Q1

Given that

xa(t) = cte-αtua(t)

0.0201= 100te-287.6821tua(t)

ua(t) = 0.0201/100 x1/(te^(-287.6821t) )

= 0.000201/〖te〗^(-287.6821t)

Sketch of xa(t)

100

Finding the Fourier of xa(t)

Magnitude plot

Energy of the signal

=∫_(-ꭃ)^ꭃ▒〖xa(t)〗 dt

=∫_(-ꭃ)^ꭃ▒〖cte ^(-αt) ua(t) 〗 dt

Given that

xa(t) = cte-αtua(t)

0.0201= 100te-287.6821tua(t)

In discrete from at at sampling of rate of 100samples/sec

x(n) = (100ne-287.6821nua(n))/100

=ne-287.6821nua(n)

Sampling rate: 100 samples/sec

Energy of the signal

= ∫_(-ꭃ)^ꭃ▒〖ne^(-287.6821n)ua(n)〗 dn

g) Z-transforms

x(n)=ne-287.6821nua(n)

= z/(z-e^aT )

= z/(z-〖ne〗^(-287.6821 ua) )

Fourier Transform

x(n)=ne-287.6821nua(n)

F(t)=e^(-at) u(t)

F(ω)=1/(a-iw)

= 1/(-287.6821-iw)

h) Plot of magnitude spectrum of x(n)

Plot of |X(ejw)|