Basic Signals & Systems Questions on “Gibb’s Phenomena, Convergence of Fourier Series”.
1. When is the gibbs phenomenon present in a signal x(t)?
A. Only when there is a discontinuity in the signal
B. Only when the signal is discrete
C. Only when there is a jump discontinuity in the signal
D. Gibbs phenomenon is not possible in continuous signals
Answer: C
Clarification: The gibbs phenomenon present in a signal x (t), only when there is a jump discontinuity in the signal.
2. Where does the gibbs phenomenon occur?
A. Gibbs phenomenon occurs near points of discontinuity
B. Gibbs phenomenon occurs only near points of discontinuity
C. Gibbs phenomenon occurs only ahead of points of discontinuity
D. Gibbs phenomenon does not occur near points of discontinuity
Answer: B
Clarification: The gibbs phenomenon present in a signal x(t), only when there is a jump discontinuity in the signal. Gibbs phenomenon occurs only near points of discontinuity that is approximated by a fourier series in which only a finite number of terms are kept constant.
3. What causes the gibbs phenomenon?
A. Abruptly terminating the signals
B. Abruptly integrating the signals
C. x(t) should be continuous only
D. Signal should be discontinuous
Answer: A
Clarification: In case gibbs phenomenon, When a continuous function is synthesized by using the first N terms of the fourier series, we are abruptly terminating the signal, giving weigtage to the first N terms and zero to the remaining. This abrupt termination causes it.
4. When a continuous function is synthesized by using the first N terms of the fourier series does the gibbs phenomenon occur?
A. True
B. False
Answer: B
Clarification: The gibbs phenomenon present in a signal x(t), only when there is a jump discontinuity in the signal. When a continuous function is synthesized by using the first N terms of the fourier series, the synthesized function approaches the signal for all t↔∞. No gibbs phenomenon occurs.
5. When is fourier convergence theorem applicable?
A. Infinite series limit
B. Continuous function limit
C. Discrete function limit
D. Break point limits
Answer: A
Clarification: According to fourier convergence theorem, near a point of discontinuity the fourier series approximation oscillates about the numerical value it should achieve, which is valid in an infinite series limit.
6. What is the fourier convergence theorem?
A. Fourier series approximation oscillates about the numerical value
B. Fourier coefficients converge near a discontinued point
C. In any finite interval, x (t) is of unbounded variation
D. In majority finite interval, x(t) is of unbounded variation
Answer: A
Clarification: According to fourier convergence theorem, near a point of discontinuity the fourier series approximation oscillates about the numerical value it should achieve. This is valid in an infinite series limit.
7. The overshoot near discontinuity vanishes as more and modes are retained.
A. True
B. False
Answer: B
Clarification: The overshoot near discontinuity does not vanish as more and modes are retained. Instead, the overshoot is finite no matter what finite numbers of modes N are retained.
8. What is the overshoot number?
A. Infinite
B. Finite
C. Zero
D. More than 10
Answer: B
Clarification: The overshoot near discontinuity does not vanish as more and modes are retained. Instead, the overshoot is finite no matter what finite numbers of modes N are retained. Even though the region of overshoot gets progressively smaller as N ↔∞.