Follow these instructions for each of the waveforms in Problems 5.6 through 5.15. (a) Determine if the waveform has dc, even, or odd symmetry. (b) Obtain its cosine/sine Fourier series representation. (c) Convert the representation to amplitude/phase format and plot the line spectra for the first five non-zero terms. (d) Convert the representation to complex exponential format and plot the line spectra for the first five non-zero terms. (e) Use MATLAB or MathScript to plot the waveform using a truncated Fourier series representation with nmax = 100. 5.6 Waveform in Fig. P5.6 with A = 10. Figure P5.6: Waveform for Problem 5.6.
5.21 The Fourier series of the periodic waveform shown in Fig. P5.21(a) is given by f1(t) = 10 − 20 π∑n = 1 ∞ 1 n sin(nπt 2). Determine the Fourier series of waveform f2(t) in Fig. P5.21(b). (a) f1(t) (b) f2(t) Figure P5.21: Waveforms of Problem 5.21.
5.24 The voltage source vS(t) in the circuit of Fig. P5.24 generates a square wave (waveform #1 in Table 5-4) with A = 10 V and T = 1 ms. (a) Derive the Fourier series representation of vout(t). (b) Calculate the first five terms of vout(t) using R1 = R2 = 2 kΩ, C = 1 μF. (c) Plot vout(t) using nmax = 100. Figure P5.24: Circuit for Problem 5.24.
5.36 The current flowing through a 10 kΩ resistor is given by a triangular waveform (#4 in Table 5-4) with A = 4 mA and T = 0.2 s. (a) Determine the exact value of the average power consumed by the resistor. (b) Using a truncated Fourier-series representation of the waveform with only the first four terms, obtain an approximate value for the average power consumed by the resistor. (c) What is the percentage of error in the value given in (b)?