MCQOPTIONS
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MCQOPTIONS
This section includes 11 Mcqs, each offering curated multiple-choice questions to sharpen your Fourier Analysis knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Find the fourier sine transform of F(x) = -x when xc and 0≤c≤π. |
| A. | \(\frac{π}{c} cos(pc) \) |
| B. | \(\frac{π}{p} cos(pc) \) c) \(\frac{π}{c} cos(pπ) \) d) \(p \frac{π}{c} cos(p |
| C. | \) b) \(\frac{π}{p} cos(pc) \) c) \(\frac{π}{c} cos(pπ) \) |
| D. | \(p \frac{π}{c} cos(pc) \) |
| Answer» C. \) b) \(\frac{π}{p} cos(pc) \) c) \(\frac{π}{c} cos(pπ) \) | |
| 2. |
Find the fourier cosine transform of e-ax * e-ax. |
| A. | \(\frac{p^2}{a^2+p^2} \) |
| B. | \(\frac{p^2}{(a^2+p^2)^2} \) |
| C. | \(4 \frac{p^2}{(a^2+p^2)^2} \) |
| D. | \(\frac{-p^2}{(a^2+p^2 )^2} \) |
| Answer» C. \(4 \frac{p^2}{(a^2+p^2)^2} \) | |
| 3. |
\(F(x) = x^{(\frac{-1}{2})} \)is self reciprocal under Fourier cosine transform. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 4. |
What is the Fourier transform of eax? (a>0) |
| A. | \(\frac{p}{a^2+p^2} \) |
| B. | \(2 \frac{a}{a^2+p^2} \) |
| C. | \(-2 \frac{a}{a^2+p^2} \) |
| D. | cant’t be found |
| Answer» E. | |
| 5. |
What is the fourier transform of e-a|x| * e-b|x|? |
| A. | \(\frac{4ab}{(a^2+p^2)(b^2+p^2)} \) |
| B. | \(\frac{2ab}{(a^2+p^2)(b^2+p^2)} \) |
| C. | \(\frac{4}{(a^2+p^2)(b^2+p^2)} \) |
| D. | \(\frac{a^2 b^2}{(a^2+p^2)(b^2+p^2)} \) |
| Answer» B. \(\frac{2ab}{(a^2+p^2)(b^2+p^2)} \) | |
| 6. |
If Fourier transform of \( e^{-|x|} = \frac{2}{1+p^2} \), then find the fourier transform of \(t^2 e^{-|x|}. \) |
| A. | \(\frac{4}{1+p^2} \) |
| B. | \(\frac{-2}{1+p^2} \) |
| C. | \(\frac{2}{1+p^2} \) |
| D. | \(\frac{-4}{1+p^2} \) |
| Answer» C. \(\frac{2}{1+p^2} \) | |
| 7. |
Find the Fourier Cosine Transform of F(x) = 2x for 0 |
| A. | \(fc(p) = \frac{32}{(p^2 π^2)} (cos(pπ)-1)p \) not equal to 0 and if equal to 0 \( fc(p) = 16 \) |
| B. | \(fc(p) = \frac{32}{(p^2 π^2)} (cos(pπ)-1)p \) not equal to 0 and if equal to 0 \( fc(p) = 32 \) |
| C. | \(fc(p) = \frac{64}{(pπ^2)} (cos(pπ)-1)p \) not equal to 0 and if equal to 0 \( fc(p) = 16 \) |
| D. | \(fc(p) = \frac{32}{(pπ^2)} (cos(pπ)-1)p \) not equal to 0 and if equal to 0 \( fc(p) = 64 \) |
| Answer» B. \(fc(p) = \frac{32}{(p^2 π^2)} (cos(pπ)-1)p \) not equal to 0 and if equal to 0 \( fc(p) = 32 \) | |
| 8. |
In Finite Fourier Cosine Transform, if the upper limit l = π, then its inverse is given by ________ |
| A. | \(F(x) = \frac{2}{π} ∑_{p=1}^∞ fc (p)cos(px)+ \frac{1}{π} fc(0) \) |
| B. | \(F(x) = \frac{2}{π} ∑_{p=1}^∞ fc (p)cos(px) \) |
| C. | \(F(x) = \frac{2}{π} ∑_{p=1}^∞ fc (p)cos(\frac{px}{π}) \) |
| D. | \(F(x) = \frac{2}{π} ∑_{p=0}^∞ fc (p)cos(px)+ \frac{1}{π} fc(0) \) |
| Answer» B. \(F(x) = \frac{2}{π} ∑_{p=1}^∞ fc (p)cos(px) \) | |
| 9. |
Find the fourier sine transform of \( \frac{x}{(a^2+x^2)}. \) |
| A. | \(2πe^{-ap} \) |
| B. | \(\frac{π}{2} e^{-ap} \) |
| C. | \(\frac{2}{π} e^{-ap} \) |
| D. | \(πe^{-ap} \) |
| Answer» C. \(\frac{2}{π} e^{-ap} \) | |
| 10. |
Fourier Transform of \(e^{-|x|} \, is \) \( \frac{2}{1+p^2} \). Then what is the fourier transform of \( e^{-2|x|} \)? |
| A. | \(\frac{4}{(4+p^2)} \) |
| B. | \(\frac{2}{(4+p^2)} \) |
| C. | \(\frac{2}{(2+p^2)} \) |
| D. | \(\frac{4}{(2+p^2)} \) |
| Answer» B. \(\frac{2}{(4+p^2)} \) | |
| 11. |
In Fourier transform \(f(p) = \int_{-∞}^∞ e^{(ipx)} F(x)dx, e^{(ipx)} \) is said to be Kernel function. |
| A. | True |
| B. | False |
| Answer» B. False | |