Consider the sawtooth wave given by f(x)=x, T x T. 1. Find the Fourier...

 

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Consider the sawtooth wave given by f(x)=x, T ≤ x ≤ T. 1. Find the Fourier coefficients for this function. 2. Plot the Fourier series for n = 4, 6, 10 terms in the interval - ≤ x ≤ T. You can do this using Mathematica, where the n'th order Fourier approx- imation to expr in x is given by the Fourier Series [expr,x,n] call. 3. Do you get better approximation of this function when n is increased ? What happens in the vicinity of x = ± ? Consider the sawtooth wave given by f(x)=x, T ≤ x ≤ T. 1. Find the Fourier coefficients for this function. 2. Plot the Fourier series for n = 4, 6, 10 terms in the interval - ≤ x ≤ T. You can do this using Mathematica, where the n'th order Fourier approx- imation to expr in x is given by the Fourier Series [expr,x,n] call. 3. Do you get better approximation of this function when n is increased ? What happens in the vicinity of x = ± ?

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