MCQOPTIONS
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MCQOPTIONS
This section includes 9 Mcqs, each offering curated multiple-choice questions to sharpen your Signals Systems knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Find the fourier transform of the unit step function. |
| A. | πδ(ω) + \(\frac{1}{ω}\) |
| B. | πδ(ω) + \(\frac{1}{jω}\) |
| C. | πδ(ω) – \(\frac{1}{jω}\) |
| D. | δ(ω) + \(\frac{1}{jω}\) |
| Answer» C. πδ(ω) – \(\frac{1}{jω}\) | |
| 2. |
Which of the following is not a fourier transform pair? |
| A. | \(u(t) \leftrightarrow πδ(ω) + \frac{1}{jω}\) |
| B. | \(sgn(t) \leftrightarrow \frac{2}{jω}\) |
| C. | \(A \leftrightarrow 2πδ(\frac{ω}{2})\) |
| D. | \(G(t)\leftrightarrow sa(\frac{ωτ}{2})\) |
| Answer» E. | |
| 3. |
Bandwidth of the gate function is __________ |
| A. | τ Hz |
| B. | \(\frac{1}{τ}\) Hz |
| C. | 2τ Hz |
| D. | \(\frac{2}{τ}\) Hz |
| Answer» C. 2τ Hz | |
| 4. |
Find the fourier transform of the gate function. |
| A. | \(\frac{1}{ω} sin(\frac{ωτ}{2})\) |
| B. | \(\frac{1}{ω} cos(\frac{ωτ}{2})\) |
| C. | \(\frac{2}{ω} sin(\frac{ωτ}{2})\) |
| D. | \(\frac{2}{ω} cos(\frac{ωτ}{2})\) |
| Answer» D. \(\frac{2}{ω} cos(\frac{ωτ}{2})\) | |
| 5. |
Gate function is defined as ______________ |
| A. | \(G(t)=\begin{cases}1 &\text{\(|t|<\frac{τ}{2}\)} \\0 &\text{elsewhere} \\\end{cases} \) |
| B. | \(G(t)=\begin{cases}1 &\text{\(|t|>\frac{τ}{2}\)} \\0 &\text{elsewhere} \\\end{cases}\) |
| C. | \(G(t)=\begin{cases}1 &\text{\(|t|≤\frac{τ}{2}\)} \\0 &\text{elsewhere} \\\end{cases}\) |
| D. | \(G(t)=\begin{cases}1 &\text{\(|t|≥\frac{τ}{2}\)} \\0 &\text{elsewhere} \\\end{cases}\) |
| Answer» B. \(G(t)=\begin{cases}1 &\text{\(|t|>\frac{τ}{2}\)} \\0 &\text{elsewhere} \\\end{cases}\) | |
| 6. |
Find the fourier transform of the function f(t) = e-a|t|, a>0. |
| A. | \(\frac{2a}{a^2-ω^2}\) |
| B. | \(\frac{2a}{a^2+ω^2}\) |
| C. | \(\frac{2a}{ω^2-a^2}\) |
| D. | \(\frac{a}{a^2+ω^2}\) |
| Answer» C. \(\frac{2a}{ω^2-a^2}\) | |
| 7. |
Find the fourier transform of an exponential signal f(t) = e-at u(t), a>0. |
| A. | \(\frac{1}{a+jω}\) |
| B. | \(\frac{1}{a-jω}\) |
| C. | \(\frac{1}{-a+jω}\) |
| D. | \(\frac{1}{-a-jω}\) |
| Answer» B. \(\frac{1}{a-jω}\) | |
| 8. |
Choose the correct synthesis equation. |
| A. | \(f(t) = \frac{1}{2π} \int_{-∞}^∞ F(ω) e^{-jωt} \,dω\) |
| B. | \(f(t) = \frac{1}{2π} \int_{-∞}^∞ F(ω) e^{jωt} \,dω\) |
| C. | \(f(t) = \frac{1}{2π} \int_0^∞ F(ω) e^{-jωt} \,dω\) |
| D. | \(f(t) = \frac{1}{2π} \int_0^∞ F(ω) e^{jωt} \,dω\) |
| Answer» C. \(f(t) = \frac{1}{2π} \int_0^∞ F(ω) e^{-jωt} \,dω\) | |
| 9. |
Which of the following is the Analysis equation of Fourier Transform? |
| A. | \(F(ω) = \int_{-∞}^∞ f(t)e^{jωt} \,dt\) |
| B. | \(F(ω) = \int_0^∞ f(t)e^{-jωt} \,dt\) |
| C. | \(F(ω) = \int_0^∞ f(t)e^{jωt} \,dt\) |
| D. | \(F(ω) = \int_{-∞}^∞ f(t)e^{-jωt} \,dt\) |
| Answer» E. | |