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

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download