Let v (t) be the sawtooth waveform listed in Table T.2 (page 850, Carlson), and let v_n (t) be the approximation obtained with the first n nonzero terms of trigonometric Fourier series. Write a matlab M-file (function) to determine the percentage energy E_n contained in v_n(t) as a function ofn. Plot E_n as a function of n for n=1 to 100. Table T.2 Fourier Series Definitions If v(f) is a periodic with fundamental period To = 1/fo = 21/W, then it can be written as the exponential Fourier series v(e) = con loans noo The series coefficients are c = te f**erele tant de u(t)e nw dt where t, is arbitrary. When v(t) is real, its Fourier series may be expressed in the trigonometric forms u(t) = c + 12cn| cos (nwo t + arg cn) = C, + (a, cos nwot + bsin nw, t) ra where an = 2 Re [cn] bn = 2 Im [cn] Coefficient calculations If a single period of v(t) has the known Fourier transform 249) = s[von (47)] then cn = 2010) The following relations may be used to obtain the exponential series coeffi- cients of a waveform that can be expressed in terms of another waveform u(t) whose coefficients are known and denoted by c,(n). Waveforms Coefficients Ac,(0) + B n = 0 Av(t) + B Ac,(n) no u(t td) cu(n)ejmwold du(t)/dt (j27nfo),(n) u(t) cos (mwgt + ") { cu(n m)evis + cu(n + m)els Series coefficients for selected waveforms The waveforms in the following list are periodic and are defined for one period, either 0