SIGNALS LAB

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)|

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