# CWT-Continuous wavelet transform

In mathematics, a continuous wavelet transform (CWT) is used to divide a continuous-time function into wavelets. Unlike Fourier transform, the continuous wavelet transform possesses the ability to construct a time-frequency representation of a signal that offers very good time and frequency localization.

Figure 3.7 – Wavelet transform of the 4th monitor point on the 1st cylinder on 2D

In this picture, in order to observe the Kármán vortex frequency, which corresponds to a $St=0.23$ ( 514 points in a period ), we have use a defined scales from 450 to 600. We have found exactly the same value of the $St_K=0.23$.

# AR-Autoregressive power spectral density estimate

Compared to the FFT approach, AR estimate has a better stability for short segments of signal, a better spectral resolution and a better resolution as function of time. We will present the results on the 4th monitor point in the following part.

Figure 3.8 – AR transform of the 4th monitor point on the 1st cylinder on 2D

Here we have observed the $St_K=0.23$ which corresponds well to our previous study. But in this case, we can't observe the phenomena of shear layer vortex. So in the following part, we will at first filter the low frequency signal ( for example, $Fc=2.2$ for the strouhal number ), then we excuter a AR transform.

Figure 3.9 – High-pass filtered signal of the variation pressure

Here we define the $Fc=2.20$ in order to observe the Strouhal number corresponding to the Kelvin Helhomltz instability.​

Figure 3.10 – AR transform of the 4th monitor point on the 1st cylinder on 2D with a high-pass filter Fc=2.2

With a high-pass filter, we can observe the  Kelvin Helhomltz instability phenomena which corresponds to a $St=2.3$.