Response Analysis 2
Response Analysis 2 : for any linear system, an input i 0 function X (t) and an output function X (t) can be related according to the formula: X0 o I (t) = I X (t - J)W(J)dJ + noise(t) 4 where W(J) is the impulse response of the system and its. Fourier Transform: Z(F O ) = I W (J)E = R(F)E 4 -2bifj In(F) is The System's Admittance (Coherent Output/Input) At21 Frequency F. in Practice, The Integrals Are Replaced By I Summations; X , W, and Z Are Generally Complex. The D 0 Iscrete Set of W Values Are Termed Response Weights; X (T) I is Ordinarily An Observed Tidal Time Series and X (T) The Tide Potential or The Tide At Some Nearby Place. A Future Prediction Can Be Prepared By Applying The Weights To An I Appropriate X (T) Series. in General: * Z * = R(F) and Tan(Z) = N(F) Measure The Relative Magnification and Phase Lead of The Station At Frequency F
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