PHY308S/408S - Time Series Analysis

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Table of Contents

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People

Instructor: R.C. Bailey

            MP501

            978-3231

bailey@physics.utoronto.ca

 

Demonstrator: TBA


Days, Dates and Times

There is a one hour lecture on Wednesday, 3-4PM, MP134.

There is a laboratory section scheduled for Friday afternoons, 3-5PM.  If enrolment requires it, a second section may be scheduled, probably on Monday from 12-2PM. The laboratory meets in the Nortel Applied Physics Laboratory, MP239. 


Assessment

Late penalties: 10% per business day.


Oral Exam

An oral examination (less than a half hour) will occur at the end of the course.

 


Schedule

Provisional Schedule Spring 2006

 

 

 

 

 

 

 

 

 

Day

Date

 

Event

Probable Lecture Topic

Lab Topic Handed Out

Due

Wed.

11 January 2006

 

Lecture

MATLAB

0) MATLAB Exercise

 

Fri.

13 January 2006

 

Lab Section 1

 

 

 

Mon.

16 January 2006

 

Lab Section 2

 

 

 

Wed.

18 January 2006

 

Lecture

Linear Systems and Convolution

1) Convolution

 

Fri.

20 January 2006

 

Lab Section 1

 

 

0 due

Mon.

23 January 2006

 

Lab Section 2

 

 

 

Wed.

25 January 2006

 

Lecture

Fourier Transforms

 

 

Fri.

27 January 2006

 

Lab Section 1

 

 

 

Mon.

30 January 2006

 

Lab Section 2

 

 

 

Wed.

1 February 2006

 

Lecture

DFT and FFT

2) FFT

1 due

Fri.

3 February 2006

 

Lab Section 1

 

 

 

Mon.

6 February 2006

 

Lab Section 2

 

 

 

Wed.

8 February 2006

 

Lecture

Z-transforms

 

 

Fri.

10 February 2006

 

Lab Section 1

 

 

 

Mon.

13 February 2006

 

Lab Section 2

 

 

 

Wed.

15 February 2006

 

Lecture

Digital Filters

3) Digital filters

2 due

Fri.

17 February 2006

 

Lab Section 1

 

 

 

Mon.

20 February 2006

 

Reading Week

 

 

 

Wed.

22 February 2006

 

Reading Week

 

 

 

Fri.

24 February 2006

 

Reading Week

 

 

 

Mon.

27 February 2006

 

Lab Section 2

 

 

 

Wed.

1 March

 2006

 

Lecture

Stochastic Processes

 

 

Fri.

3 March

2006

 

Lab Section 1

 

 

 

Mon.

6 March

2006

 

Lab Section 2

 

 

 

Wed.

8 March 2006

 

Lecture

Power Spectra

 

3 due

Fri.

10 March 2006

 

Lab Section 1

 

 

 

Mon.

13 March 2006

 

Lab Section 2

 

 

 

Wed.

15 March 2006

 

Lecture

Power Spectral Estimation

4) Power spectral estimation

 

Fri.

17 March 2006

 

Lab Section 1

 

 

 

Mon.

20 March 2006

 

Lab Section 2

 

 

 

Wed.

22 March 2006

 

Lecture

Wiener filters

 

 

Fri.

24 March 2006

 

Lab Section 1

 

 

 

Mon.

27 March 2006

 

Lab Section 2

 

 

 

Wed.

29 March 2006

 

Lecture

Wavelets

5) Wiener filters

4 due

Fri.

31 March 2006

 

HOLIDAY

 

 

 

Wed.

3 March 2006

 

Lecture

Imaging applications

 

 

Mon.

5 April 2006

 

Lab Section 2

 

 

 

Fri.

7 April 2006

 

Lab Section 1

 

 

 

Wed.

10 April 2006

 

Lecture

Review

Oral exams

5 due

 
 


 

Priming Questions: These are a set of sample oral questions that I have (in past incarnations of this course) given to my co-examiners to give them an idea of the scope and difficulty of the course.  Questions on the actual oral exam will certainly not be limited to these!

1. What is meant by the impulse response of a system?
2. What is aliasing?
3. A sine wave of frequency 6 hz is sampled 3 times a second. What is its apparent frequency?
4. A discrete Fourier transform makes an estimate of the Fourier Transform at some frequency f. What is the relationship of this to the true FT?
5. Making power spectral estimates of natural stochastic processes requires some care in working out how much data of what type is required. Elaborate.
6. Why is it unnecessary to compute or store the negative frequency part of the Fourier transform of a real function of time?
7. What is a time series?
8. What is the Z transform of a time series?
9. Why are Z transforms useful? Why not just use Fourier transforms?
10. What is the inverse Z transform of (z + 3)2 ?
11. How is the Z transform related to the Fourier Transform?
12. When is a Fourier series representation of a function of time appropriate?
13. What is the general form of a convolution?
14. State the convolution theorem? What useful procedure does it justify?
15. When is recursive digital filtering likely to be better than direct convolution?
16. To convolve a thousand point filter with a million point time series, roughly how many operations are likely to be required for direct convolution? For circular (Fourier) convolution?
16. When is the Fast Fourier Transform actually fast? What is the Slow Fourier transform?
17. In general terms, how does the FFT achieve its speed?
18. Write the Z-transform of a simple narrow band filter; how are the parameters in it related to the characteristics of the filter in the frequency domain?
19. What does the impulse response of a narrow band filter look like?
20. What general and sometimes frustrating relation holds between the bandwidth of a filter and the length of its impulse response?
21. What is a stochastic process?
22. What is the autocorrelation function of a stochastic process, and what is it supposed to tell you?
23. What is the power spectrum of a stochastic process, and what is it supposed to tell you?
24. How are the power spectrum and autocorrelation function of a stochastic process related?
25. How would you know what the frequency resolution and error of a power spectral estimate were going to be?
26. Show that the filter 1/(1-z) performs numerical integration on a time series.
27. Why might Fourier convolution of two time series go wrong? How would you fix it?
28. What filtering operations can undo the effects of aliasing?