FFT on an irregular wave from JONSWAP spectrum

Please refer to the following jupyter-notebook file:

FFT+on+an+irregular+wave+from+JONSWAP+spectrum.ipynb

0.11MB

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Result summary

1. JONSWAP spectrum

2. irregular wave generated by doing the IFT (inverse fourier transform) on the JONSWAP spectrum

3. Compare the reconstructed FFT graph and the normalized JONSWAP spectrum (the normalization is conducted according to Eq. (2.15) in my pf's thesis)

 

※ normalization of the JONSWAP spectrum

The following figure shows Eqs. (2.14)-(2.15) in my pf's thesis. The normalization is conducted by Eq. (2.15) where $S(w)$ refers to the JONSWAP spectrum and $\Delta w$ denotes a frequency interval.