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DUHAMEL INTEGRAL / CONVOLUTION INTEGRAL to solve. DO NOT USE
FOURIER SERIES.
Problem 4- Consider...
Green's function 2 The Green function (10 P) The Fourier transform plays a tantamount role in the theory of inhomog...
Green's function
2 The Green function (10 P) The Fourier transform plays a tantamount role in the theory of inhomogeneous, linear differential equations. If as was shown in the lecture - G is a so called fundamental solution of the differential equation CG(z,z') = δ(z-z') one may calculate a particular solution for an inhomogeneity g by convolution G is called Green function. Since the Fourier transform maps derivatives to multiplications, it simplifies the calcu- lation of the Green function to...
Question 4. Calculate the Fourier sine series and the Fourier cosine series of the function f(x)...
Question 4. Calculate the Fourier sine series and the Fourier cosine series of the function f(x) = sin(x) on the interval [0, 1]. Hint: For the cosine series, it is easiest to use the complex exponential version of Fourier series. Question 5. Solve the following boundary value problem: Ut – 3Uzx = 0, u(0,t) = u(2,t) = 0, u(x,0) = –2? + 22 Question 6. Solve the following boundary value problem: Ut – Uxx = 0, Uz(-7,t) = uz (77,t)...
Use MATLAB to solve this question: Lab Exercises: Fourier Series Coefficients 4 In this lab, the...
Use MATLAB to solve this question: Lab Exercises: Fourier Series Coefficients 4 In this lab, the objective is to create a set of functions that will enable us to do the following 1. Evaluate the Fourier Series coefficients for the following periodic signal which is defined over one period to be rt)240sin (100nt) for 0ts 1/100 (6) The period is 1/100 seconds. This signal is called a full-wave rectified sinusoid, because it contains only the positive lobe of the sinusoidal...
4. Consider the periodic function 0, -1<t<- f(t) cos(#(t + 1)), } <t< 0 cos(at), 0<t<...
4. Consider the periodic function 0, -1<t<- f(t) cos(#(t + 1)), } <t< 0 cos(at), 0<t< 0, }<t<i with f(t) = f(t+2). (a) Determine a general expression for the Fourier series of f. (b) Use MATLAB to plot both f and the sum of the first 5 non-zero terms of the Fourier series for f on the same set of axes for -1<t<3.
In the remaining exercises use multiple Fourier series to solve the BVP (double series except in ...
In the remaining exercises use multiple Fourier series to solve the BVP (double series except in the last exercise where you can use triple Fourier series). Exercise 13. Uz(0, y, t) ux(2, y, t) = 0, a(z, 0, t) = u(x, 1, t) = 0, u(z, y, 0) = 100 0 < y < 1, t > 0 0 < x < 2, t > 0 0<x<2, 0<p<1.
In the remaining exercises use multiple Fourier series to solve the BVP...
Consider the Fourier Series for the periodic function: x(t) = 4+ 4 cos(5t)+ 6 sin (10t)...
Consider the Fourier Series for the periodic function: x(t) = 4+ 4 cos(5t)+ 6 sin (10t) a.) Find the Fourier coefficients of the exponential form. b.) Find the Fourier Coefficients of the combined trigonometric form. c.) Sketch the one-sided power spectral density
Problem 3: Find the Fourier series expansion for x(t)- | cos(Ttt/2) Problem 4: Determine the Fourier...
Problem 3: Find the Fourier series expansion for x(t)- | cos(Ttt/2) Problem 4: Determine the Fourier transform of the signal x(t) shown below which consists of three rectangular pulses. (Note: this is not a periodic function.) x(t) TI Sayfa Sonu Problem 5: Use the duality property of Fourier transform to find the Fourier transform of x(t) - sinc(Wt)
please help solve HW #2 EE 3200 Convolution and Fourier series Problem #1) Evaluate the following...
please help solve
HW #2 EE 3200 Convolution and Fourier series Problem #1) Evaluate the following convolutions: a) x/t-4)*8(1-4)* 8(+3)* 8(1-6) b) X(4-7)*1/2[8(8-20)+ 8(f+20) e) NE * 12 1² 2 -2 * D tof 10 Problem #2) The following spectra for C, are given. The first nonzero Cis Cil a) Find for all harmonics (for example Co-2, C,? Etc, note: C.-C.C) b) From magnitude spectrum, find fundamental frequency, fo, period, fax, and.BW Find total power carried by signal. IC, of=nfo...
