Use MATLAB To Plot π(π₯) = Ln(π₯) For π₯ β (0, 5], Along With Taylor Approximations Around π₯ = 1 With π = 0, 2, 4, 6: Maths Assignment, UOG, Ireland
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- Use MATLAB to plot π(π₯) = ln(π₯) for π₯ β (0, 5], along with Taylor approximations around π₯ = 1 with π = 0, 2, 4, 6
- Use an appropriate Taylor series to write a MATLAB function M-file that approximates π(π₯) = sin(2π₯) for all x with a maximum error of 0.01. That is, your M-file should take values of x as input, and return values of sin(2π₯) as output, but should not use MATLABβs built-in sine function i.e., sin.m.
- Use numerical experiments using MATLAB to arrive at a conjecture about whether the following infinite series converges or not.
- Determine the exponential Fourier series of the waveform of the function f(x) shown in Figure 1. i.Β Obtain the expressions for the amplitude and phase spectra. ii.Β Using MATLAB, plot the amplitude and phase spectra for π = 1, 2, 3, β¦ , π, where π = 11. iii.Β Plot the reconstructed waveform of the function for π = 1, 2, 3, β¦ , π, where π = 11. Explain the Gibbs Phenomenon from the obtained plot..Β Using MATLAB compute DFT of π₯[π] i.e., π[π]. ii.Β Plot DFT magnitude and phase as functions of k. iii.Β Compute and plot the IDFT of π[π].
