12.714 Computational Data Analysis: Section 2

 

Alan Chave (alan@whoi.edu)

Thomas Herring (tah@mit.edu),

MW 10:30-noon

http://geoweb.mit.edu/~tah/12.714

 

Section 2: Class notes and matlab scripts

 

References and Lecture notes are based on:

Percival, D.B., and A.T. Walden, Spectral Analysis for Physical Applications, Cambridge University Press, 1993. (PW)

Bracewell, R, N., The Fourier Transform and its Applications, McGraw-Hill Book Company, New York, pp. 444, 1978

Box, G.E.P., Jenkins, G.M., Reinsel, G.C., "Time Series Analysis: Forecasting and Control", 3rd edition, Prentice Hall, 1994.

 

 

 

Lec

Date

Contents

01

03/19/12

Introduction to spectral analysis

Notes: PDF PPT  PW Chapter 1.

Matlab: CDA_S2L01.m

Data: WindS.dat WillametteR.dat AtomC.dat OceanN.dat

02

03/21/12

Stationary stochastic processes

Notes: PDF PPT PW Chapter 2.

Matab: CDA_S2L02.m

03

04/09/12

Deterministic spectral analysis I

Notes: PDF PPT PW Chapter 3 and Bracewell, R, N., The Fourier Transform and its Applications, McGraw-Hill Book Company, New York, pp. 444, 1978

Matab: CDA_S2L03.m

04

04/11/12

Deterministic spectral analysis II

Notes: PDF PPT PW Chapter 3, second half.

Matlab: CDA_S2L04.m

 

 

Problem Set for Sec2 PS01: Due Wednesday Apr 25, 2012

PDF Data files for Question 1: CDA_S2PS01_Q1a.dat : CDA_S2PS01_Q1b.dat : CDA_S2PS01_Q1c.dat : CDA_S2PS01_Q1d.dat

Solution 12.714_S02PS01_soln.pdf

05

04/18/12

Concentration and discrete FFT

Notes: PDF PPT PW Chapter 3, Final section on concentration and discrete FFT.

Matlab: CDA_S2L05.m

06

04/30/12

Foundations of stochastic spectral analysis

Notes: PDF PPT PW Chapter 4: Foundations of stochastic spectral analysis

Matlab: CDA_S2L06.m

 

05/02/12

Practical in class exercise: PDF

Solution will be added after the class.

12.714_PracS02_Soln.pdf

CDA_S2Practical.m

07

05/07/12

Linear Time Invariant Filters

Notes: PDF PPT PW Chapter 5: Linear Time Invariant Filters

Matlab: CDA_S2L07.m Data File: mit_060422.erp

08

05/09/12

Means, auto covariance sequence, periodograms, tapers

Notes: PDF PPT PW Chapter 6: Means, acvs, periodograms and start of tapers.

Matlab: CDA_S2L08.m

09

05/14/12

Pre-whittening and lag window estimators

Notes: PDF PPT PW Chapter 6: Pre-whittening and lag window estimators.

Matlab: CDA_S2L09.m

 

 

Problem Set for Sec2 PS02: Due Wednesday May 16, 2012.

PDF

10

05/16/12

Variance characteristics of lag window estimators and Welch overlapped segment averaging

Notes: PDF PPT PW Chapter 6: Variance characteristics of lag window estimators and Welch overlapped segment averaging.

Matlab: CDA_S2L10.m

           

Acronyms and definitions

acs

Auto-correlation sequence: Discrete

acf

Auto-correlation function: Continous

Spectrum

Variances of the Fourier coefficients of the time series specified over a finite interval with fixed spacing.

dB

10 log10 (S)

{Xt}

Discrete stochastic process

{X(t)}

Continuous stochastic process

cpdf

Cumulative probability distribution function

acvs

Autocovariance sequence: Discrete

acvf

autocovariance function: Continuous

DirichletŐs Kernel

Effects on spectrum of using finite duration of data

GibbŐs phenomena

Ripple in spectrum due to sharp edges and finite data duration.  Determined using the DirichletŐs Kernel

FejerŐs Kernel

Rescaled version of DirichletŐs kernel squared that reduces the ripple in the GibbŐs phenomena.

dpss

Discrete prolate spheroidal sequence

dpswf

Discrete prolate spheroidal wave function

sdf

Spectral density function

psdf

Power spectral density function.

LTI

Linear time invariant