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 Matlab:
CDA_S2L01.m |
02 |
03/21/12 |
Stationary
stochastic processes 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. |
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. |
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 |