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The Exponential Form of the Fourier SeriesThe waveform of Figure 7.30 is a rudimentary presentation of the capacitor voltage for the circuitof Figure 7.27. However, it will improve if we add a sufficient number of harmonics in (7.87).We can obtain a more accurate waveform for the capacitor voltage of Figure 7.27 with the Simulinkmodel of Figure 7.31.Figure 7.31. Simulink model for the circuit of Figure 7.27The input and output waveforms are shown in Figure 7.32.Figure 7.32. Input and output waveforms for the model of Figure 7.317.8 The Exponential Form of the Fourier SeriesThe Fourier series are often expressed in exponential form. The advantage of the exponentialform is that we only need to perform one integration rather than two, one for the , andanother for the b n coefficients in the trigonometric form of the series. Moreover, in most casesthe integration is simpler.The exponential form is derived from the trigonometric form by substitution ofa ncosωt=e jωte – jωt---------------------------+2(7.88)Signals and Systems with MATLAB ® Computing and Simulink ® Modeling, Fourth EditionCopyright © Orchard Publicationse jωte – jωtsinωt = --------------------------–j2(7.89)7−31