I really appreciate it. please explain in detail. Thank you.
Homework Answers
a) fourier integral representation through formula solved
b)fourier cosine representation
c)fourier sine representation
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I really appreciate it. please explain in detail. Thank you.
a) f(t) = r|t| -1<t<1 t...
Problem 1. Expand f(x) em 1. Expand fo) (1.0 ,-π < x < 0 0, 0<X<T...
Problem 1. Expand f(x) em 1. Expand fo) (1.0 ,-π < x < 0 0, 0<X<T in a sine, cosine Fourier series. write out a few 0, 0<x<π in sine,cosine Fourier series Write out aferw terms of the series
0and / is an odd function of t, find the Fourier sine sin wt d for 0<t< 1 10, (a) If f(t) = for t a 0 transfor...
0and / is an odd function of t, find the Fourier sine sin wt d for 0<t< 1 10, (a) If f(t) = for t a 0 transform of f. Deduce thato s if0<t < a. What is the value of the integral for t2 a? for 0 < t < b (b) If g(t)-{ b-t and g is an even function of t, find the Fourier 0 cosine transform of g. Deduce that foo 1-w2bw cosa t dw =...
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
Please solve for part (b) and (c) thank you! 1. Consider the function f(x) = e-x...
Please solve for part (b) and
(c) thank you!
1. Consider the function f(x) = e-x defined on the interval 0 < x < 1. (a) Give an odd and an even extension of this function onto the interval -1 < x < 1. Your answer can be in the form of an expression, or as a clearly labelled graph. [2 marks] (b) Obtain the Fourier sine and cosine representation for the functions found above. Hint: use integration by parts....
A periodic signal f(t) is produced by periodically repeating the function alt) - S2t|t| for -1<t<1...
A periodic signal f(t) is produced by periodically repeating the function alt) - S2t|t| for -1<t<1 g(t) = to otherwise over the time domain-00<t<0. Determine the Fourier series representation of f(t) in the following forms. A. f(t) = a, + acos(nw,t) + b sin(nw,t); na1 B. f(0) = { Chelmuese n -00
1. Consider the unit circle: (x,y) : x2 y2 = 1. T. Let f R2 ->R...
1. Consider the unit circle: (x,y) : x2 y2 = 1. T. Let f R2 ->R be defined by f(x,y) = x2-y, and let F : R2 -> R be defined by F(x, y) Compute the integral of f and F around the unit circle. For the integral of F, proceed in the standard (anticlockwise) direction
4. Compute Fourier integral representation for f(x) = S\sinx[xST [x] > T = {leine $ "...
4. Compute Fourier integral representation for f(x) = S\sinx[xST [x] > T = {leine $ " cosas # 1 (cos") ds = TT and deduce that 2:
Hi, really appreciate someone can help with these 2 questions. Question 5 (a) Let f, g...
Hi, really appreciate someone can help with these 2
questions.
Question 5 (a) Let f, g : [a,bl->R be continuous functions, Suppose that f(a)g(a), and fb)>g(b) Use the properties of continuity of function to show that there is a c in (a, b) such that (6 marks) f(c) g(c) b alb - n+1 n+2 (b) Given a, b are real numbers, show that converges by considering the sequence of partial sums. What is the sum of the series?. (14 marks)
Find the Laplace transform of f(0) = 1, for 0 <t<1 5, for 1<t<2. e-l for...
Find the Laplace transform of f(0) = 1, for 0 <t<1 5, for 1<t<2. e-l for t > 2
Let f and g be differentiable on R such that f(1) = g(1), and f'(x) <...
Let f and g be differentiable on R such that f(1) = g(1), and f'(x) < '() for all r ER. Prove that f(x) = g(2) for 3 >1.
Problem 1. Expand f(x) em 1. Expand fo) (1.0 ,-π < x < 0 0, 0<X<T in a sine, cosine Fourier series. write out a few 0, 0<x<π in sine,cosine Fourier series Write out aferw terms of the series
0and / is an odd function of t, find the Fourier sine sin wt d for 0<t< 1 10, (a) If f(t) = for t a 0 transform of f. Deduce thato s if0<t < a. What is the value of the integral for t2 a? for 0 < t < b (b) If g(t)-{ b-t and g is an even function of t, find the Fourier 0 cosine transform of g. Deduce that foo 1-w2bw cosa t dw =...
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
Please solve for part (b) and
(c) thank you!
1. Consider the function f(x) = e-x defined on the interval 0 < x < 1. (a) Give an odd and an even extension of this function onto the interval -1 < x < 1. Your answer can be in the form of an expression, or as a clearly labelled graph. [2 marks] (b) Obtain the Fourier sine and cosine representation for the functions found above. Hint: use integration by parts....
A periodic signal f(t) is produced by periodically repeating the function alt) - S2t|t| for -1<t<1 g(t) = to otherwise over the time domain-00<t<0. Determine the Fourier series representation of f(t) in the following forms. A. f(t) = a, + acos(nw,t) + b sin(nw,t); na1 B. f(0) = { Chelmuese n -00
1. Consider the unit circle: (x,y) : x2 y2 = 1. T. Let f R2 ->R be defined by f(x,y) = x2-y, and let F : R2 -> R be defined by F(x, y) Compute the integral of f and F around the unit circle. For the integral of F, proceed in the standard (anticlockwise) direction
4. Compute Fourier integral representation for f(x) = S\sinx[xST [x] > T = {leine $ " cosas # 1 (cos") ds = TT and deduce that 2:
Hi, really appreciate someone can help with these 2
questions.
Question 5 (a) Let f, g : [a,bl->R be continuous functions, Suppose that f(a)g(a), and fb)>g(b) Use the properties of continuity of function to show that there is a c in (a, b) such that (6 marks) f(c) g(c) b alb - n+1 n+2 (b) Given a, b are real numbers, show that converges by considering the sequence of partial sums. What is the sum of the series?. (14 marks)
Find the Laplace transform of f(0) = 1, for 0 <t<1 5, for 1<t<2. e-l for t > 2
Let f and g be differentiable on R such that f(1) = g(1), and f'(x) < '() for all r ER. Prove that f(x) = g(2) for 3 >1.
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