Exercise 2. Consider the function (1 if <t< v(t) = -1 if <t<T. 10 if elsewhere...
4. Consider the signal co(t) = et, 0<t<1 , elsewhere Determine the Fourier transform of each of the signals shown in Figure 2. You should be able to do this by explicitly evaluating only the transform of co(t) and then using properties of the Fourier transform. X(t) X2(t) Xolt) Xp(t) -Xol-t) X3(t) Xolt +1) X4(t) Xolt) txo(t) My Lane 1 0
Consider the following signal t/2+1 -2 <t<0 2(t) = {-t/2+1 0<t<2 elsewhere a) Draw x() b) Draw y(t) = +(2(1 – t)) and show all the intermediate steps in your transformation.
" 2.9.2 USC volalled in Example 2.5.1. Represent the signal f(t)*= 1 -1<t< 0 0<i<1 elsewhere over the interval (-2,2). a) Use the exponential Fourier series. b) Use the trigonometric Fourier series. c) Compare your results using Eqs. (2.49)-(2.51).
Exercise 5. Let f(t) denote the 2-periodic function f(t) = 1+2 - <t< . a) Make a representative plot of f(t) showing at least 3 periods. b) Using the numerical integration routine you wrote in your Home work 1 (Exercise 3) compute approx- imately the values of the Fourier series coefficients all of f() for k in the range -20 to 20. c) Make a plot of laul
[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...
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.
Exercise 1. Let 0<a<7. Let f(t) denote the 27t-periodic function 10, if a<\t]<1. a) Make a representative plot of f(t) showing at least 3 periods for a = 7/8, 7/2, and 7/8. b) Compute explicitly the Fourier series coefficients as of f(t). c) Make a representative plot of the absolute values of the Fourier coefficients, lax for a= /8, 7/2, and 7/8. The plot must at least show (0-20) through a 2013 d) By looking at the plots in parts...
Consider f(x), a 27 periodic function defined by: f(x) = 1o, 1 if if -T <I< 0 0 < < Calculate the DC component of the Fourier series of f(x):
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...
- Express the Fourier series of that particular function - when - 1 < x < 0 4 f(x) = { when 0<x<T