e) Formulate the FS Coefficient $a_n$ (formulate the integral that gives $a_n$, you are not
asked to actually solve the integral)
Answer $a_n$ =
f) Justify and find by inspection the signal FS Coefficient $b_n$
Answer: $b_n$ = ______ because ______
5) The input to the LTI system at rest shown below is $x(t) = 5e^{-t}u(t)$ and the system
impulse response is $h(t) = e^{-t}u(t)$.
x(t)
$h(t)$
y(t)
system
Using the Fourier Transform find the system Frequency Response is:
Answer: $H(\omega) = $
6) Assume that the magnitude of the Fourier transform of voltage signal $v(t)$ is as
shown in the figure below. This voltage is applied to a 1-ohm resistor. Note that
$|V(\omega)|$, as given, is an even function of $\omega$.
10
$|V(\omega)|$
$\omega$ [rad/sec]
The total energy delivered to the one-ohm resistor is: Answer: $E_1 = $
7) The unit sample response of a discrete time filter is:
$h[n] = 8[n] - 48[n-1] + 26[n-2]$,
Find the output of the filter when the input is: $x[n] = 8[n] + 38[n-1] + 48[n-2] + 58[n-3]$
Answer: $y[n] = $
