3. Consider the periodic function defined by -ae sin(x) 0 x < 7T f(x) and f(x)...
3. Consider the periodic function defined by f(x) =sin(r) 0 x<T 0 and f(x) f(x+27) (a) Sketch f(x) on the interval -3T < 3T (b) Find the complex Fourier series of f(r) and obtain from it the regular Fourier series.
3. Consider the periodic function defined by f(x) =sin(r) 0 x
3. Consider the periodic function defined by sin(x f(x)-く 0T and f(x)-f(x + 27). 1 (a) Sketch f(x) on the interval-3π 〈 3T. 9 (b) Find the complex Fourier series of f(x) and obtain from it the regular Fourier series.
3. Consider the periodic function defined by sin(x f(x)-く 0T and f(x)-f(x + 27). 1 (a) Sketch f(x) on the interval-3π 〈 3T. 9 (b) Find the complex Fourier series of f(x) and obtain from it the regular Fourier series.
Please show all steps with clear hand writing
3. Consider the periodic function defined by sin(x) 0<x< f(r) = and f(x) = f(x + 27). (a) Sketch f(x) on the interval-3r < r 〈 3T. etch fx on the interva (b) Find the complex Fourier series of f(x) and obtain from it the regular Fourier series.
3. Consider the periodic function defined by sin(x) 0
1. Consider the function defined by 1- x2, 0< |x| < 1, f(x) 0, and f(r) f(x+4) (a) Sketch the graph of f(x) on the interval -6, 6] (b) Find the Fourier series representation of f(x). You must show how to evaluate any integrals that are needed 2. Consider the function 0 T/2, T/2, T/2 < T. f(x)= (a) Sketch the odd and even periodic extension of f(x) for -3r < x < 3m. (b) Find the Fourier cosine series...
Consider f(x), a 27 periodic function defined by: f(x) = 1o, 1 if if -T <I< 0 0 < < Calculate the DC component of the Fourier series of f(x):
Consider a periodic function f(x) given as -7, f(x) = { - < x < 0, 0 < x <, TT – I, f(x) = f(x + 27). i) Sketch the graph of f(x) in the interval –37 < x < 37. Then, deter- mine whether f(x) is even, odd or neither. (3 marks) ii) Hence, find the Fourier series of f(x). (12 marks)
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)
There are 3 questions on this assignment. The marks awarded for each part are indi- cated in boxes. 1. Consider the function defined by f(x) = 0 and f(x)-f(x +4) 1 (a) Sketch the graph of f(x) on the interval -6,6 (b) Find the Fourier series representation of f(z). You must show how to evaluate any integrals that are needed 2. Consider the function f(x) (a) Sketch the odd and even periodic extension of f(x) for-3< x < 3m (b)...
3. Consider the function defined by f(x) = 1, 0 < r< a, | 0, a< x < T, where 0a < T (a) Sketch the odd and even periodic extension of f (x) on the interval -3n < x < 3« for aT/2 (b) Find the half-range Fourier sine series expansion of f(x) for arbitrary a. (e) To what value does the half-range Fourier sine series expansion converge at r a? [8 marks
3. Consider the function defined by...
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3. (20 pts.) Consider the function f defined on (0, 2) by 2+1 f(x) = = { 0<x< 1 1<x< 2 (a) Denote by fs the sum of the sine Fourier series of f (on (0,2]). Plot the graph of the function fs for x € (-2, 4), indicating the values at each point in that interval. Compute fs(0) and fs(2). [You do not have to compute the coefficients of the Fourier series.] (b) Denote...