kronecker delta function.

* If the open-loop transfer function has a zero pole of multiplicity, then the Nyquist plot has a discontinuity at.

A single neuron with tap delayed inputs ( the number of inputs is bounded by the lowest frequency present and the Nyquist rate ) can be used to determine the higher order transfer function of a physical system via the bi-linear z-transform.

* Nyquist plot

Although these restrictions usually are met, if they are not another method must be used, such as the Nyquist plot.

Two related plots that display the same data in different coordinate systems are the Nyquist plot and the Nichols plot.

The Nyquist plot displays these in polar coordinates, with magnitude mapping to radius and phase to argument ( angle ).

Image: Nyquist. svg | A Nyquist plot.

# REDIRECT Nyquist plot

A Nyquist plot.

The Nyquist plot is named after Harry Nyquist, a former engineer at Bell Laboratories.

Assessment of the stability of a closed-loop negative feedback system is done by applying the Nyquist stability criterion to the Nyquist plot of the open-loop system ( i. e. the same system without its feedback loop ).

When drawn by hand, a cartoon version of the Nyquist plot is sometimes used, which shows the shape of the curve, but where coordinates are distorted to show more detail in regions of interest.

These response measurements can be plotted in three ways: by plotting the magnitude and phase measurements on two rectangular plots as functions of frequency to obtain a Bode plot ; by plotting the magnitude and phase angle on a single polar plot with frequency as a parameter to obtain a Nyquist plot ; or by plotting magnitude and phase on a single rectangular plot with frequency as a parameter to obtain a Nichols plot.

In that case, the Nyquist rate for a waveform with no frequencies ≥ B can be reduced to just B ( complex samples / sec ), instead of 2B ( real samples / sec ).

Nyquist criteria apply to z-domain transfer functions as well as being general for complex valued functions.

Bandwidth typically refers to baseband bandwidth in the context of, for example, sampling theorem and Nyquist sampling rate, while it refers to passband bandwidth in the context of Nyquist symbol rate or Shannon-Hartley channel capacity for communication systems.

In calculations of the maximum symbol rate, the Nyquist sampling rate, and maximum bit rate according to the Hartley formula, the bandwidth refers to the frequency range within which the gain is non-zero, or the gain in dB is below a very large value.

This is barely noticeable at low frequencies but is quite evident at frequencies close to the Nyquist frequency.

As a consequence of the Nyquist – Shannon sampling theorem, any spatial waveform that can be displayed must consist of at least two pixels, which is proportional to image resolution.

* Harry Nyquist ( 1889 – 1976 ), developed the Nyquist stability criterion for feedback systems in the 1930s.

These include graphical systems like the root locus, Bode plots or the Nyquist plots.

The Nyquist – Shannon sampling theorem states that a signal can be exactly reconstructed from its samples if the sampling frequency is greater than twice the highest frequency of the signal ; but requires an infinite number of samples.

For even N, notice that the Nyquist component is handled specially.

Before the advent of computer filter synthesis tools, graphical tools such as Bode plots and Nyquist plots were extensively used as design tools.

* 1889 – Harry Nyquist, important contributor to information theory ( d. 1976 )

A sufficient condition for recovering s ( t ) ( and therefore S ( ƒ )) from just these samples is that the non-zero portion of s ( t ) be confined to a known interval of duration P, which is the frequency domain dual of the Nyquist – Shannon sampling theorem.

* The use of non-uniform grids is an active research area, attempting to bypass the traditional Nyquist limit.

Doppler measurement is reliable only if the sampling rate exceeds the Nyquist frequency for the frequency shift produced by radial motion.

Examples of these are thermometers based on the equation of state of a gas, on the velocity of sound in a gas, on the thermal noise ( see Johnson – Nyquist noise ) voltage or current of an electrical resistor, on blackbody radiation, and on the angular anisotropy of gamma ray emission of certain radioactive nuclei in a magnetic field.

* April 4 – Harry Nyquist, American information theory pioneer ( b. 1889 )

* February 7 – Harry Nyquist, Swedish-American contributor to information theory ( d. 1976 )

The Nyquist – Shannon sampling theorem, after Harry Nyquist and Claude Shannon, in the literature more commonly referred to as the Nyquist sampling theorem or simply as the sampling theorem, is a fundamental result in the field of information theory, in particular telecommunications and signal processing.

Since the theorem was also discovered independently by E. T. Whittaker, by Vladimir Kotelnikov, and by others, it's also known as the Nyquist – Shannon – Kotelnikov, Whittaker – Shannon – Kotelnikov, Whittaker – Nyquist – Kotelnikov – Shannon, WKS, as well as the Cardinal Theorem of Interpolation Theory.