chapt7x - Stat 153 - 13 Oct 2008 D. R. Brillinger Chapter 7...

Info iconThis preview shows pages 1–14. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Stat 153 - 13 Oct 2008 D. R. Brillinger Chapter 7 - Spectral analysis 7.1 Fourier analysis X t = μ + α cos ωt + βsin ωt + Z t ω known versus ω unknown, "hidden frequency" Study/fit via least squares Cases
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Fourier frequencies ω p = 2πp/N, p = 0,. ..,N-1 Fourier components Σ t=1 N x t cos 2πpt/N Σ t=1 N x t sin 2πpt/N a p +i b p = Σ t=1 N x t exp{i2πpt/N}, p=0,. ..,N-1 = Σ t=1 N x t exp{iω p t/N}
Background image of page 4
7.3 Periodogram at frequency ω p I(ω p ) = t=1 N x t exp{iω p t/N}| 2 /πN basis for spectral density estimates Can extend definition to I(ω) Properties I(ω) 0 I(-ω) = I(ω) I(ω+2π) = I(ω) Cp. f(ω) = N(a p 2 + b p 2 )/4π
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Correcting for the mean X X t - work with
Background image of page 6
dynamic spectrum
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
f(ω) = 0 + 2 Σ k=1 γ k cos ωk]/π I(ω p ) = [c 0 + 2 Σ k=1 N-1 c k cos ω p k]/π Relationship - periodogram and acv River height Manaus, Amazonia, Brazil daily data since 1902
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Periodogram properties . Asymptotically unbiased
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 14
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/19/2009 for the course MATH 611 taught by Professor Jsdkasj during the Spring '09 term at Kansas.

Page1 / 37

chapt7x - Stat 153 - 13 Oct 2008 D. R. Brillinger Chapter 7...

This preview shows document pages 1 - 14. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online