Question

-l 2. Consider the continuous-time signal: 0 x(t)- 1sts1 0, otherwise Find the Fourier transform X(a) of x(t). Simplify ths expression as much as po e simplest expression does not involve any complex numbers.) Draw a rough plot of o) as a function of w. Identify the peak value of X(w). Identify the location of the X( first null on either side of the vertical axis.

Answer 1

x(t) = {2, 0, -1 lessthanorequalto t lessthanorequalto 1 otherwise x(omega) = integral_-infinity^+ infinity x(t) e^_j omega t dt x(omega) = integral_01^1 (2) e^-j omega t dt = 2[e^-j omega t/(-j omega)]_1^1 = 2[e^j omega - e^-j omega]/j omega = 2(2j) sin(omega)/j omega x(omega) = 4 sin (omega)/omega