Continuous Wavelet Transform (CWT) Niño3 SST¶

This is the final result:

How can anyone turn a 1D to 2D information? The code will explain to you!

The code is structed in two scripts:

lib_wavelet.py : python’s functions library
wavetest.py : call functions and plot

                     +----------------+
                     |  wavetest.py   |
                     +----------------+
                            |
                    +----------------+
                    | lib_wavelet.py |
                    +----------------+
                            |
          +----------------+  +----------------+
          |  def wavelet   |--| def wave_signif|
          +----------------+  +----------------+
                  |
+----------------+  +----------------+
| def nextpow2   |--| def wave_bases |
+----------------+  +----------------+

Note

The Morlet wavelet is used as default in this code.

Building the puzzle ...

Why/when should I use the wavelet analysis¶

The wavelet analysis is used for detecting and characterizing its possible singularities, and in particular the continuous wavelet transform is well suited for analyzing the local differentiability of a function (Farge, 1992).

“Therefore the wavelet analysis or synthesis can be performed locally on the signal, as opposed to the Fourier transform which is inherently nonlocal due to the space-filling nature of the trigonometric functions. ” (Farge,1992).

Fourier Wavelet

context sound image

character stationary nonstationary

to see global features singularities

Choose the right glasses for what you want to see !

More info:¶

Fonte: Domingues (2012)

Papers:¶

Farge, M. 1992. Wavelet transforms and their applications to turbulence. Annu. Rev. Mech., 24: 395-457

Domingues, M. O.; Kaibar, M.K. 2012. Wavelet biortogonais. Revista brasileira de Ensino de Física,n.3, 34: 3701