(Solved): Question 1 Show that the Forrier Series for the triangular waveform shown below is gives by the infi ...
Question 1 Show that the Forrier Series for the triangular waveform shown below is gives by the infinite sorier: [34 marky]
f(t)=(8)/(\pi ^(2))(sin(t)-(1)/(9)sin(3t) (1)/(25)sin(5t)-(1)/(49)sin(7t) cdots)(a) Calculate and state the correctly formatied piccewise function that represents the periodic
f(e)given in the problem statement. [6 marks] (b) State the Full Renge Fourier Series along with mathematical expressions for the Fourier Consant and the Fourier Coefficients appropriate for the periodle function shown in the problem statement having a period of
T=2r. (c) Calculate the Fourier constant,
a_(0), and the Fourier coefficients
a_(n), and
b_(n), where needed. STATE any simplifying assumpetions incorporated into your calculations. [6 marks] [16 marks] (d) Generate the Fourier Series expression for
f(t)using summing notation. [4 marks] (e) Write out the calculated Fourier Serles terms and compare them to the terms provided in the problem statement. [2 marks]
