Question

Problem 03 A linear system has an impulse response h(t) Where $h(t) = A \cdot t \cdot e^{-Bt} \cdot u(t)$ A=0.6 B=1.1 The input to the system [X(t)] is: One-sided White Noise ($N_0 = 8 \cdot \frac{V^2}{Hz}$) plus a DC voltage (2.5VDC) Find, a) Find the Fourier Transform of h(t) b) The Fourier Transform of the System Input c) The Fourier Transform of the System Output d) The Mean value of the output of the system e) The variance of the output f) The Mean-Square value of the output

          Problem 03
A linear system has an impulse response h(t)
Where $h(t) = A \cdot t \cdot e^{-Bt} \cdot u(t)$
A=0.6
B=1.1
The input to the system [X(t)] is: One-sided White Noise ($N_0 = 8 \cdot \frac{V^2}{Hz}$) plus a DC
voltage (2.5VDC)
Find,
a) Find the Fourier Transform of h(t)
b) The Fourier Transform of the System Input
c) The Fourier Transform of the System Output
d) The Mean value of the output of the system
e) The variance of the output
f) The Mean-Square value of the output

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Problem 03
A linear system has an impulse response h(t)
Where h(t) = A · t · e^-Bt· u(t)
A=0.6
B=1.1
The input to the system [X(t)] is: One-sided White Noise (N0 = 8 ·(V^2)/(Hz)) plus a DC
voltage (2.5VDC)
Find,
a) Find the Fourier Transform of h(t)
b) The Fourier Transform of the System Input
c) The Fourier Transform of the System Output
d) The Mean value of the output of the system
e) The variance of the output
f) The Mean-Square value of the output

Added by Madeline M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Shaiju T

Step 1

The Fourier Transform of e^(-Bt) * u(t) is 1 / (jω + B), where j is the imaginary unit and ω is the frequency. The Fourier Transform of t is j / ω^2. Show more…

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A linear system has an impulse response h(t) where h(t) = A - t : e^(-Bt) * u(t). Find: a) Find the Fourier Transform of h(t). b) The Fourier Transform of the System Input. c) The Fourier Transform of the System Output. d) The Mean value of the output of the system. e) The variance of the output. f) The Mean-Square value of the output. Given: A = 0.6 B = 1.1 Plus a DC voltage (2.5VDC).

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