Homework Answers
![冫400). 뉴],郭她ゃ网 n TT n仄 even enpann](http://img.homeworklib.com/images/8a5fcaaa-7e49-42fb-8728-eb1d6f8c96b7.png?x-oss-process=image/resize,w_560)
Add Answer to:
Problem 4 (Half-Range Expansions) Compute both the even and odd half-range expansions of the foll...
Problem 6: Find the cosine series for the symmetric (even) extension (or "cosine half-range expansion") f...
Problem 6: Find the cosine series for the symmetric (even) extension (or "cosine half-range expansion") f (t) of the function g(t) by using the complex Fourier series and the method of jumps f(t) = g(t) = sin t , g(-t) =-sin t , 0<t<π [Vol.III-Ch.1, 6 -r < t < 0
1. If fand g are both even functions, is the product fg even? If f and...
1. If fand g are both even functions, is the product fg even? If f and g both odd functions, is fg odd? What if f is even and g is odd? Justify your answers. (10 points) Find the domain g(x) =-. (10 points) 2. of the composited function fog, where f(x)=x+ and x +1 x+2 3. Let ifx <1 g(x) = x-3 ifx >2 Evaluate each of the following, if it exists. (10 points) lim g(x) lim gx)(i) lim...
You are given a finite step function xt=-1 0<t<4 1 4<t<8. Hand calculate the FS coefficients of...
You are given a finite step function xt=-1 0<t<4 1 4<t<8. Hand calculate the FS coefficients of x(t) by assuming half- range expansion, for each case below. Modify the code below to approximate x(t) by cosine series only (This is even-half range expansion). Modify the below code and plot the approximation showing its steps changing by included number of FS terms in the approximation. Modify the code below to approximate x(t) by sine series only (This is odd-half range expansion).. Modify...
3) (Symmetries and Fourier Coefficients) Compute the Fourier Series Coefficients a, b and XTk] for the following periodic repeating signals. Where appropriate, simplify the results for odd or even va...
3) (Symmetries and Fourier Coefficients) Compute the Fourier Series Coefficients a, b and XTk] for the following periodic repeating signals. Where appropriate, simplify the results for odd or even values of k. Note: You can not use the half-wave symmetry integrals if the half-wave symmetry is "hidden" (i.e. if there is a DC offset).] xft) Signal i x(t) Signal5 x(t) Signal 4 aeP O80 0.5 -1 4 8 I 2 4
3) (Symmetries and Fourier Coefficients) Compute the Fourier Series...
(a) The heat flux through the faces at the ends of bar is found to be...
(a) The heat flux through the faces at the ends of bar is found to be proportional to un au/an at the ends. If the bar is perfectly insulated, also at the ends x 0 and x L are adiabatic conditions, Q1 ux(0, t) = 0 0 (2'7)*n prove that the solution of the heat transfer problem above (adiabatic conditions at both ends) gives as, 2 an: nnx u(x, t) Ao t An cos n-1 where Ao and An are...
3. This is an exercise about convolution. Consider the signals f and g below, both periodic with ...
3. This is an exercise about convolution. Consider the signals f and g below, both periodic with T -2. t sin(2t), -1-t 〈 0; (1+1), It _ 0.51, 一1 〈 t 〈 0; 0
Sketch the graph of f and then sketch the graphs of the even and odd extensions of f of period
Let$$ f(x)= \begin{cases}x, & 0 \leqslant x<2 \\ 1, & 2 \leqslant x<3\end{cases} $$Sketch the graph of f and then sketch the graphs of the even and odd extensions of f of period T = 2L = 6. You may do this all on the same set of axes if you can clearly indicate the different graphs (for example, use different colors).
How to do 5.2, now that we know from 5.1 that the function is odd? Problem...
How to do 5.2, now that we know from 5.1 that the function is
odd?
Problem 5. Consider the function f(t) = 47, IE(- 5) 5.1. (3%) The function f is: (a) odd, (B) even. 5.2. (7%) We extend the function f(3) = 42, IE(-5,5) periodically. Then ts Fourier Series is: (-1)+1 - sin(2nr), ( 4-1)+1 - sin(2nx), πη 12 (1)• (-1)"#* sin(2n2), ($ ^(-1) = 1) sin(m2).
k for 2 5. Consider the function f(x) = 37T 0 for 2 Hint: See examples...
k for 2 5. Consider the function f(x) = 37T 0 for 2 Hint: See examples of functions of a generic period t; James, 4th ed. pg. 581, Ex. 7.7 & 7.8 (a) State wether it has even or odd symmetry (b) Find the Fourier series representation for f. Plot graphs of the first three partial sums SI (c) Using the result in part (b), show that 1 + 1 +.. 7 4
k for 2 5. Consider the function...
Given, f(x) = {x +1,25x<4 4,0<x<2 (a) Sketch the graph of f(x) and its even half-range...
