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V(t) Question 5: (10) 2π For the voltage v() given in the picture: a. Is this function even or od...
Question Help 9.1.13 The values of a period 2π function f(t) in one full period are given. Sketch...
Question Help 9.1.13 The values of a period 2π function f(t) in one full period are given. Sketch several periods of its graph and find its Fourier series. f(t) = Sketch several periods of its graph. Choose the correct graph below A. frt) frt) f(U) -2x 2t -2 -2J 2x 2x Find its Fourier series. f(t) (Type a series using n as the index variable and 1 as the starting index, Type an exact answer, using π as needed. Use...
Consider the following problems related to the exponential Fourier series. (a) The exponential Fourier series of...
Consider the following problems related to the exponential Fourier series. (a) The exponential Fourier series of a periodic signal x(t) of funda- 4.7 mental period To is 3 i. Determine the value of the fundamental period To ii. What is the average or dc value of x(t)? iii. Is x(t) even, odd, or neither even nor odd function of time? iv. One of the frequency components of x(t) is expressed as Acos(ST) 0- What is A? (b) A train of...
Find the Fourier series representation of the function below. The voltage is in volts. v(t) 2T...
Find the Fourier series representation of the function below. The voltage is in volts. v(t) 2T 3T t
1. For the function (t) below, T 2 and Vm-100 V. vt) 3 2 012 3...
1. For the function (t) below, T 2 and Vm-100 V. vt) 3 2 012 3 (a) Sketch v'(t) and derive the Fourier coefficients for '(t). (b) Use your results from part (a) to determine for Fourier coefficients for v(t). Express your solution in the complex form of the Fourier series, nugt and verify your solution by plotting your results using Matlab. 2. Assume that the signal above is the input to the bandpass filter shown below. y (t (a)...
(a) Determine the period, amplitude, and frequency of a signal given by, v(t) (120nt). Plot this ...
(a) Determine the period, amplitude, and frequency of a signal given by, v(t) (120nt). Plot this signal both in the time-domain and frequency domain. (b) For the following square wave v(t), determine if it is a periodic signal, and if yes, what 10 V sin 4. [61 are its amplitude, period T and fundamental frequency f? Why do we need to convert this signal into sine/cosine wave for transmission? 2 o-oims (c) () According to Fourier Theorem, the above signal...
QUESTION 3 (a) If the Fourier transform of (t) is X(c) = 12 (a+2)j@+6) determine the...
QUESTION 3 (a) If the Fourier transform of (t) is X(c) = 12 (a+2)j@+6) determine the transform for (-21-1). [5 marks] (b) Based on Figure Q3(b), give the expression for signal xt) in unit step function. From your obtained expression, find the Fourier transform of x(). Then compare your answer using the formula of Fourier transform. x() 10 0 Figure Q3(b) [9 marks] 다. For the linear system in Figure Q3(e), when the input voltage is vr(t) = 2sgn(t) V....
2. complex numbers a voltage v(t) is given: v(t)=v1(t)+v2(t)=1 V sin( omega t -45) – 2...
2. complex numbers a voltage v(t) is given: v(t)=v1(t)+v2(t)=1 V sin( omega t -45) – 2 V cos(omega t-60) a)convert the voltages to phasors and sketch a phasor diagram of V1,V2 and V b)reduce the expression of v(t) to the form v(t)=Vm cos(omega*t + fi(its angle)) do u see normaly 3 exercise _? Problem 4. laplace transform of discontinuous function for the function illustrated a) sketch f'(t) b)find la place transform of f'(t)
6. The function 1-1 f(t) = {0 for – 2 <t < -1 for –1<t< 0...
6. The function 1-1 f(t) = {0 for – 2 <t < -1 for –1<t< 0 for t = 0 for 0 <t<1 for 1<t V VI can be extended to be periodic of period 4. (a) Is the extended function even, odd, or neither? (b) Find the Fourier Series of the extended function.(Just write the final solution.)
Question 2 The function u(x,t) is governed by the wave equation 82u 182u 8x2 c2 8t2 Subject to th...
Fourier Wave Equation
Question 2 The function u(x,t) is governed by the wave equation 82u 182u 8x2 c2 8t2 Subject to the following conditions having c2 3 i. At x 0 and x-1, u 0 for all t 2 0. i. Whent 0, for sx s 1 Use the method of separation of variables to establish that the solution for u(x, t). From the solution established, given a condition t0, usinx(1 + cosx) for 0 s x s1. Find the...
