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need help with second question, please include all
steps.
2. Consider a z-transform given by 22...
Please solve the following with full steps. 2. Given the following z-transform of the impulse response h [n], of a causal LTI system Ti H1 (z) = (,-1)(z-0.5) (a) Find hin (b) Verify the first three no...
Please solve the following
with full steps.
2. Given the following z-transform of the impulse response h [n], of a causal LTI system Ti H1 (z) = (,-1)(z-0.5) (a) Find hin (b) Verify the first three non-zero values of hi[n] using long division. (c) Find the z transform Hs(z) of hs[n]-2"hi[n], and specify the ROC. (d) Find thez transform H4() of han+n -1], and specify the ROC. e) Find the impulse response, hs[n], of the system Ts, which is the...
Im having trouble understanding 6(a) and 6(b) Question 6 Consider the second order non-constant coefficient differential...
Im having trouble understanding 6(a) and 6(b)
Question 6 Consider the second order non-constant coefficient differential equation y"- 2ryy= 0, (4) and a power series solution with the general form y()=C n-0 relationship for a,. 6(a) Find a recurrence solution 6(b) Find two linearly independent solutions of (4). Show that is a polynomial and obtain the first three non-zero terms in the series expansion of the other one
Question 6 Consider the second order non-constant coefficient differential equation y"- 2ryy=...
5. The z transform is a very useful tool for studying difference equations. Often difference and ...
5. The z transform is a very useful tool for studying difference equations. Often difference and differential equations are used to describe causal systems and only the causal solution is of interest. This is the "initial condition" problem of a differential equations course. But both difference and differential equations describe more than just the causal system. For instance, "backwards" solutions and "two point boundary value" solutions. One way in which to think about the problem is the ROC of the...
23. Consider the function w(z) = 2-2 (a) Where in the complex z-plane are the poles of w(z)? (b) ...
23. Consider the function w(z) = 2-2 (a) Where in the complex z-plane are the poles of w(z)? (b) Determine the first three terms for the Taylor series expansion of w(z) about 0 (c) Identify the region of convergence for the Taylor series of part (b). (d) Determine the general expression for the n'h coefficient of the Taylor series expansion of part (b) 208 INTRODUCTION TO COMPLEX VARIABLES (e) There is a Laurent series expansion for wC) about-= 0 in...
I just need 23, I have 21 and 22, but since it is a parts question...
I just need 23, I have 21 and 22, but since it is a parts
question this is context. Thank you!
Question 21 1 pts Recall the power series expansion 1 = 1 - x + x2 – 23 + ... on the interval (-1, 1). Use the given expansion to derive a power series expansion for 1772 Show at least 3 non-zero terms. • 1-x2 + x4 - x +... 0 - 1 + x2-x4 + x + ......
answer this question with steps: 3. In special relativity, the kinetic energy of a particle of...
answer this question with
steps:
3. In special relativity, the kinetic energy of a particle of mass m and velocity v is given byKE=yme-me, where γ = 1/ and c is the speed of light. (a) (2 points) Find the first three non-zero terms of the Taylor series expansion of γ, in the non-relativistic limit u/c 1. Hint: You can expand in either v/c orv/c2 (b) (1 point) What is the first non-zero term for the kinetic energy KE in...
Question 6 Consider the function defined over the interval 0<x<L. Extend f(x) as a function of...
Question 6 Consider the function defined over the interval 0<x<L. Extend f(x) as a function of period 2L by using an odd half-range expansion 1) Sketch the extended function over the interval -3L<XS3L. 2) Calculate the coefficients for the Fourier Series representation of the extended function. 3) Write the first 5 non-zero terms of the Fourier Series. (10 marks)
Consider the tollowing initial value problem, Note: For each part below you must give your answers in terms of fraction...
Consider the tollowing initial value problem, Note: For each part below you must give your answers in terms of fractions (as appropriate), not decimals (a) This diferential equation has singular points at Note: You must use a semicolon here to separate your answers (b) Since there is no singular point at -0, you can find a normal power series solution for y() about -0,ie y(z) = Σ amzm n-0 As part of the solution process you must determine the recurrence...
Consider the equation 3x²y" + x(2 – xy + xy = 0 with regular singular point...
Consider the equation 3x²y" + x(2 – xy + xy = 0 with regular singular point Xo = 0. (a) Find the indicial roots ri, r2, with ri r2. Show your calculations. (b) Which of the following is true for the equation above: Indicate the letter of your choice and explain your choice. % There are two linearly independent convergent series solutions of the form yı (x) = x Š cux" and y(x) = x Š b,x". H0 N=0 (1)...
