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Astronomy 193: 
Noise and Data Analysis in Astrophysics
James M. Moran

General Information | Lecture Information | Course Outline

Astronomy 193 – Noise and Data Analysis in Astrophysics
  
Time & Place: Monday & Wednesday, 2:10-3:40 p.m.
   Observatory Classroom A
  
Instructor: James Moran
M-337, 160 Concord Avenue - next to St. Peter's Church, across the street from the Observatory at 60 Garden Street
Mail Stop 42
Telephone:  :(617) 495-7477
Fax:  (617) 496-7736
email:  moran@cfa.harvard.edu
Course Website
Instructor Website
Office hours: By appointment or drop in
  
Teaching Fellow: Dr. Avery Broderick
P-223 (Observatory)
Telephone: (617) 496-2634
email: abroderick@cfa.harvard.edu
Office hours: TBD
  
Prerequisites: Math 21b or equivalent (Taylor series, multivariate calculus, elementary complex variables, some linear algebra, some probability). Much of the homework will involve computer simulations and access to a random number generator. Hence, computer programming experience and access to a computer will be essential.
  
Work: Homework:  about 10 problem sets (50%)
Quiz:  (25%)
Project:  (25%)
  
Project: Look into some aspect of the course more deeply. Present results orally at a special class at end of term. Submission: copies of viewgraphs.
  
Text: The following three books are strongly recommended (Roman numerals refer to items in the following page of this syllabus). They are all readily available (shipped same day) on Amazon.com:

1.  Numerical Recipes, Press, Flannery, Teukolsky, Vetterling ($61) (ch. 7, 12-14) (III, IV, V)
2.  Data Analysis, A Bayesian Tutorial, Sivia ($32) (I, III)
3.  The Fourier Transform and Its Applications, Bracewell, 3rd ed., 2000 ($100 used) (I, IV, V, VI)
  
Other References: Bayesian Logical Data Analysis for the Physical Sciences, Gregory (2005) ($52) (I-VI)
Data Reduction and Error Analysis for Physical Sciences, Bevington, Robinson (III)
Probability, Random Variables, and Stochastic Processes, Papoulis, 1st ed., 1965 (II, IV)
Digital Filters, Hamming (V)
Statistics in Physical Science, Hamilton (III)
Random Signal Analysis and Kalman Filtering, Brown (III)
Astrostatistics, Babu and Feigelson (II, III)
Two-Dimensional Imaging, Bracewell (VI)
Statistics in Theory and Practice, Lupton (II, III)
  
  
Astronomy 193 Lectures

(23 Lectures)
  Back to Top
0. Introduction (1)
I. Fourier transforms (5)

Convolution theorem, Parseval's theorem, and other basic theorems; piecewise linear functions; two-dimensional Fourier transforms; applications to projection problems; Fourier series.
II. Probability theory (5)

Bayes theorem, Bernoulli trials, DeMoivre-LaPlace theorem, random variables, distributions, functions of random variables, transformations, moments and characteristic functions, central limit theorem, generation of random numbers, confidence intervals.
III. Parameter estimation (4)

Maximum likelihood method and weighted least-mean-squares analysis, simulated annealing, nonlinear parameter estimation, constraints, tests of fit, Monte Carlo simulations, bootstrap method, Bayesian analysis.
IV. Stochastic processes (2)

Stationarity, ergodicity, correlation functions, power spectra, Gaussian and Poisson processes, Wiener-Khinchin theorem, weighting functions, linear systems, noise processes in periodic phenomena, 1/f noise.
V. Digital signal processing (4)

Nyquist (Shannon) sampling theorem, aliasing, digital filtering, Fast Fourier transforms, spectrum of quantized data samples, channel capacity and the transmission of data on noisy channels. Wavelet analysis.
VI. Image processing (2)

Image enhancement, spatial filtering, deconvolution algorithms, maximum entropy image compression.



Astronomy 193 – Noise and Data Analysis in Astrophysics

Course Outline
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1 Jan 31 W Introduction
2 Feb 5 M Fourier transforms I
3 Feb 7 W Fourier transforms II
4 Feb 12 M Fourier transforms III
5 Feb 14 W Fourier transforms IV
   Feb 19 M HOLIDAY
6 Feb 21 W Fourier transforms V
7 Feb 26 M Probability theory I
8 Feb 28 W Probability theory II
9 Mar 5 M Probability theory III
10 Mar 7 W Probability theory IV
11 Mar 12 M Probability theory V (reschedule)
12 Mar 14 W Parameter estimation I (reschedule)
13 Mar 19 M Parameter estimation II
14 Mar 21 W Parameter estimation III
   Mar 26 M SPRING BREAK
   Mar 28 W SPRING BREAK
15 Apr 2 M Parameter estimation IV
16 Apr 4 W Stochastic processes I
17 Apr 4 W Stochastic processes II
18 Apr 11 W Digital signal processing I
19 Apr 16 M Digital signal processing II
20 Apr 18 W Digital signal processing III
21 Apr 23 M Digital signal processing IV
22 Apr 25 W Image processing I
23 Apr 30 M Image processing II
24 May 16 (TBD) Student lectures

 

 
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Last modified on January 31, 2007