The sketch of the following periodic function f (t) given in one period f(t) t2 -1, 0s t s 2 is given as follows f(t) 2 -1 We proceed as follows to find the Fourier series representation of f (t) (Note:Jt2 cos at dt = 2t as at + (a--)sina:Jt2 sin at dt = 2t sin at + sin at. Г t2 sin at dt-tsi. )cos at.) Please scroll to the bottom of page for END of question a) The...
4. Consider the periodic function 0, -1<t<- f(t) cos(#(t + 1)), } <t< 0 cos(at), 0<t< 0, }<t<i with f(t) = f(t+2). (a) Determine a general expression for the Fourier series of f. (b) Use MATLAB to plot both f and the sum of the first 5 non-zero terms of the Fourier series for f on the same set of axes for -1<t<3.
Problem 3. 0 Figure 2 Given: f(t) = { 2.5, -1.5 <=<= 1.5 f(t) = { 0 otherwise See figure(2) above. A) Find the Fourier transform for f( (see figure 2) and sketch its waveform. B) Determine the values of the first three frequency terms (w1, W2, W3) where F(w) = 0. C) Given x(t) = 1.58(-0.8) edt Determine whether or not Fourier transform exists for x(t). If yes, find the Fourier transfe not explain why it does not. Problem...
(1 point) Consider the function f(x) = f* cos(t) – 1 dt. t2 Which of the following is the Taylor Series for f(x) centred at x = 0? w A. (-1)" (2n – 1)(2n)! -x2n- +C. n=0 (-1)"(2n – 2) 2n–3. B. (2n)! n=1 c. Σ (-1)" (2n + 1)! -x2n-2 n=1 D. Š (-1)" -X2n-1 (2n – 1)(2n)! n=1
Find the trigonometric Fourier series (FS) and the exponential FS of the following: x(t) TT Ana -3т -2n -TT 2TT d) x(t) πι -no -TT 0 TE 2TT exponential FS f(t) = En=-- Cnejnwot Where (n = +S40+" f(t)e-inwot dt trigonometric 30 f(t)=a, + a, cos(no),t)+b, sin(no,t n-1 ao 1 T. 2 to a. So f(t)dt -5° f(t)cos(no),1)dt Sº f(t)sin(no,t)dt oy b 2 T
(1 point) Consider the function cos(t) f(x) = dt. Which of the following is the Taylor Series for f(2) centred at x = 0? O (-1)" A. 2n-1 (2n - 1)(2n)! O B. (-1)" (2n – 1)(2n)! 2n-1 +C n0 O C. (-1)" 220-2 (2n +1)! (-1)"(2n - 2) (2n)! D. n=1 2n 3
(1 point) Consider the function f(x) = Es cos(t) – 1 t2 dt. Which of the following is the Taylor Series for f(x) centred at x = 0? 2n-1 Α.Σ (-1)" (2n – 1)(2n)! X +C. n=0 oo 2n-1 B. (-1)" (2n – 1)(2n)!" X n=1 (-1)" X20-2 (2n + 1)! M n=1 D. iM: (-1)"(2n – 2), 2n–3 (2n)! X n=1
' cos(3t), t<n/2, 2. Let f(t) = sin(2t), 7/2<t< , Write f(t) in terms of the unit step e3 St. function. Then find c{f(t)}.
Problem 12. (1 point) Consider the function f(0) = %,* cos(t) – 1 dt. +2 Which of the following is the Taylor Series for f(2) centred at x = 0? O (-1)" A. n1 (2n – 1)(2n); 22n-1 (-1)"(2n - 2) B. n1 22n-3 (2n)! (-1) C. n0 -22n-1 +C (2n-1)(2n)! D. (-1) 2n-2 1 (2n +1)!
For the function y 1-x for 0 s x s 1 Graph the function's 3 periods 1) Find its formulas for the Fourier series and Fourier coefficients 2) Write out the first three non-zero terms of the Fourier Series 3) 4) Graph the even extension of the function 5) Find the Fourier series and Fourier coefficients for the even extension 6) Write out the first three non-zero terms of the even Fourier series 7) Graph the odd extension of the...