Q1. A periodic function is represented by a Fourier series that has a finite number of terms. The amplitude and phase spectra are shown in Fig. Q1(a) and (b), respectively. a) Write the expression for the function using the trigonometric form. b) Is the function an even, odd function or half-wave symmetry? c) Calculate the rms value d) Write the exponential form of the Fourier series. e) Using MATLAB, plot the periodic signal. 0.38 0.25 Tiit 0.16 0.11 0.08 0.06 0.05 0w 2π 3m 4m 5m 6m (a) 270⁰ 180° 90° 0 237.8° 90° 258° 90° 262.7° 90° 2п 3п 4п 5п бп (h) @0

! Required information x(t) A - The given figure is a graph of one fundamental period of a periodic function x(f). A CTFS harmonic function cx[k] is found based on the representation time being the same as the fundamental period To, where A1 = 5, A2 = -3, and To = 5. Determine the numerical value of cx[0]. The numerical value of cx[O] is

it says COSINE not sine  Is the signal x(t)=2+ sin 2 - 3 cosлt periodic? Can it be expressed using complex exponentials

m Figure 2 The Fourier series of the full-wave rectified wave shown above is given by: Cos754.29t Cos1508.57t Cos2262.87t 3 15 35 25 F(t) = e = 100 π a. What is the frequency of the waveform? b. Which harmonics are present in the rectified wave? c. What is the magnitude of the direct current component? d. Determine the rms value of the waveform. + .ot e. Given that the waveform forms the input of a circuit of resistance 552, write the Fourier expression for the current flowing in the circuit. Hence determine its rms value. f. The circuit, in "e" is modified by including a 15.92mH inductor in series with the resistor. What is the power factor of the new circuit?