Question

Suppose x(t) is the continuous-time function given by x(t) = 1 on the interval [0; 1] and x(t) = 0 elsewhere. a) Calculate the continuous time Fourier transform of x(t). Call this X(j????). b) Suppose x1 (t) = x(2t). Provide the explicit definition for x1 (t) (i.e. over what interval

Answer 1

a) X( w ) = 1 /jw - e^-jw / jw

b) X1(t) = 1 for 0.5

X1(t) = 0 for elsewhere

Explanation:

x(t) continuous time function = 1

interval ( 0,1 ) also x(t) = 0 outside the given interval

a) Determine the continuous time Fourier transformation of x(t)

x( t ) = u(t) - u(t - 1 )

x ( w ) = 1 /jw - e^-jw / jw

b) supposing x1(t) = x(2t)

x1(t) = u(t) - u ( t - 0.5 )

x1(t) = 1 for 0.5

x1(t) = 0 for elsewhere