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14.9 ZERO-STATE RESPONSE BY FREQUENCY-DOMAIN ANALYSIS
Fourier transform of output is given by the product of Fourier transform of input
and system function. Input is u(t) and its transform is
πδ
(j
ω
) ⫹ 1/j
ω
.
The second term contains an impulse at
ω
⫽ 0 scaled in magnitude by
ω
. The
scaling factor that comes into effect is zero since
ω
⫽ 0 is the point at which its area is
concentrated. Therefore, this term is zero in effect.
The right side can be expressed as a sum of fractions as below:
Comparing the coefficients of numerator polynomial with those of the actual
numerator polynomial, we get, A ⫹ B ⫽ 0 and 1.91A ⫹ 13.09B ⫽ 5.
Solving for A and B, we ...