o
What is the coefficient of the 6th harmonic for periodic signal x(t) with period To =...
SIGNAL: 1. Find the THD of the signal including the 6th harmonic. 2. Find the RMS of the signal using Fourier series expansion including to the 6th harmonic. 3. Comparing the RMS including the 6th harmonic to the RMS including the 5th harmonic, what is: Sin 2 Stわ Sin 2 Stわ
Q4. For each signal, if it is periodic, find the fundamental period T. (in seconds) and the fundamental frequency (in rad/s). Otherwise prove that the signal is not periodic. [1 + 1 - 2 marks) a) X(t) = cos(5t) + sin(25t) b)x() = sin 91 + + sin(61 - 7) + cos(391)
4. Given that x(t) has the Fourier transform X(a), p(t) is a periodic signal with frequency of ??. p(t)-??--o nejnaot, where Cn is the Fourier series coefficient of p) (1) Assume y(t)-x(t)p(t), determine Y(?), the Fourier transform of the modulated signal y(t) in terms of X(). (2) Given the spectrum sketch of x(?) shown below, p(t)-cos(2t) cos(t), determine and sketch the Y() X(w) -1
3. For the periodic signal shown below, find the period T and compute the main harmonics. For our purposes, “main” means having at least 2% of the amplitude of the fundamental harmonic. Use MATLAB to plot the signal for two periods. Also plot approximations to the signal using finitely many harmonics.. For the periodic signal shown below, find the period T and compute the main harmonics. For our purposes, "main" means having at least 2% of the amplitude of the...
The Signal x(t)= e^(j*(3pi/2)*t)*cos((5pi/2)*t)+j*sin(pi*t) i) show that x(t) is periodic and what is the fundamental period? ii) What is the average value and power of x(t)?
11. Giving the following periodic signal of period T-4, (answer by inspection) x(t) 2 6 -1 a. Its average value is ao 0 b. It is an even signal. c. The trigonometric FS coefficient an 0 d. The trigonometric FS coefficient b,-0. e. Choices a, and c are true. f. Choices a, and d are true. g. None of the above. Show transcribed image text
3. Consider the periodic signal x(t) = 0 otherwise (a) Plot r(t). (b) What is the period T of x(t)? (c) Find the CTFS coefficients ak for (t). 3. Consider the periodic signal x(t) = 0 otherwise (a) Plot r(t). (b) What is the period T of x(t)? (c) Find the CTFS coefficients ak for (t).
Given a real periodic signal X(t), if its combined trigonometric form is given as follow, what are the average value of the signal x(t) and Fourier Coefficients Cx, respectively? 8 x(t) = 2 + cos (kwyt +30°) kn 2 and 2 and 8 O and O and 8
Problem 4: A signal x(t) is given mathematically as follows: x(t) = 4.5+ 3.8cos(27 74t - 31/11) - 2 cos(21 296t+1/3) 4.1. Sketch the spectrum of the signal. Is x(t) periodic? If so, what is its fundamental frequency and what are the signal harmonics? Write down the number of each harmonic (0, 1, 2, ... etc) and the frequency of each harmonic. Verify in MATLAB 4.2. A new signal z(t) is created by adding a sinusoidal signal y(t) to x(t)....
Signal system 8. Consider the periodic signal x(t) = cos(2nt) + cos(2nt) I. a. Find the Fourier series coefficients for this signal. (4 points). b. If this signal passes through a LTI system with the impulse response h(t)=e* u(t), particularly, would the output signal also be a periodic signal ? If so, what would be the Fourier coefficients of the output signal ? (4 points). c. Give the mathematical expression for the output signal y(t). (2 points).