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6.1: Descriptions

MEE 390 OER · LibreTexts

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    1. Classification
      1. Stochastic - random elements that incorporate uncertainty of measurement to functional form
      2. Deterministic - something for which written functional form can be produced
      3. Periodic - repeats the trend/behavior at some frequency
        1. Recall that simple periodics have single frequency: \[ x(t) = A\cos(\omega t) \]
        2. Complex periodic functions have multiple combinations of characteristics that can be summed together: \[ y(t) = A_{0} + \sum_{i} C_{i}\cos(2\pi f_{i} t + \phi_{i}) \]
          1. Subscript \(i\) indicates a unique combination of amplitude, frequency, and phase shift
          2. Time \(t\) is the continuous variable
          3. Adding more combinations \(i \rightarrow \infty\) gets closer to representing observations
      4. Observed results can be a combination of all three features
        1. Isolation of terms within deterministic functions are already covered in weighted-least-square regression
        2. Periodic representation can be determined from Fourier coefficients of \(C_{i}\) (section 6.2)
        3. Stochastic features can be removed through statistical or filtering mechanisms (section 6.3)

    6.1: Descriptions is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by LibreTexts.