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Consider the following signal t/2+1 -2 <t<0 2(t) = {-t/2+1 0<t<2 elsewhere a) Draw x() b)...
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 a signal x(t) which is given as 1 x(t) - 2 <t<2 2 0, otherwise a) Sketch x(t) b) Sketch 3x(t – 1) c) Sketch – 2x(-t - 1) Identify all labels and amplitudes to get the whole score.
" 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).
Consider the signal 2, defined for allt e Ras sin(at) 1<t<4 (t) 0 otherwise. Define the signal y as y(t) = x(4 – t) for allt ER For which value of t does (x+y)(t) assume its maximum value? 3 2 6 none of the other answers 4 0
Consider the following signal with period T = 4: It ä(t) = { 14- t 0<t<2 2 <t<4 Find the Fourier series of r(t).
Let f(x,y) = cx( 1-y), 0 < x < 2y < 1, zero elsewhere. a) Find c. b) Are X and Y independent? Why or why not? c) Find PX +Y05)
2) Suppose that X has density function f(a)- 0, elsewhere Find P(X < .3|X .7).
6. Consider a random variable X with pdf given by 0 elsewhere. (a) What is c? Plot the pdf. (b) Plot the cdf of X. Find P(X 0.5< 0.3).
For f(x, y) = k(x2 + y2), 0<x< 1 and 0 <y<1 and 0 elsewhere: a) Find k. b) Are X and Y independent? c) Find P(X<0.5, Y>0.5), P( X = 0.5, Y>0.5).
Consider the following. x = sin(t) y = csc(t) 0<t</2 (a) Eliminate the parameter to find a Cartesian equation of the curve. 1 y = X y