Question

Assume you are given a rectangular pulse expressed as below. \begin{equation} \pi \left(\frac{t}{T}\right) = \begin{cases} 1, & \left|t\right| \leq \frac{T}{2} \\ 0, & \left|t\right| > \frac{T}{2} \end{cases} \end{equation} (10 pts) a) Plot the rectangular function in the given time domain b) Determine the Fourier transform of this equation and express it as a sinc function. c) Plot the frequency response (sinc function) in the frequency domain

          Assume you are given a rectangular pulse expressed as below.
\begin{equation*}
\pi \left(\frac{t}{T}\right) = \begin{cases}
1, & \left|t\right| \leq \frac{T}{2} \\
0, & \left|t\right| > \frac{T}{2}
\end{cases}
\end{equation*}
(10 pts)
a) Plot the rectangular function in the given time domain
b) Determine the Fourier transform of this equation and
express it as a sinc function.
c) Plot the frequency response (sinc function) in the frequency
domain

Assume you are given a rectangular pulse expressed as below.

π((t)/(T)) =
1, |t| ≤(T)/(2)

0, |t| > (T)/(2)

(10 pts)
a) Plot the rectangular function in the given time domain
b) Determine the Fourier transform of this equation and
express it as a sinc function.
c) Plot the frequency response (sinc function) in the frequency
domain

Added by Calvin R.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Kamlesh Goyal

Step 1

To plot the rectangular function in the time domain, we need to define the function and the time range. The rectangular function, also known as the unit step function, is defined as: rect(t) = 1, for 0 <= t < 1 rect(t) = 0, otherwise Let's plot this function for Show more…

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a. Plot the rectangular function in the given time domain. b. Determine the Fourier transform of this equation and express it as a sinc function. c. Plot the frequency response (sinc function) in the frequency domain.