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Help with Numerical Methods Review (CMPS407) 1. State in your own words what is the least...

Help with Numerical Methods Review (CMPS407)

1. State in your own words what is the least square method? Why we need to use this method? Write a Matlab or C/C++ to do least square fitting on the following data points: data point: (-2, 13), (-1, 5), (0, 7), (1, 12), (2, 29).

2. When can aliasing happen in the Fourier series processing? How to prevent this?

3. What’s Gibbs phenomenon? How to avoid this? Write a flow chart to implement your idea (only algorithm is needed). If you write detailed Matlab/C++ code, extra credit will be given.

4. What’s the advantages of FFT? Show an example we can take the advantages.

5. What’s digital watermark? Based on your Project 3 found below, how the digital signature is confirmed in your project? If you implement it using FFT, will the complexity different from wavelet transform? Project 3 Given the following data point: (-2, 13), (-1, 5), (0, 7), (1, 12), (2, 29), using cubic spline interpolation method to find out S(z) in (-2,2). Plot the graph to show data points and the piecewise polynomial values. Note: You may use Matlab, C/C++, Fortran, Linux shell script etc. for your coding/program/script.

6. State in your own words how to do formula finding in real data processing? How do we know whether the data formula fitting is good enough?

7. Minor points: Which topics are you interested in and you think that they are important for your future jobs/careers? What topics you feel “boring” to learn/study?

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