3.(2 points) Determine whether the given function is periodic. If so, find its funda- mental period....
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.
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 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...
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)...
Let be a function defined by: We define by extension the odd, periodic function of period p = 2 which coincides with the function f (x) on the interval [0, 1]. Draw over the interval [−1, 3] the graph of the function towards which the Fourier series of the odd continuation of the function f (x) converges. f(x) = 1 + x2 pour 0 < x < 1.
function is defined over (0,6) by f(x)={14x00<xandx≤33<xandx<6. We then extend it to an odd periodic function of period 12 and its graph is displayed below. calculate b1,b2,b3,b4, Thanks so much A function is defined over (0,6) by 0<x and x <3 f (x) = 3<x and x < 6 We then extend it to an odd periodic function of period 12 and its graph is displayed below. 1.5 1 у 0.5 -10 5 10. 15 -1 -1.5 The function may be...
Sketch the function with its (a) odd periodic extension and (b) even then find the Fourier Sine and Fourier Cosine series, respectively. periodic extension, 0< x < X f(x) = -< x< 2 2 Sketch the function with its (a) odd periodic extension and (b) even then find the Fourier Sine and Fourier Cosine series, respectively. periodic extension, 0
thank you so much for helping! Problem 4. (20 pts) Determine whether function f : {NU0} + {NUO} defined by f(x) = ſx-1, if r is odd x+1, is even is a) one-to-one b) onto. Problem 5. Given f(x) = x+1 and g(x) = -2, find (fog)(x) (5 pts)
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)
4. Consider the periodic function given below: f(x)-x 0 ㄨㄑㄧ (i) State its fundamental period, and sketch the function for 3 periods. (5 marks) i) Find the Fourier series of the given periodic function, and expand the series to give the first three non-zero a and b terms (15 marks) ii) Use the answer obtained in Q4(ii) and the given periodic function, find the sum of the series 4(2n-1 )2 (5 marks)