Response Analysis

Science / Tides and Currents / Response Analysis: For any linear system, an input function Xi(t) and an output function X0(t) can be related according to the formula: X0(t) = oi4xi (t – J)W(J)dj + noise(t), where W(J) is the impulse response of the system and its Fourier transform: Z(f) = oi4w (J)e-2bifj = R(f)ein(f), is the system's admittance (coherent output/input) at frequency f. In practice, the integrals are replaced by summations; Xi, W, and Z are generally complex. The discrete set of W values are termed response weights; X0(t) is ordinarily an observed tidal time series and Xi(t) the tide potential or the tide at some nearby place. A future prediction can be prepared by applying the weights to an appropriate Xi(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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