Spectral Analysis and Time Series - max planck research school ...
Spectral Analysis and Time Series - max planck research school ...
Spectral Analysis and Time Series - max planck research school ...
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
A. Lagg – <strong>Spectral</strong> <strong>Analysis</strong><br />
Discretization of CWT: Wavelet <strong>Series</strong><br />
> sampling the time – frequency (or scale) plane<br />
advantage:<br />
sampling high for high frequencies (low scales)<br />
scale s <strong>and</strong> 1 rate N 1<br />
sampling rate can be decreased for low<br />
frequencies (high scales)<br />
scale s 2<br />
<strong>and</strong> rate N 2<br />
N 2<br />
= s 1<br />
s 2<br />
N 1<br />
N 2<br />
= f 2<br />
f 1<br />
N 1<br />
continuous wavelet<br />
discrete wavelet<br />
, s<br />
= 1 s t−<br />
s t = s − j/2 −<br />
j , k 0<br />
s j 0<br />
t−k 0<br />
, j , k<br />
x<br />
j , k =∫<br />
t<br />
xt = c ∑<br />
j<br />
*<br />
xt j , k<br />
tdt<br />
∑<br />
k<br />
x<br />
j , k j , k<br />
t<br />
orthonormal<br />
WLtransformation<br />
reconstruction of<br />
signal
Change language