Ge 165: Digital Data Analysis Fall, 2007

Instructors:

Rob Clayton, x6909, clay@gps.caltech.edu

Office Hours: Usually in my office 8:15-12:00am

Teaching Assistant: YoungHee Kim ykim@gps.caltech.edu

Classes:MW10-11, 162 SMudd, TT10-11, 215 NMudd

Homework/Grading Policy: Final Grade for the course will be approximately 40% HWK, 20% Project, and 40% final. Homework is due as announced

Topics:

1. Sampled Time Series:
Representations,
Spaces,
Aliasing.

2. Discrete Fourier Transform:
Definition and Conventions,
Fast Fourier Transform.

3. Convolution and Correlation:

4. Classification of Waveforms:
Causality
Minimum Phase

5. Hilbert Transform and Analytic Signals:

6. Digital Filters:
Pole-Zero Representations,
Bilinear Tranformation,
DFT Filters.

7. Inverse Filtering:
Spectral Factorization,
Toeplitz Method/Levinson Algorithm,
Shaper Filters.

8. Models For Continuous Processes:
ARMA Models, Kalman Filters
AR Models,
Spectral Estimators (MEM, Multi-Taper).

9. Deconvolution:
Frequency Domain,
Predictive Deconvolution.

10. Resolution vs Variance in Time Series Estimators:
Uncertainty Principle,
Resolution vs Variance,
Power Spectrum of Noise,
Central Limit Theorem.

11. Multi-Channel Time Series:
Convolution and Correlation
Deconvolution

12. Wavelets

13. Multi-dimensional Time Series:

14. Optional: Finite-Differences :

Homework Datasets

HWK 5: Spectral Estimation.

The data set "Solar Motions" is a 1024 synthetically derived sample points of the motion of our sun due to planet rotations. The three columns are respectively time in earth years, x and y motions in A.U. Find the spectral peaks of as many planets as you can. One of the planets is rotating backwards, see if you can figure out which on it is? A longer version of the time series (4096 points) is available in Orbit4096 Use may find the following pages provide usefull information for this problem Planet Properties and Solar Info

HWK 6: Signal Prediction

The data set "AR Sample" has 200 samples of a time series that was generated by an ARMA process. Use the first 100 points to predict the second 100 points. Plot (on one plot) both the predicted time series, and the actual one. Try a number of different orders of the AR predictor. Compute the power spectrum of the 1) original 200 point time series, 2) first 100 points, padded with zeros to 200 points, and 3) the 200 point time series with the last 100 points created by prediction. Use the simple Fourier Transform method to determine the power spectrum.

Not Assigned

Dow Jones Index: The Dow Jones stock index from 1896 to 1996. The four columns are time (in days since start), date, value and interpolation flag. The interpolation flag is 1 for real data and 0 for a value that has been linearly interpolated. The latter generally occur on weekends and hollidays. It is interesting note the work-week in the early days.