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

Question

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?

Explanation / Answer

If the dimensionality of X is greater than 2, the fft2 function returns the 2-D DFT for each higher dimensional slice of X. For example, if size(X) = [100 100 3], then fft2computes the DFT of X(:,:,1), X(:,:,2) and X(:,:,3).

Y = fft2(X,m,n) truncates X, or pads X with zeros to create an m-by-n array before doing the transform. The result is m-by-n.

Data Type Support

fft2 supports inputs of data types double and single. If you call fft2 with the syntax y = fft2(X, ...), the output y has the same data type as the input X.

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