We want to fit two Least Squares polynomials to the 20-point data on the left. Notice that the interval of interest is [-p,p]. Matlab.
| x-values | y-values |
| -3.14159265358979 | 0.00000000000000 |
| -2.81089869005402 | -0.43702230525987 |
| -2.48020472651826 | -0.78170987707147 |
| -2.14951076298249 | -0.85207605602719 |
| -1.81881679944672 | -0.52335935447908 |
| -1.48812283591095 | 0.22121102681686 |
| -1.15742887237519 | 1.27130734031775 |
| -0.82673490883942 | 2.41089249371528 |
| -0.49604094530365 | 3.37539264122665 |
| -0.16534698176788 | 3.92749194128624 |
| 0.16534698176788 | 3.92749194128624 |
| 0.49604094530365 | 3.37539264122665 |
| 0.82673490883942 | 2.41089249371528 |
| 1.15742887237519 | 1.27130734031775 |
| 1.48812283591095 | 0.22121102681686 |
| 1.81881679944672 | -0.52335935447908 |
| 2.14951076298249 | -0.85207605602719 |
| 2.48020472651826 | -0.78170987707147 |
| 2.81089869005402 | -0.43702230525987 |
| 3.14159265358979 | 0.00000000000000 |
| We want to fit two Least Squares polynomials to the 20-point data on the left. Notice that the interval of interest is . You will have to cut and paste the data into your computer program.Part-IGoal: Approximate the data by a 4th degree polynomial,P4(x) = ao+ a1x+ a2x2+ a3x3+ a4x4 and write your coefficients in the space provided. Round your final answers to 4 decimal digits. Also plot the data points and the curve y= P4(x) together, in the spaces provided below. Do not connect the data points.Part-IIGoal: Approximate the data by a Trig Polynomial,S3(x)=a0/2+(a3/2)Cos3x+a1Cosx+a2Cos2x+b1Sinx+b2Sin2x and write your coefficients in the space provided. The final answers must be rounded to 4 decimal digits. Notice that the forms of ao and a3 are compatible with our book and well suited for Cooley-Tukey Fast Fourier Transform. Also plot the data points and the curve y= S3(x) together, in the spaces provided below. Do not connect the data points. |
Your output/notes should be printed below:
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(a) Print the Coefficients for Part-I here, rounded to 4 decimal digits:
| ao = | a1= | a2= | a3= | a4= |
(b) Print the Coefficients for Part-II here, rounded to 4 decimal digits:
| = | a1= | a2= | = | b1= | b2= |
(c) Plot the graph for Part-I here, For full credit, your graph should be labelled properly.
(d) Plot the graph for Part-II here, For full credit, your graph should be labelled properly.
e) Your notes for Part-I must be typed up here. Any assumptions, equations, techniques that you used.
f) Your notes for Part-II must be typed up here. Any assumptions, equations, techniques that you used.
