Consider the set of orthogonal basis signals fan(t)g in Figure 4.55 and the four signals y(t) in Figure 4.56 defined on the interval =2, )Figure 4.56  2. In this question, each of this signals y(t) is...

Consider the set of orthogonal basis signals fan(t)g in Figure 4.55 and the four signals y(t) in Figure 4.56 defined on the interval =2, )Figure 4.56 2. In this question, each of this signals y(t) is to be estimated as a linear combination of the signals fan(t)g. (a) For each y(t) determine the DC component by inspection. This is the component of a0(t) that is required.(b) Identify each y(t) as being odd or even, and eliminate by inspection any an(t) that could not usefully contribute to y(t ). These terms are zero. (c) Use the signal inner product as required to find the best approximation to the signal y(t) using the orthogonal basis signals fan(t)g in Figure 4.55. In other words, find fA0, A1, A2, A3g and express your answer in the form of a linear combination of the signals fan(t)g as:(d)       Check your answer by reconstructing your estimate of y(t) from the linear combination and sketch your approximation.