Nyquist critical frequency

The Nyquist critical frequency or critical angular frequency is... 

A = sampling interval (e.g., time between samples) The Nyquist critical frequency or critical angular frequency is 1 K... 

The upper value of n corresponds exactly to the critical sampling frequency of two sample points per cycle (i.e., the Nyquist critical frequency). Thus, in general, the discrete Fourier transform maps N complex numbers into N/2 complex numbers [75],... 

When the sample interval is At, then the frequency range covered ts-fc[Pg.300]

A final point needs to be made regarding taking measurements in time. Suppose we sample a signal y(t) at a sampling rate of A. Nyquist showed that if there exists a critical frequency /c = 1 /(2A) for a system such that measurements are limited to frequencies smaller than fc, then the function y t) is completely determined by these measurements. 

There is a parameter x=RC called "time constant," which is associated with this circuit, and a corresponding "characteristic circular" frequency C0(, = 1/t and "characteristic" or "critical relaxation" frequency/, = l/27t c = 1/2tiRC = 15.9 Hz. At very high frequencies the impedance is completely capacitive, while at low frequencies it becomes completely resistive and approaches the value of R, which equals the diameter of the Nyquist plot semicircle. The phase angle 0 tends towards -90° at high frequency and towards 0° at low frequency, and critical frequency /(, corresponds to a midpoint transition where the phase angle is -45° and = R/2. 

There is some critical value of gain at which the G, B plot goes right through the (—1, 0) point. This is the limit of closedloop stability. See Fig. 13.3e. The value of K, at this limit should be the ultimate gain that we have dealt with before in making root locus plots of this system. We found in Chap. 10 that = 64 and Let us see if the frequency-domain Nyquist stability... 

In Chap. 12 we presented three different kinds of graphs that were used to represent the frequency response of a system Nyquist, Bode, and Nichols plots. The Nyquist stability criterion was developed in the previous section for Nyquist or polar plots. The critical point for closedloop stability was shown to be the 1,0) point on the Nyquist plot. 

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