Determine the discrete least squares trigonometric polynomial S 3 (x), using m = 4 for f(x) = e x cos 2x on the interval [-]. Compute the error E(S 3). Section 8.6 Fast Fourier Transforms 2) Determine...

Determine the discrete least squares trigonometric polynomial S₃(x), using m = 4 for
f(x) = e^xcos 2x on the interval [-]. Compute the error E(S_3).

Section 8.6 Fast Fourier Transforms
2)
Determine the trigonometric interpolating polynomial of degree 4 for f(x) = x(on the interval [-] using:

1. Direct calculation;


2. B. The Fast Fourier Transform Algorithm.

3)
Use the Fast Fourier Transforms Algorithm to compute the trigonometric interpolating polynomial of degree 4 on [-] for the following functions.

1. f(x) = (x- d. f(x) = x cos x²
   + e^x
   cos e^x
   

Section 8.5 Trigonometric Polynomial Approximation 9) Determine the discrete least squares trigonometric polynomial S3(x), using m = 4 for f(x) = excos 2x on the interval [-]. Compute the error E(S3). Section 8.6 Fast Fourier Transforms 2) Determine the trigonometric interpolating polynomial of degree 4 for f(x) = x(on the interval [-] using: a. Direct calculation; b. B. The Fast Fourier Transform Algorithm. 3) Use the Fast Fourier Transforms Algorithm to compute the trigonometric interpolating polynomial of degree 4 on [-] for the following functions. a. f(x) = (x- d. f(x) = x cos x2 + ex cos ex