Question

Consider a continuous-time LTI system whose frequency response is \frac{\sin(4\omega)}{\omega} H(j\omega) = If the input to this system is a periodic signal \begin{cases} 0, & 0 \le t \le 4 \\ 0, & -4 \le t \le 8 \end{cases} x(t) = with period $T = 8$, (a) determine Fourier series coefficients $x(t)$ (b) determine the corresponding system output $y(t)$ (c) sketch the output $y(t)$

          Consider a continuous-time LTI system whose frequency response is
\frac{\sin(4\omega)}{\omega}
H(j\omega) = 
If the input to this system is a periodic signal
\begin{cases}
0, & 0 \le t \le 4 \\
0, & -4 \le t \le 8
\end{cases}
x(t) = 
with period $T = 8$,
(a) determine Fourier series coefficients $x(t)$
(b) determine the corresponding system output $y(t)$
(c) sketch the output $y(t)$

Consider a continuous-time LTI system whose frequency response is
(sin(4ω))/(ω)
H(jω) =
If the input to this system is a periodic signal

0, 0 ≤t ≤4

0, -4 ≤t ≤8

x(t) =
with period T = 8,
(a) determine Fourier series coefficients x(t)
(b) determine the corresponding system output y(t)
(c) sketch the output y(t)

Added by Carol P.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Ameer Said

Step 1

The rectangular pulse function can be represented as: rect(t) = 1, for 0 ≤ t < T/2 rect(t) = 0, for T/2 ≤ t < T Since the period T = 8, we have T/2 = 4. The complex exponential Fourier series representation of rect(t) is given by: rect(t) = Σ [Cn * Show more…

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Please show your work fully and clearly. Thank you so much! Consider a continuous-time LTI system whose frequency response is sin(4) H(jw)= If the input to this system is a periodic signal 00t4 )= [0,48 with period T = 8, (a) determine Fourier series coefficients (t) Rectangular Snip (b) determine the corresponding system output y(t) (c) sketch the output y(t)