[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...
Consider the function f(e) (T2) that is to be represented by a Fourier series expansion over the interval-π t π and f(t) = f(t + 2n). (b) Pertimbangkan fungsi f(c)(r t2) yang diwakili oleh kembangan siri π dan f(t) f(t + 2π). Founer dalam selang-π t Determine the Fourier series expansion. (i) Tentukan kembangan siri Fourer (7 marks/markah) (i) By using your answer in (), show that Dengan menggunakan jawapan anda dalam (), tunjukkan bahawa. -)n+1 (5 marks/markah) Consider the...
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....
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 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...
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
*Fourier Series Expansion A function f(x) has a period 2t and function values over one cycle is shown in the table below. x0 0 30 60 90 120 150 180 210 240 270 300 330 f(x) 4.1 5.5 9.3 10.4 5.2 3.3 4.1 3.3 5.2 10.4 9.3 5.5 Given that Σ,21f(xr) sin(%) DE1f(x) sin(%)-Σ 21f(xr) sin(3%) 0.Find the Fourier series expansion up to the third harmonic. All calculation must be correct to 3 decimal places. A function f(x) has a...
5. (a) (6) Carefully sketch the odd periodic extension, of period 2m, of the function f(x)1, 0 < x < π. (Only sketch over the interval z E [-2π, 2π). (b) (10) Find the Fourier sine series of the function in part (a) 5. (a) (6) Carefully sketch the odd periodic extension, of period 2m, of the function f(x)1, 0
Let f (x) be a periodic function on R with period 21. On the interval (-11,), f(x) is given by f(x)=sin(x) 0<x51, = Let F(x) be the Fourier series of f(x). Select all correct statements from below. The Fourier series of -f (x) is -F(x). F(-1) = 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...
Let f be the function of period 6 such that F(x) = ch that Fx10-35x< ch that X, OSX<3 (a) Sketch the graph of F on the interval (-6, 6]. At which points in this interval is f discontinuous? (b) Find the Fourier series of f on the interval (-3,3]. What is the value of the constant term in the series expansion? What is the value of the coefficient a? What is the value of the coefficient bz? (c) To...