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 c

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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 c

ontinuous 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

Mathematics

1 answer:

borishaifa [10] · Answer 1 · 2022-09-30T20:18:24+03:00

Answer:

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

b) X1(t) = 1 for 0.5

X1(t) = 0 for elsewhere

Step-by-step 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