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![(b)If f is piecevise onl -L, L then Fourier series of fis ere a =- 2 2T 2 C0(s) [Γ.-rsin(m)dx +Γ.xsm(nx)d]](http://img.homeworklib.com/questions/d79575b0-b449-11ea-b79a-91a0aa7ba22e.png?x-oss-process=image/resize,w_560)
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(EOTIO -4 Soalan 3 (a) State w utakon sonst cach of the following function is odd,...
1. Cousider the followving periodic function a) Determine whether the following function is odd, even or...
1. Cousider the followving periodic function a) Determine whether the following function is odd, even or neither f(x) = sin 2x cos 3a. 2marks] Consider the following periodic function b) ㄫㄨ for -2 < x < 0 for 0< S 2 f(x) = { sin 0 f(x) = f(x + 4). i. Sketch the graph of the function over the interval-6< r <6. 2marks] Find the Fourier Series of f(x). (6marks ii.
Fourier Series for Odd Functions Recall that if f is an odd function, f(-x)f(x). An odd Fourier series has only the...
Fourier Series for Odd Functions Recall that if f is an odd function, f(-x)f(x). An odd Fourier series has only the sine terms, and can be approximate an odd function, so Fo(x) b sinx)+b2 sin(2x)+ b, sin(3x)+. Why is there no b, term in the series F, (x)? 1. 2. Using steps similar to those outlined for even functions, develop a rule for finding the coefficients to approximate any odd function on the interval [-π, π]. 3. If f (x)sin...
Question 3 Soalan 31 (a) Using appropriate illustrations, explain basic concept and development of signal using...
Question 3 Soalan 31 (a) Using appropriate illustrations, explain basic concept and development of signal using Fourier series. Dengan menggunakan illustrasi-ilustrasi yang sesuai, terangkan konsep dan pembangunan asas isyarat menggunakan sivi Fourier (4 Marks/ Markah) (b) Given: Diberikan:) x(0) = 2 + cos (7)e+ tsineze Identify the fundamental radian frequency, w, and the Fourier series coefficients (X[k]). Kenalpasti frekuensi radian asas, w dan pekali-pekali siri Fourier (X[k]. (6 Marks/ Markah) (c) A square wave function is shown in Figure 4....
[EUM 114 1. Let f(x) be a function of period 2 (a) over the interval 0<x<2 such that f(x) = - f(x)pada selan...
[EUM 114 1. Let f(x) be a function of period 2 (a) over the interval 0<x<2 such that f(x) = - f(x)pada selang Diberikan f(x) sebagai fungsi dengan tempoh 2t yang mana 0<x<2m Sketch a graph of f (x) in the interval of 0 <x< 4 (1 marks/markah) Demonstrate that the Fourier Series for f(x) in the interval 0<x< 2n is (ii) 1 2x+-sin 3x + 1 sin x + (6 marks/markah) Determine the half range cosine Fourier series expansion...
1. Determine whether the function f(x) = (x2 - 1) sin 5x is even, odd, or...
1. Determine whether the function f(x) = (x2 - 1) sin 5x is even, odd, or neither. A. Even B. Odd C. Neither 2. a). Find the Fourier sine series of the function f(x) shown below. b). Sketch the extended function f(x) that includes its two periodic extensions. TT/2 TT Formula to use: The sine series is f(x) = 6 sin NIT P where b. - EL " (x) sin " xd
(a) Determine algebraically whether the functions below are even, odd or neither. i. r+6 f(x)=- r-r?...
(a) Determine algebraically whether the functions below are even, odd or neither. i. r+6 f(x)=- r-r? (2 marks) ii. f(x) = 2x sinx (2 marks) (b) A periodic function is defined by: f(x) = 4-x?, -25x52, f(x+4)= f(x) i. Sketch the graph of the function over -10<x<10. (4 marks) ii. Based on result in (i), identify whether the function is even or odd. Give your reason. (2 marks) ii. Calculate the Fourier series expansion of f(x). (12 marks) (c) An...
Consider the periodic function defined by 1<t0, 0<t<1, f(t)= f(t+2) f(), and its Fourier series F(t): Σ A,...
Consider the periodic function defined by 1<t0, 0<t<1, f(t)= f(t+2) f(), and its Fourier series F(t): Σ A, cos(nmi) +ΣB, sin (nπί), F(t)= Ao+ n1 n=1 (a) Sketch the function f(t) the function is even, odd or neither even nor odd. over the range -3<t< 3 and hence state whether (b) Calculate the constant term Ao
Consider the periodic function defined by 1
A periodic function y lxl for-r ? is shown below. x -? (1) Is this function...
A periodic function y lxl for-r ? is shown below. x -? (1) Is this function even or odd or neither? (2) Calculate the Fourier series coefficients. Hint: Use integration by parts. . + ?4, cos(nox) + bn sin(nox) 2 ] ,f (x)- 21 where a,-J()cos(noxi, )innoxy
2) (3 points; J2) The function below is even, odd, or nelther even nor odd. Select...
2) (3 points; J2) The function below is even, odd, or nelther even nor odd. Select the statement below which best describes which it is and how you know. f(x) = 5 x6 - x2 + 8 A) This function is even because f(-x) = f(x). B) This function is odd because f(-x) = -f(x). C) This function is even because f(-x) = -f(x). D) This function is odd because f(-x) = f(x). E) This function is neither even nor...
