Unit 3: Fourier series representation of periodic signals - Practice Quiz

1 A signal is said to be periodic with period if it satisfies which of the following conditions for all ?

2 The Fourier series is used to represent which type of signals?

3 The fundamental frequency of a continuous-time periodic signal with period is given by:

4 In the exponential Fourier series, a periodic signal is expressed as a weighted sum of which basis functions?

5 The Fourier series coefficient of a continuous-time periodic signal is computed as:

6 The Fourier series coefficient represents which quantity of the signal?

7 In the trigonometric Fourier series, a periodic signal is expressed using which functions?

8 The harmonics in a Fourier series occur at frequencies that are:

9 The conditions that guarantee the convergence of a Fourier series are known as:

10 One of the Dirichlet conditions requires that over one period, the signal must be:

11 According to the Dirichlet conditions, the number of maxima and minima of in one period must be:

12 The behavior in which the Fourier series overshoots near a discontinuity of the signal is called:

13 According to the Dirichlet conditions, the number of discontinuities in one period must be:

14 If a periodic signal is real and even, its Fourier series coefficients are:

15 According to the linearity property, if and , then has coefficients:

16 A time shift of a periodic signal, , affects its Fourier coefficients by:

17 Parseval's theorem for Fourier series relates the average power of a periodic signal to:

18 If is a real signal, its Fourier coefficients satisfy the conjugate symmetry property:

19 In software tools like MATLAB, the frequency spectrum of a periodic signal is commonly plotted using:

20 The plot of the magnitudes of Fourier coefficients against frequency is called the:

21 A periodic signal has a fundamental period of ms. What is its fundamental frequency in radians per second?

22 Two periodic signals have periods s and s. What is the fundamental period of their sum?

23 For the Fourier series synthesis equation , which expression correctly gives the analysis (coefficient) equation?

24 The signal is expressed in exponential Fourier series form. What are the nonzero coefficients?

25 For a real-valued periodic signal , what is the relationship between the Fourier coefficients and ?

26 The DC component (average value) of a periodic signal corresponds to which Fourier series coefficient?

27 A periodic square wave with period has value 1 for half the period and 0 for the other half. What is its DC coefficient ?

28 Which of the following is NOT one of the Dirichlet conditions for the convergence of a Fourier series?

29 At a point of discontinuity in a periodic signal, the Fourier series converges to which value?

30 The overshoot near discontinuities that persists even as more Fourier terms are added is known as:

31 As the number of harmonics used to reconstruct a signal increases, the Gibbs overshoot near a discontinuity:

32 If , what are the Fourier series coefficients of the time-shifted signal ?

33 If with fundamental frequency , the coefficients of are:

34 Parseval's relation for continuous-time periodic signals states that the average power equals:

35 If is a real and even periodic signal, its Fourier series coefficients are:

36 Using the frequency-shift property, if , then has coefficients:

37 The Fourier series coefficients of the time-reversed signal , given , are:

38 When plotting the magnitude spectrum of a periodic signal in software, the horizontal axis is best represented as:

39 In simulating a periodic signal's Fourier spectrum, why does using more harmonics improve the reconstructed waveform for signals with sharp edges?

40 When numerically computing Fourier coefficients of a periodic signal over one period using samples, the integration step size should be:

41 A continuous-time periodic signal has exponential Fourier series coefficients with fundamental frequency . What is the average power of the signal?

42 Let have Fourier coefficients with period . The signal has coefficients . Which expression is correct?

43 For a square wave with jump discontinuities, the Fourier series exhibits the Gibbs phenomenon. As the number of terms , the maximum overshoot near a discontinuity of unit height:

44 If is real and its Fourier coefficients satisfy (real and even), then must be:

45 The Fourier series coefficient of a periodic signal equals:

46 Given with coefficients and period , the derivative has Fourier coefficients:

47 Two periodic signals and with the same period have coefficients and . The coefficients of the product are given by:

48 Which of the following is NOT one of the Dirichlet conditions guaranteeing convergence of the Fourier series?

49 For a periodic impulse train , the Fourier series coefficients are:

50 If is real and odd, its Fourier series coefficients are:

51 A signal with period has coefficients . The time-scaled signal (with ) has period and coefficients:

52 Consider . How many nonzero exponential Fourier series coefficient pairs (positive and negative ) does it contain?

53 The rate at which Fourier coefficients decay as depends on signal smoothness. For a signal that is continuous but has a discontinuous first derivative, the coefficients decay as:

54 When numerically computing Fourier coefficients of a periodic signal via the FFT, sampling the signal below the Nyquist rate of its highest significant harmonic causes:

55 In an FFT-based spectral analysis of a periodic signal, spectral leakage is most effectively minimized by:

56 If a periodic signal satisfies (half-wave odd symmetry), then its Fourier series contains:

57 A periodic signal has trigonometric Fourier series with (cosine) and (sine) coefficients. The relationship to the exponential coefficient (for ) is:

58 The Fourier series of a signal converges to the value at a point where the signal has:

59 For a real periodic signal, Parseval's theorem relates average power to coefficients as . If the DC coefficient is and a single harmonic pair has , with all others zero, the total average power is:

60 The primary reason sinusoids (complex exponentials) are chosen as basis functions for representing periodic signals in LTI system analysis is that they are: