fourier series 1. For each of the following functions id ther oddoces = {1+2 and v(t...
Fourier Series for Odd Functions Recall that if f is an odd function, f(-x)f(x). An odd Fourier series has only the sine terms, and can be approximate an odd function, so Fo(x) b sinx)+b2 sin(2x)+ b, sin(3x)+. Why is there no b, term in the series F, (x)? 1. 2. Using steps similar to those outlined for even functions, develop a rule for finding the coefficients to approximate any odd function on the interval [-π, π]. 3. If f (x)sin...
Computing a fourier series : Compute the Fourier series for the function f(2)= {I 0 if – <r<0 1 if 0 <<< on the interval -1 <I<.
Find the Fourier series of the following functions in the given intervals. f(x) = r +, - <x< g(t) = { inter) 0. -T<r <0, sin(x), 0<x< 1.
Consider the following problems related to the exponential Fourier series. (a) The exponential Fourier series of a periodic signal x(t) of funda- 4.7 mental period To is 3 i. Determine the value of the fundamental period To ii. What is the average or dc value of x(t)? iii. Is x(t) even, odd, or neither even nor odd function of time? iv. One of the frequency components of x(t) is expressed as Acos(ST) 0- What is A? (b) A train of...
Question 4. Calculate the Fourier sine series and the Fourier cosine series of the function f(x) = sin(x) on the interval [0, 1]. Hint: For the cosine series, it is easiest to use the complex exponential version of Fourier series. Question 5. Solve the following boundary value problem: Ut – 3Uzx = 0, u(0,t) = u(2,t) = 0, u(x,0) = –2? + 22 Question 6. Solve the following boundary value problem: Ut – Uxx = 0, Uz(-7,t) = uz (77,t)...
1. Using the Fourier series analysis Equation 3 for the periodic function r(t) shown in Figure 2.1, determine both the DC coefficient ao and a general expression for the other Fourier series coefficients ak. Do this by hand, not in Matlab. Show all your work in your lab report. You can add these pages as hand-written pages, rather than typing them in to your lab report, if you prefer Hint 1: It will be easiest to integrate this function from...
Let x(t) = t, 0<t 1 and Fourier series coefficients a , be a periodic signal with fundamental period of T 2 -t,-1t0 dz(t) a) Sketch the waveform of r(t)d3 marks) b) Calculate ao (3 marks) c) Determine the Fourier series representation of gt)(4 rks) d) Using the results from Part (c) and the property of continuous-time Fourier series to dr(t) determine the Fourier series coefficients of r(t) (4 marks)
Find a Fourier series expansion of the periodic function 0 -T -asts 2 - f(t) = 6 cost T <<- 2 2 0 I SISE 2 f(t) = f (t +21) Select one: a f(t)= 12 12 5 (-1)** cos nt 1 2n-1 b. f(t) = 12.12 F(-1)** cos 2nt T 4n-1 C 6 12 =+ 125 (-1) C05 211 472-1 6 12 (-1) * cosm d
Problem 6. (15 points.) Determine the Fourier series coefficients of the following signal c(t) = y g(t/2+1 – 4m) m=- where g is the gate function
1 & 5 Solve the following heat equations using Fourier series ux Ut, 0 <x <1,t>0, u (0,t) = 0 = u(1,t), u(x,0) = x/2 1/ 2/ Ux=Ut, 0<x< m ,t>0 ,u(0,t) = 0 = u( 1, t), u(x, O) = sinx- sin3x 3/ usxut, O <x < 1 ,t>0, u(0,t) = 0 = u,(1, t), u(x,0) = 1 -x2 Ux=Ut,O<x <m ,t>0, u(0, t) = 0 = u,( rt , t) , u(x, 0) = (sinxcosx)2 4/ 5/Solve the...