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  2. Zeros and poles - Wikipedia

    en.wikipedia.org/wiki/Zeros_and_poles

    In this case a point that is neither a pole nor a zero is viewed as a pole (or zero) of order 0. A meromorphic function may have infinitely many zeros and poles. This is the case for the gamma function (see the image in the infobox), which is meromorphic in the whole complex plane, and has a simple pole at every non-positive integer.

  3. Pole–zero plot - Wikipedia

    en.wikipedia.org/wiki/Polezero_plot

    A pole-zero plot shows the location in the complex plane of the poles and zeros of the transfer function of a dynamic system, such as a controller, compensator, sensor, equalizer, filter, or communications channel. By convention, the poles of the system are indicated in the plot by an X while the zeros are indicated by a circle or O.

  4. Root locus analysis - Wikipedia

    en.wikipedia.org/wiki/Root_locus_analysis

    The root locus plots the poles of the closed loop transfer function in the complex s-plane as a function of a gain parameter (see polezero plot). Evans also invented in 1948 an analog computer to compute root loci, called a "Spirule" (after "spiral" and "slide rule"); it found wide use before the advent of digital computers.

  5. Bode plot - Wikipedia

    en.wikipedia.org/wiki/Bode_plot

    The second Figure 3 does the same for the phase. The phase plots are horizontal up to a frequency factor of ten below the pole (zero) location and then drop (rise) at 45°/decade until the frequency is ten times higher than the pole (zero) location. The plots then are again horizontal at higher frequencies at a final, total phase change of 90°.

  6. Z-transform - Wikipedia

    en.wikipedia.org/wiki/Z-transform

    where is the zero and is the pole. The zeros and poles are commonly complex and when plotted on the complex plane (z-plane) it is called the polezero plot . In addition, there may also exist zeros and poles at z = 0 {\displaystyle z{=}0} and z = ∞ . {\displaystyle z{=}\infty .}

  7. Argument principle - Wikipedia

    en.wikipedia.org/wiki/Argument_principle

    The simple contour C (black), the zeros of f (blue) and the poles of f (red). Here we have ′ () =. In complex analysis, the argument principle (or Cauchy's argument principle) is a theorem relating the difference between the number of zeros and poles of a meromorphic function to a contour integral of the function's logarithmic derivative.

  8. Root-finding algorithm - Wikipedia

    en.wikipedia.org/wiki/Root-finding_algorithm

    In numerical analysis, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function f is a number x such that f ( x ) = 0 . As, generally, the zeros of a function cannot be computed exactly nor expressed in closed form , root-finding algorithms provide approximations to zeros.

  9. Closed-loop pole - Wikipedia

    en.wikipedia.org/wiki/Closed-loop_pole

    When the transfer function method is used, attention is focused on the locations in the s-plane where the transfer function is undefined (the poles) or zero (the zeroes; see Zeroes and poles). Two different transfer functions are of interest to the designer.