Answer Happy

The Fourier transform of x(t), denoted by X (w) is defined as: =100² x(t)e-jwt dt X(w) = (1) For a particular frequency w, X(w) denotes the contribution of the complex exponential ejut to the signal x(t). As an analogy, X(w) shows how many grams of ejot we need to use to form x(t). Answer the following questions and include the answers to your report. You can directly use the result given in the book for part a. For the other parts show your work clearly. If it is possible, you are required to use the properties of the Fourier transform (linearity, scaling, time shift etc.). a) Let x(t) = exp(j2л fot). What is X(w)? b) Let x(t) = cos(2л fot). What is X(w)? c) Let x(t) = rect(). What is X (w)? d) Let x(t) = exp(j2 fot)rect(). What is X(w)? e) Let x(t) = cos(27 fot)rect(). What is X(w)? f) Let x(t) = rect(¹7). What is X(w)? g) Let x(t) = exp(j27 ft)rect(). What is X (w)? h) Let x(t) = cos(27 fot)rect (70). What is X(w)?