MCQOPTIONS
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MCQOPTIONS
This section includes 14 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. |
Given x (t) = 1, |t|<T1; 0, T1<|t|< ( frac{T_0}{2} ). The DC component of x(t) is ___________ |
| A. | ( frac{T_1}{T_0} ) |
| B. | ( frac{2T_1}{T_0} ) |
| C. | ( frac{T_1}{2T_0} ) |
| D. | ( frac{T_0}{T_1} ) |
| Answer» C. ( frac{T_1}{2T_0} ) | |
| 2. |
The Inverse Fourier transform of the signal 2 ( ) + ( -4 ) + ( +4 ) is ______________ |
| A. | 2 (1 cos 4 t) |
| B. | (1 cos 4 t) |
| C. | 1 + cos 4 t |
| D. | 2 (1 + cos 4 t) |
| Answer» D. 2 (1 + cos 4 t) | |
| 3. |
The Fourier transform of the signal u(t+1) 2u(t) + u(t-1) is ____________ |
| A. | ( frac{2 sin u2061 -2}{j } ) |
| B. | ( frac{2 cos u2061 -2}{j } ) |
| C. | ( frac{2 cos u2061 +2}{j } ) |
| D. | ( frac{2 sin u2061 +2}{j } ) |
| Answer» C. ( frac{2 cos u2061 +2}{j } ) | |
| 4. |
The Fourier transform of the signal e-|t| in [-2,2] is _____________ |
| A. | ( frac{2 + 2e^{-2} cos u20612 + 2 e^{-2} ,sin u20612 }{1- ^2} ) |
| B. | ( frac{2 2e^{-2} cos u20612 2 e^{-2} ,sin u20612 }{1+ ^2} ) |
| C. | ( frac{2 2e^{-2} cos u20612 + 2 e^{-2} ,sin u20612 }{1+ ^2} ) |
| D. | ( frac{2 + 2e^{-2} cos u20612 + 2 e^{-2} ,sin u20612 }{1- ^2} ) |
| Answer» D. ( frac{2 + 2e^{-2} cos u20612 + 2 e^{-2} ,sin u20612 }{1- ^2} ) | |
| 5. |
The Fourier transform of the signal ( frac{1}{a^2+w^2} ) is _____________ |
| A. | ( frac{ }{a} e^{a| |} ) |
| B. | ( frac{ }{a} e^{-a| |} ) |
| C. | ( frac{2}{a} e^{-a| |} ) |
| D. | ( frac{ }{a} e^{a| |} ) |
| Answer» C. ( frac{2}{a} e^{-a| |} ) | |
| 6. |
The Fourier transform of the signal u (t) is ____________ |
| A. | ( ) |
| B. | ( frac{1}{j } ) |
| C. | ( ) + ( frac{1}{j } ) |
| D. | ( frac{1}{j } ) |
| Answer» D. ( frac{1}{j } ) | |
| 7. |
The Fourier transform of the signal sgn (t) is ____________ |
| A. | ( frac{-2}{j } ) |
| B. | ( frac{4}{j } ) |
| C. | ( frac{2}{j } ) |
| D. | ( frac{1}{j } + 1 ) |
| Answer» D. ( frac{1}{j } + 1 ) | |
| 8. |
The Fourier transform of the signal sin(2 t) e-t u (t) is ____________ |
| A. | ( frac{1}{2j} left( frac{1}{1+j( -2 )} + frac{1}{1+j( +2 )} right) ) |
| B. | ( frac{1}{2j} left( frac{1}{1+j( -2 )} frac{1}{1+j( +2 )} right) ) |
| C. | ( frac{1}{2j} left( frac{1}{1+j( +2 )} frac{1}{1+j( -2 )} right) ) |
| D. | ( frac{1}{j} left( frac{1}{1+j( +2 )} frac{1}{1+j( -2 )} right) ) |
| Answer» C. ( frac{1}{2j} left( frac{1}{1+j( +2 )} frac{1}{1+j( -2 )} right) ) | |
| 9. |
For a periodic signal () = 30 sin 1000 + 10 cos 3000 + 6 sin(5000 + 4), the fundamental frequency in rad/s is __________ |
| A. | 1000 |
| B. | 3000 |
| C. | 5000 |
| D. | 15000 |
| Answer» B. 3000 | |
| 10. |
The Fourier transform of the signal ( _{m=0}^ a^m (t-m) ) is _____________ |
| A. | ( frac{1}{1+ae^{-j }} ) |
| B. | ( frac{1}{1+ae^{j }} ) |
| C. | ( frac{1}{1-ae^{j }} ) |
| D. | ( frac{1}{1-ae^{-j }} ) |
| Answer» E. | |
| 11. |
The trigonometric Fourier series of an even function of time does not have ___________ |
| A. | The dc term |
| B. | The cosine terms |
| C. | The sine terms |
| D. | The odd harmonic terms |
| Answer» D. The odd harmonic terms | |
| 12. |
The Fourier transform of the signal (t+1) + (t-1) is ____________ |
| A. | ( frac{2}{1+j } ) |
| B. | ( frac{2}{1-j } ) |
| C. | 2 cos |
| D. | 2 sin |
| Answer» D. 2 sin | |
| 13. |
The trigonometric Fourier series of a periodic time function can have only ___________ |
| A. | Only cosine terms |
| B. | Only sine terms |
| C. | Both cosine and sine terms |
| D. | Dc and cosine terms |
| Answer» E. | |
| 14. |
The Fourier series of an odd periodic function, contains __________ |
| A. | Only odd harmonics |
| B. | Only even harmonics |
| C. | Only cosine terms |
| D. | Only sine terms |
| Answer» E. | |