Univariate

JONSWAP{K}(α,ωₚ,γ,r)
JONSWAP{K}(x)

4 parameter JONSWAP model for vertical displacement.

Type parameter

The type parameter K is a non-negative integer representing the ammount of aliasing to be done. This is useful as some devices have high-pass filters which limit the ammount of aliasing that will be present in a recorded series. In particular, a JONSWAP{K} model for a series recorded every Δ seconds would be appropriate for a series sampled every Δ seconds and filtered with a high-pass filter at (2K-1)π/Δ.

Arguments

• α: The scale parameter.
• ωₚ: The peak angular frequency.
• γ: The peak enhancement factor.
• r: The tail decay index.

Vector constructor arguments

• x: Vector of parameters [α,ωₚ,γ,r].

Background

The JONSWAP spectral density function is

\[f(ω) = αω^{-r}\exp\left \{-\frac{r}{4}\left(\frac{|ω|}{ωₚ}\right)^{-4}\right \}γ^{δ(|ω|)}\]

where

\[δ(ω) = \exp\left\{-\tfrac{1}{2 (0.07+0.02\cdot\mathbb{1}_{ωₚ>|ω|})^2}\left (\tfrac{|ω|}{ωₚ}-1\right )^2\right\}.\]