Problem 04: A voltage source is expressed by the following Fourier series: v(t) = -2 +...
Problem 04: A voltage source is expressed by the following Fourier series: v(t) = -2 + 5* sin(t) – 5*cos(t) – 3* sin(2*t) + 4*cos(2*t) – sin(3*t) – 6*cos(3*t) + 4*sin(4*t) + 6*cos(4*t). Now, (a) Express v(t) in amplitude-phase form. (b) Draw the amplitude and phase spectra of v(t) (c) Determine the effective value (rms value) of the voltage v(t) (d) If the voltage is applied across an impedance block as shown in the circuit below, determine the average power...
Question Help 9.1.13 The values of a period 2π function f(t) in one full period are given. Sketch several periods of its graph and find its Fourier series. f(t) = Sketch several periods of its graph. Choose the correct graph below A. frt) frt) f(U) -2x 2t -2 -2J 2x 2x Find its Fourier series. f(t) (Type a series using n as the index variable and 1 as the starting index, Type an exact answer, using π as needed. Use...
Consider the following problems related to the exponential Fourier series. (a) The exponential Fourier series of a periodic signal x(t) of funda- 4.7 mental period To is 3 i. Determine the value of the fundamental period To ii. What is the average or dc value of x(t)? iii. Is x(t) even, odd, or neither even nor odd function of time? iv. One of the frequency components of x(t) is expressed as Acos(ST) 0- What is A? (b) A train of...
Find the Fourier series representation of the function below. The voltage is in volts. v(t) 2T 3T t
1. For the function (t) below, T 2 and Vm-100 V. vt) 3 2 012 3 (a) Sketch v'(t) and derive the Fourier coefficients for '(t). (b) Use your results from part (a) to determine for Fourier coefficients for v(t). Express your solution in the complex form of the Fourier series, nugt and verify your solution by plotting your results using Matlab. 2. Assume that the signal above is the input to the bandpass filter shown below. y (t (a)...
(a) Determine the period, amplitude, and frequency of a signal given by, v(t) (120nt). Plot this signal both in the time-domain and frequency domain. (b) For the following square wave v(t), determine if it is a periodic signal, and if yes, what 10 V sin 4. [61 are its amplitude, period T and fundamental frequency f? Why do we need to convert this signal into sine/cosine wave for transmission? 2 o-oims (c) () According to Fourier Theorem, the above signal...
QUESTION 3 (a) If the Fourier transform of (t) is X(c) = 12 (a+2)j@+6) determine the transform for (-21-1). [5 marks] (b) Based on Figure Q3(b), give the expression for signal xt) in unit step function. From your obtained expression, find the Fourier transform of x(). Then compare your answer using the formula of Fourier transform. x() 10 0 Figure Q3(b) [9 marks] 다. For the linear system in Figure Q3(e), when the input voltage is vr(t) = 2sgn(t) V....
6. The function 1-1 f(t) = {0 for – 2 <t < -1 for –1<t< 0 for t = 0 for 0 <t<1 for 1<t V VI can be extended to be periodic of period 4. (a) Is the extended function even, odd, or neither? (b) Find the Fourier Series of the extended function.(Just write the final solution.)
Fourier Wave Equation
Question 2 The function u(x,t) is governed by the wave equation 82u 182u 8x2 c2 8t2 Subject to the following conditions having c2 3 i. At x 0 and x-1, u 0 for all t 2 0. i. Whent 0, for sx s 1 Use the method of separation of variables to establish that the solution for u(x, t). From the solution established, given a condition t0, usinx(1 + cosx) for 0 s x s1. Find the...
Problem 04: A voltage source is expressed by the following Fourier series: v(t) = -2 + 5* sin(t) – 5*cos(t) – 3* sin(2*t) + 4*cos(2*t) – sin(3*t) – 6*cos(3*t) + 4*sin(4*t) + 6*cos(4*t). Now, (a) Express v(t) in amplitude-phase form. (b) Draw the amplitude and phase spectra of v(t) (c) Determine the effective value (rms value) of the voltage v(t) (d) If the voltage is applied across an impedance block as shown in the circuit below, determine the average power...
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