Solution required in MATLAB 1. Convolution and Discrete-Time Fourier Series (DTFS) (a) Generate a periodic signal r2[n]...
Solution required in MATLAB
1. Convolution and Discrete-Time Fourier Series (DTFS) (a) Generate a periodic signal r2[n] with the fundamental period N ralla-sin(2nn/ İ0) + sin(2m, 2 ) + sin(2nn/30) for 0 < n < N-1 Find the fundamental frequency Ω0-2, N, with the fundamental period N. (b) Generate a periodic signal h2[n] with the fundamental period N haln] = (1/2)", for 0 < n < N-1 (e) Using the com ftuction n Matab, compute the compvolution (d) Using the...
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...
Green's function
2 The Green function (10 P) The Fourier transform plays a tantamount role in the theory of inhomogeneous, linear differential equations. If as was shown in the lecture - G is a so called fundamental solution of the differential equation CG(z,z') = δ(z-z') one may calculate a particular solution for an inhomogeneity g by convolution G is called Green function. Since the Fourier transform maps derivatives to multiplications, it simplifies the calcu- lation of the Green function to...
Question 4. Calculate the Fourier sine series and the Fourier cosine series of the function f(x) = sin(x) on the interval [0, 1]. Hint: For the cosine series, it is easiest to use the complex exponential version of Fourier series. Question 5. Solve the following boundary value problem: Ut – 3Uzx = 0, u(0,t) = u(2,t) = 0, u(x,0) = –2? + 22 Question 6. Solve the following boundary value problem: Ut – Uxx = 0, Uz(-7,t) = uz (77,t)...
Use MATLAB to solve this question: Lab Exercises: Fourier Series Coefficients 4 In this lab, the objective is to create a set of functions that will enable us to do the following 1. Evaluate the Fourier Series coefficients for the following periodic signal which is defined over one period to be rt)240sin (100nt) for 0ts 1/100 (6) The period is 1/100 seconds. This signal is called a full-wave rectified sinusoid, because it contains only the positive lobe of the sinusoidal...
4. Consider the periodic function 0, -1<t<- f(t) cos(#(t + 1)), } <t< 0 cos(at), 0<t< 0, }<t<i with f(t) = f(t+2). (a) Determine a general expression for the Fourier series of f. (b) Use MATLAB to plot both f and the sum of the first 5 non-zero terms of the Fourier series for f on the same set of axes for -1<t<3.
In the remaining exercises use multiple Fourier series to solve the BVP (double series except in the last exercise where you can use triple Fourier series). Exercise 13. Uz(0, y, t) ux(2, y, t) = 0, a(z, 0, t) = u(x, 1, t) = 0, u(z, y, 0) = 100 0 < y < 1, t > 0 0 < x < 2, t > 0 0<x<2, 0<p<1.
In the remaining exercises use multiple Fourier series to solve the BVP...
Problem 3: Find the Fourier series expansion for x(t)- | cos(Ttt/2) Problem 4: Determine the Fourier transform of the signal x(t) shown below which consists of three rectangular pulses. (Note: this is not a periodic function.) x(t) TI Sayfa Sonu Problem 5: Use the duality property of Fourier transform to find the Fourier transform of x(t) - sinc(Wt)
please help solve
HW #2 EE 3200 Convolution and Fourier series Problem #1) Evaluate the following convolutions: a) x/t-4)*8(1-4)* 8(+3)* 8(1-6) b) X(4-7)*1/2[8(8-20)+ 8(f+20) e) NE * 12 1² 2 -2 * D tof 10 Problem #2) The following spectra for C, are given. The first nonzero Cis Cil a) Find for all harmonics (for example Co-2, C,? Etc, note: C.-C.C) b) From magnitude spectrum, find fundamental frequency, fo, period, fax, and.BW Find total power carried by signal. IC, of=nfo...
Solution required in MATLAB
1. Convolution and Discrete-Time Fourier Series (DTFS) (a) Generate a periodic signal r2[n] with the fundamental period N ralla-sin(2nn/ İ0) + sin(2m, 2 ) + sin(2nn/30) for 0 < n < N-1 Find the fundamental frequency Ω0-2, N, with the fundamental period N. (b) Generate a periodic signal h2[n] with the fundamental period N haln] = (1/2)", for 0 < n < N-1 (e) Using the com ftuction n Matab, compute the compvolution (d) Using the...
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...
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