A periodic waveform #(t) with period T = 4 sec is defined over one period by the equa- tion 2(t) = e, 0st < 4 (a) Carefully sketch r(t) (b) Determine the fundamental frequency, wo, of z(t) (c) Determination the Fourier series coefficients, at, for the above waveform 1(t). Give a general formula valid for any integer k. 2n/3rad/sec, (d) If r(t) is passed through an ideal LPF whose cutoff frequency is weo = determine the output signal, y(t)

C) Put (TRUE) or (FALSE) and say why : - Fourier series is only applicable for periodic signals.

V 25 Figure 2 The Fourier series of the full-wave rectified wave shown above is given by: 100 F(t) = e = - Cos754.29t Cos1508.57t Cos2262.87t) 3 15 35 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?

one contain the question and the another contain the correction for the equation

M7

I want answers to question A4,A5,A6,A7 and A8

x(t) is a continuous time (CT), non periodic signal as shown in the figure.

1) For the signals shown in below, a) Find the Fourier transform of the half-cosine pulse in figure (a). Sketch amplitude spectrum of the G(f). b) Apply the time-shifting property to the result obtained in part (a) to evaluate the spectrum of the half-sine pulse shown figure (b). Sketch amplitude spectrum of the G(f). c) What is the spectrum of a half-sine pulse in figure (b) having a duration equal to aT ? Sketch amplitude spectrum of the G(f). d) What is the spectrum of the negative half-sine pulse shown in figure (c) ? Sketch amplitude spectrum of the G(f). e) Find the spectrum of the single sine pulse shown in figure (d). Sketch amplitude spectrum of the G(f). g(t) g(f) -T/4 0 T/4 T/2 (b) g(f) g(t) -T/2 -T/2 0. 0. T/2 -A -A (d)

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?