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# appdx_e_ocr - APPENDIX E TABLE OF RANDOM-INPUT DESCRIBING...

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APPENDIX E TABLE OF RANDOM-INPUT DESCRIBING FUNCTIONS (RIDFs) In this table we employ the probability function (cf. Sec. 7.2) denoted by and its integral, the probability integral, denoted by PZ(X) = = 1 1" exp (- g) dv 4 2 ~ -a These functions are plotted in Fig. E.2-1. This table is given in three sections: E. 1 Gaussian-input RIDFs E.2 Gaussian-plus-bias-input RIDFs E.3 Gaussian-plus-bias-plus-sinusoid-input RIDFs E.1 GAUSSIAN-INPUT RlDFs x(t) = r(t) an unbiased Gaussian process

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-- TABLE OF RANDOM-INPUT DESCRIBING FUNCTIONS (RIDFs) (Continued) Nonlinearity Comments 16. Linear gain

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-- TABLE OF RAN DOM-INPUT DESCRIBING FUNCTIONS (RIDFs) (Continued) Nonlinearity Comments See Sec. 7.2 n = 2 , 4 , 6 , ... See Sec. 7.2 - y = 4 x (x 2 0) = -4-x (x < 0) 26. Odd square root See Fig. E.l-3 y = ~ 1 1 % 27. Cube root characteristic r ( x ) is gamma function

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574 RANDOM-INPUT DESCRIBING FUNCTIONS Figure E.1-2 RIDFs for litniter and tlrr.esholrl characteristics.
R A N D O M - I N P U T DESCRIBING F U N C T I O N S 575 Figure E.1-3 RZDFfor the simple polynonlial nonlinearity y = c,xn (n odd) ory = c,xn-' 1x1 (n even).

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RANDOM-INPUT DESCRIBING FUNCTIONS Figure E.1-4 Harmonic nonlinearity RIDF.
E.2 GAUSSIAN-PLUS-BIAS-INPUT RlDFs x(t) = r(t) + B The gain to the gaussian input component is given by: and the corresponding gain to the bias input component is: 1 N,(a,B) = - jm B)exp (- \$) dr ~ Z O B This section uses the additional function G(x) = xPI(x) + PF(x).

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appdx_e_ocr - APPENDIX E TABLE OF RANDOM-INPUT DESCRIBING...

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