Spectral Analysis and Time Series - Max Planck Society
Spectral Analysis and Time Series
Andreas Lagg
Part I: fundamentals on time series
classification prob. density func. autocorrelation power spectral density crosscorrelation applications preprocessing sampling trend removal
Part II: Fourier series
definition method properties convolution correlations leakage / windowing irregular grid noise removal
Part III: Wavelets
why wavelet transforms? fundamentals: FT, STFT and resolution problems multiresolution analysis: CWT DWT
Exercises
A. Lagg ? Spectral Analysis
Basic description of physical data
deterministic: described by explicit mathematical relation
x t=X cos
k t
t
n noon deterministic: no way to predict an exact value at a future instant of time
n
d
e
t
e
r
m
A. Lagg ? Spectral Analysis
Classifications of deterministic data
Deterministic
Periodic
Nonperiodic
Sinusoidal Complex Periodic Almost periodic Transient
A. Lagg ? Spectral Analysis
Sinusoidal data
time history
x t =X sin 2 f 0 t T =1/ f 0
frequency spectrogram
A. Lagg ? Spectral Analysis
Complex periodic data
x t =x t?nT n=1,2,3,...
x t
=
a0 2
an cos 2 n f 1 t bn sin 2 n f 1 t
(T = fundamental period)
time history
frequency spectrogram
A. Lagg ? Spectral Analysis
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