Aug 19, 2017

Compare the results reported in Example 13.10 and in particular Figure 13.8 to those obtained in Exercise 9

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Compare the results reported in Example 13.10 and in particular Figure 13.8 to those obtained in Exercise 9. Explain similarities and differences.

Example 13.10

Let the data consist of the values y= ln(1 + 2πi/32), i = 0,1,…,31. The results may then be compared against those of Exercise 9. Applying the DCT algorithm leads to Figure 13.8.

Exercise 9

Consider using a DFT to interpolate the function f (x) = log(x +1) on the interval [0,2π] as in the examples of Section 13.2.

(a) Construct and plot the interpolant on [0,2π] for l = 16 and l = 32. Explain why the results look unsatisfactory.

(b) Consider an even extension of f (x), defining

Apply DFT interpolation to g(t) and plot the results on [0,2π]. Find maximum errors for l = 16 and l = 32. Are they better than before? Why?


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