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Consider f(x), a 27 periodic function defined by: f(x) = 1o, 1 if if -T <I<...
11. (10 points) Let f(t) be a 27-periodic function defined by f(t) = -{ 2 if – <t<0, -2 if 0 <t<, f(t + 2) = f(t). a) Find the Fourier series of f(t). b) What is the sum of the Fourier series of f at t = /2.
A periodic function f(x) with period 21 is defined by: X + -1<x< 0 2 f(x) = 0<x< 2 Determine the Fourier expansion of the periodic function f(x). X - TT
3. Consider the periodic function defined by -ae sin(x) 0 x < 7T f(x) and f(x) f(x2t) - (a) Sketch f(x) on the interval -37 < x < 3T. (b) Find the complex Fourier series of f(x) and obtain from it the regular Fourier series
Consider the 2-periodic function given on the interval [0,27) by if 0 <<< 2 (x - 72 if <<< 27. 1. Sketch the graph of this function. 2. Find its Fourier series.
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)
A function is defined over (0,6) by 0 <and I <3 f(1) = - { 3<; and <6 We then extend it to an odd periodic function of period 12 and its graph is displayed below. N y 1 0 -10 5 5 10 15 X The function may be approximated by the Fourier series f (t) = a0 + 1 (an cos (021 ) + bn sin ( 122 )), where L is the half-period of the function. Use...
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)
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
A periodic function ft) of period T-2 is defined as ft)-2t over the period (a) Sketch the function over the interval -3m<<3x. [3] (b) Find the cireular frequency a and the symmetry of the function (odd, even or neither). 21 (e) Determine the trigonometric Fourier coefficients for the function f) [10] (d) Write down its Fourier series for n=0, 1, 2, 3 where n is the harmonic number. [5] (e) Determine the Fourier series for the function g(t)-2r-1 over the...
[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...