[4 Mar (c) Consider the following periodic function, defined as: fO) = 7? - ?, -...
[4 Mar (c) Consider the following periodic function, defined as: fO) = 7? - ?, - <t<T and f(t) = f(t + 27) (0 ) State the period, P. [1 Marks) ( 11) Sketch a graph of f(t). [2 marks] State if f(t) is either even or odd, or neither. (1 Marks) (iv) Which Fourier coefficients are zero and why? [1 Marks) (v) Compute do [2 marks] (vi) Compute the non-zero Fourier coefficients. [5 Marks) (vii) Write down the Fourier...
1. Cousider the followving periodic function a) Determine whether the following function is odd, even or neither f(x) = sin 2x cos 3a. 2marks] Consider the following periodic function b) ㄫㄨ for -2 < x < 0 for 0< S 2 f(x) = { sin 0 f(x) = f(x + 4). i. Sketch the graph of the function over the interval-6< r <6. 2marks] Find the Fourier Series of f(x). (6marks ii.
Fourier Series for Odd Functions Recall that if f is an odd function, f(-x)f(x). An odd Fourier series has only the sine terms, and can be approximate an odd function, so Fo(x) b sinx)+b2 sin(2x)+ b, sin(3x)+. Why is there no b, term in the series F, (x)? 1. 2. Using steps similar to those outlined for even functions, develop a rule for finding the coefficients to approximate any odd function on the interval [-π, π]. 3. If f (x)sin...
Question 3 Soalan 31 (a) Using appropriate illustrations, explain basic concept and development of signal using Fourier series. Dengan menggunakan illustrasi-ilustrasi yang sesuai, terangkan konsep dan pembangunan asas isyarat menggunakan sivi Fourier (4 Marks/ Markah) (b) Given: Diberikan:) x(0) = 2 + cos (7)e+ tsineze Identify the fundamental radian frequency, w, and the Fourier series coefficients (X[k]). Kenalpasti frekuensi radian asas, w dan pekali-pekali siri Fourier (X[k]. (6 Marks/ Markah) (c) A square wave function is shown in Figure 4....
[EUM 114 1. Let f(x) be a function of period 2 (a) over the interval 0<x<2 such that f(x) = - f(x)pada selang Diberikan f(x) sebagai fungsi dengan tempoh 2t yang mana 0<x<2m Sketch a graph of f (x) in the interval of 0 <x< 4 (1 marks/markah) Demonstrate that the Fourier Series for f(x) in the interval 0<x< 2n is (ii) 1 2x+-sin 3x + 1 sin x + (6 marks/markah) Determine the half range cosine Fourier series expansion...
1. Determine whether the function f(x) = (x2 - 1) sin 5x is even, odd, or neither. A. Even B. Odd C. Neither 2. a). Find the Fourier sine series of the function f(x) shown below. b). Sketch the extended function f(x) that includes its two periodic extensions. TT/2 TT Formula to use: The sine series is f(x) = 6 sin NIT P where b. - EL " (x) sin " xd
(a) Determine algebraically whether the functions below are even, odd or neither. i. r+6 f(x)=- r-r? (2 marks) ii. f(x) = 2x sinx (2 marks) (b) A periodic function is defined by: f(x) = 4-x?, -25x52, f(x+4)= f(x) i. Sketch the graph of the function over -10<x<10. (4 marks) ii. Based on result in (i), identify whether the function is even or odd. Give your reason. (2 marks) ii. Calculate the Fourier series expansion of f(x). (12 marks) (c) An...
Consider the periodic function defined by 1<t0, 0<t<1, f(t)= f(t+2) f(), and its Fourier series F(t): Σ A, cos(nmi) +ΣB, sin (nπί), F(t)= Ao+ n1 n=1 (a) Sketch the function f(t) the function is even, odd or neither even nor odd. over the range -3<t< 3 and hence state whether (b) Calculate the constant term Ao
Consider the periodic function defined by 1
A periodic function y lxl for-r ? is shown below. x -? (1) Is this function even or odd or neither? (2) Calculate the Fourier series coefficients. Hint: Use integration by parts. . + ?4, cos(nox) + bn sin(nox) 2 ] ,f (x)- 21 where a,-J()cos(noxi, )innoxy
2) (3 points; J2) The function below is even, odd, or nelther even nor odd. Select the statement below which best describes which it is and how you know. f(x) = 5 x6 - x2 + 8 A) This function is even because f(-x) = f(x). B) This function is odd because f(-x) = -f(x). C) This function is even because f(-x) = -f(x). D) This function is odd because f(-x) = f(x). E) This function is neither even nor...
[4 Mar (c) Consider the following periodic function, defined as: fO) = 7? - ?, - <t<T and f(t) = f(t + 27) (0 ) State the period, P. [1 Marks) ( 11) Sketch a graph of f(t). [2 marks] State if f(t) is either even or odd, or neither. (1 Marks) (iv) Which Fourier coefficients are zero and why? [1 Marks) (v) Compute do [2 marks] (vi) Compute the non-zero Fourier coefficients. [5 Marks) (vii) Write down the Fourier...
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