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Transfer functions

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Abstract In statistical time‐series analysis, signal processing, and control engineering, a transfer function is a mathematical relationship between a numerical input to a dynamic system and the resulting output. The theory of transfer functions describes how the input/output relationship is affected by the structure of the transfer function. Copyright © 2010 John Wiley & Sons, Inc. This article is categorized under: Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data

The path described in the complex plane by the frequency‐response function corresponding to the gain and phase functions of Figures 3 and 4. The trajectory originates, when ω = 0, in the point on the real axis marked by a dot and it travels in the direction of the arrow, of which the tip is reached when ω = π/4.

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The phase plot to accompany Figure 3.

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The gain of the transfer function depicted in Figures 1 and 2.

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The pole–zero diagram for the transfer function b(z−1)/a(z−1) corresponding to the impulse response function of Figure 1. The poles are marked by crosses and the zeros by circles.

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The impulse response of the transfer function b(z)/a(z) with a(z) = 1.0 − 0.673z + 0.463z2 + 0.486 z3 and b(z) = 1.0 + 0.208z + 0.360z2.

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Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data

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