a) A periodic signal is defined as x(t)=t over the interval (m, n) and the period TO= 2n. Sketch the function over a period of time. Find the trigonometric Fourier series of the function. The function is antisymmetric and therefore only the b's are different from zero. Use the integral from the integration table: ft sin(at) dt = 1/a' (sin(at)-at cos(at)]

a) A periodic signal is defined as x(t)=t over the interval (m, n) and the period TO= 2n. Sketch the function over a period of time. Find the trigonometric Fourier series of the function. The function is antisymmetric and therefore only the b's are different from zero. Use the integral from the integration table: ft sin(at) dt = 1/a' (sin(at)-at cos(at)]

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Similar questions

The fundamental periods of the signs x(t) and y(t) are given as T and 2T, respectively. The Fourier series coefficients of these two signs are ak and bk, respectively. Find the Fourier series coefficient dk of the periodic sign z(t) = x (t) + y (2t) in terms of ak and bk.
1. Consider the periodic function .x(t) plotted in Figure 1 E -27₁ LES Figure 1: x(t) (a) Compute the Fourier series representation of x(t). 1+2)+1). A new signal is defined as ( 1 ( - (b) Sketch the waveform of y(t) and find its Fourier series coefficients, by, in terms of the Fourier series coefficients,4, of xft).
Consider the Fourier series for the periodic function: x(t) = sin(4t) + cos(8t) +7+ cos(16t). The Fourier coefficient C₂ of the exponential series is: Select one: O 0.5e-j/2 O 0.5em/2 O 0.5 O 0.5e
Consider the following periodic impulse train δα(t): The function is shown in the figure. Find the Fourier series representation of δT (t):
For the periodic signal shown below, answer the following questions: v (V) a) w, in radians per second, b) fo in kHz, c) The Fourier series coefficients av, ak, bk Q Ara -2 -1 0 3 4 5 6 -1(s)
Item 3 Calculate the Fourier Series of Periodic Functions from the given figure. Find the Amplitude and spectra. Find the Vo(t) response of the circuit. 42 4 ww- 2H vo(t) -4 -3 -2 -101 3 4 5 6 t T =... a,... a =... b = Fourier Series (t) = .... Amplitude and Phase spectra = when n = 1,2,3,4,5,..(graph) %3D O =...... The response Vo(t)=..when n= 1,2,3,4,5,... 2.
Specify the types of symmetry for the signals shown in Figure a,b,c,d. Specify also which terms in the trigonometric Fourier series are zero.
6) Find the Fourier transform of the figure given below. sin f T 7) The signal below is modulated signal with carrier Cos(10t). Find Fourier transform of this signal using Tables in the textbook, and sketch amplitude and phase spectra. T
Question 8 An even function decomposed in Fourier series has cosine components. True False
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)
Determine the Fourier series at least six non-zero terms for the following waveforms of the given figure. For your answer, substitute the value of ω in terms of numerical value πt
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?