(1 point) In this exercise we consider the second order linear equation y" + series solution...
(1 point) In this exercise we consider the second order linear equation y" + series solution in the form y = 0. This equation has an ordinary point at x = 0 and therefore has a power y = cmx". n=0 We learned how to easily solve problems like this in several different ways but here we want to consider the power series method. (1) Insert the formal power series into the differential equation and derive the recurrence relation Cn...
Please solve the following
with full steps.
2. Given the following z-transform of the impulse response h [n], of a causal LTI system Ti H1 (z) = (,-1)(z-0.5) (a) Find hin (b) Verify the first three non-zero values of hi[n] using long division. (c) Find the z transform Hs(z) of hs[n]-2"hi[n], and specify the ROC. (d) Find thez transform H4() of han+n -1], and specify the ROC. e) Find the impulse response, hs[n], of the system Ts, which is the...
Im having trouble understanding 6(a) and 6(b)
Question 6 Consider the second order non-constant coefficient differential equation y"- 2ryy= 0, (4) and a power series solution with the general form y()=C n-0 relationship for a,. 6(a) Find a recurrence solution 6(b) Find two linearly independent solutions of (4). Show that is a polynomial and obtain the first three non-zero terms in the series expansion of the other one
Question 6 Consider the second order non-constant coefficient differential equation y"- 2ryy=...
5. The z transform is a very useful tool for studying difference equations. Often difference and differential equations are used to describe causal systems and only the causal solution is of interest. This is the "initial condition" problem of a differential equations course. But both difference and differential equations describe more than just the causal system. For instance, "backwards" solutions and "two point boundary value" solutions. One way in which to think about the problem is the ROC of the...
23. Consider the function w(z) = 2-2 (a) Where in the complex z-plane are the poles of w(z)? (b) Determine the first three terms for the Taylor series expansion of w(z) about 0 (c) Identify the region of convergence for the Taylor series of part (b). (d) Determine the general expression for the n'h coefficient of the Taylor series expansion of part (b) 208 INTRODUCTION TO COMPLEX VARIABLES (e) There is a Laurent series expansion for wC) about-= 0 in...
I just need 23, I have 21 and 22, but since it is a parts
question this is context. Thank you!
Question 21 1 pts Recall the power series expansion 1 = 1 - x + x2 – 23 + ... on the interval (-1, 1). Use the given expansion to derive a power series expansion for 1772 Show at least 3 non-zero terms. • 1-x2 + x4 - x +... 0 - 1 + x2-x4 + x + ......
answer this question with
steps:
3. In special relativity, the kinetic energy of a particle of mass m and velocity v is given byKE=yme-me, where γ = 1/ and c is the speed of light. (a) (2 points) Find the first three non-zero terms of the Taylor series expansion of γ, in the non-relativistic limit u/c 1. Hint: You can expand in either v/c orv/c2 (b) (1 point) What is the first non-zero term for the kinetic energy KE in...
Question 6 Consider the function defined over the interval 0<x<L. Extend f(x) as a function of period 2L by using an odd half-range expansion 1) Sketch the extended function over the interval -3L<XS3L. 2) Calculate the coefficients for the Fourier Series representation of the extended function. 3) Write the first 5 non-zero terms of the Fourier Series. (10 marks)
Consider the tollowing initial value problem, Note: For each part below you must give your answers in terms of fractions (as appropriate), not decimals (a) This diferential equation has singular points at Note: You must use a semicolon here to separate your answers (b) Since there is no singular point at -0, you can find a normal power series solution for y() about -0,ie y(z) = Σ amzm n-0 As part of the solution process you must determine the recurrence...
Consider the equation 3x²y" + x(2 – xy + xy = 0 with regular singular point Xo = 0. (a) Find the indicial roots ri, r2, with ri r2. Show your calculations. (b) Which of the following is true for the equation above: Indicate the letter of your choice and explain your choice. % There are two linearly independent convergent series solutions of the form yı (x) = x Š cux" and y(x) = x Š b,x". H0 N=0 (1)...
(1 point) In this exercise we consider the second order linear equation y" + series solution in the form y = 0. This equation has an ordinary point at x = 0 and therefore has a power y = cmx". n=0 We learned how to easily solve problems like this in several different ways but here we want to consider the power series method. (1) Insert the formal power series into the differential equation and derive the recurrence relation Cn...
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