Given, f(x) = {x +1,25x<4 4,0<x<2 (a) Sketch the graph of f(x) and its even half-range expansion. Then sketch THREE (3) full periods of the periodic function in the interval – 12 < x < 12. (6 marks) (b) Determine the Fourier cosine coefficients of Ql(a). (10 marks) (c) Write out f(x) in terms of Fourier coefficients you have found in Q1(b). (4 marks)
Problem 6: Find the cosine series for the symmetric (even) extension (or "cosine half-range expansion") f (t) of the function g(t) by using the complex Fourier series and the method of jumps f(t) = g(t) = sin t , g(-t) =-sin t , 0<t<π [Vol.III-Ch.1, 6 -r < t < 0
1. If fand g are both even functions, is the product fg even? If f and g both odd functions, is fg odd? What if f is even and g is odd? Justify your answers. (10 points) Find the domain g(x) =-. (10 points) 2. of the composited function fog, where f(x)=x+ and x +1 x+2 3. Let ifx <1 g(x) = x-3 ifx >2 Evaluate each of the following, if it exists. (10 points) lim g(x) lim gx)(i) lim...
3) (Symmetries and Fourier Coefficients) Compute the Fourier Series Coefficients a, b and XTk] for the following periodic repeating signals. Where appropriate, simplify the results for odd or even values of k. Note: You can not use the half-wave symmetry integrals if the half-wave symmetry is "hidden" (i.e. if there is a DC offset).] xft) Signal i x(t) Signal5 x(t) Signal 4 aeP O80 0.5 -1 4 8 I 2 4
3) (Symmetries and Fourier Coefficients) Compute the Fourier Series...
(a) The heat flux through the faces at the ends of bar is found to be proportional to un au/an at the ends. If the bar is perfectly insulated, also at the ends x 0 and x L are adiabatic conditions, Q1 ux(0, t) = 0 0 (2'7)*n prove that the solution of the heat transfer problem above (adiabatic conditions at both ends) gives as, 2 an: nnx u(x, t) Ao t An cos n-1 where Ao and An are...
3. This is an exercise about convolution. Consider the signals f and g below, both periodic with T -2. t sin(2t), -1-t 〈 0; (1+1), It _ 0.51, 一1 〈 t 〈 0; 0
How to do 5.2, now that we know from 5.1 that the function is
odd?
Problem 5. Consider the function f(t) = 47, IE(- 5) 5.1. (3%) The function f is: (a) odd, (B) even. 5.2. (7%) We extend the function f(3) = 42, IE(-5,5) periodically. Then ts Fourier Series is: (-1)+1 - sin(2nr), ( 4-1)+1 - sin(2nx), πη 12 (1)• (-1)"#* sin(2n2), ($ ^(-1) = 1) sin(m2).
k for 2 5. Consider the function f(x) = 37T 0 for 2 Hint: See examples of functions of a generic period t; James, 4th ed. pg. 581, Ex. 7.7 & 7.8 (a) State wether it has even or odd symmetry (b) Find the Fourier series representation for f. Plot graphs of the first three partial sums SI (c) Using the result in part (b), show that 1 + 1 +.. 7 4
k for 2 5. Consider the function...
Given, f(x) = {x +1,25x<4 4,0<x<2 (a) Sketch the graph of f(x) and its even half-range expansion. Then sketch THREE (3) full periods of the periodic function in the interval – 12 < x < 12. (6 marks) (b) Determine the Fourier cosine coefficients of Ql(a). (10 marks) (c) Write out f(x) in terms of Fourier coefficients you have found in Q1(b). (4 marks)
Most questions answered within 3 hours.
-
2. Binomial Distribution Suppose I have an unfair coin, it lands
on heads 75% of the...
asked 4 minutes ago -
negotiators with absolutely no alternative to a negotiated
agreement sometimes.
a. become hostile and end the...
asked 2 minutes ago -
Write a Verilog program that tests whether a 4-bit input
variable is a Fibonacci number or...
asked 12 minutes ago -
MYSQL
Consider the sql statement "select * from t1 UNION t2" where t1
and t2 are...
asked 15 minutes ago -
2. A retailer sells 10,000 units at $10. Each unit costs the
retailer $7.00 to sell,...
asked 17 minutes ago -
If the Stratosphere elevator in Las Vegas is 500 m above the
ground when the cables...
asked 30 minutes ago -
identify at least one other characteristics of the soils/sand
that may have impacted the growth of...
asked 36 minutes ago -
True or False
The following statements refer to The Web of Belief
10. An explanation of...
asked 38 minutes ago -
15)___________ A study was conducted to
test the effectiveness of aspirin on reducing
asked 45 minutes ago -
How fast must a centrifuge spin if a particle 8 cm from the axis
of rotation...
asked 46 minutes ago -
Which of the following is characteristic of a single exposure
common vehicle outbreak?
a. Wide range...
asked 49 minutes ago -
You are a member of an alpine rescue team and must get a box of
supplies,...
asked 51 minutes ago