Unit 3 - Practice Quiz

1 Which of the following signals can be represented by a Fourier Series?

2 The condition for a signal to be periodic with period is:

3 In the trigonometric Fourier series representation, the term represents:

4 The fundamental angular frequency is related to the time period by:

5 Which of the following is the correct synthesis equation for the Exponential Fourier Series?

6 The set of functions form an:

7 For the Exponential Fourier Series coefficient , what is the value of ?

8 If a periodic signal is even, i.e., , its Trigonometric Fourier Series contains:

9 If a periodic signal is odd, i.e., , which coefficients are zero?

10 The relationship between the exponential Fourier coefficient and trigonometric coefficients (for ) is:

11 The Dirichlet conditions provide sufficient conditions for:

12 Which of the following is NOT a Dirichlet condition?

13 At a point of discontinuity , the Fourier series of converges to:

14 The Gibbs phenomenon refers to:

15 For a real-valued signal , the exponential Fourier series coefficients satisfy the conjugate symmetry property:

16 A signal has half-wave symmetry if:

17 A signal with half-wave symmetry contains only:

18 Parseval's relation for the Exponential Fourier Series states that the average power is:

19 If , then the coefficients of the time-shifted signal are:

20 If , then the coefficients of the time-reversed signal are:

21 The Fourier series coefficients of the derivative of a periodic signal are related to (coefficients of ) by:

22 For the integration property to hold (i.e., coefficients become ), what condition must the signal satisfy?

23 Multiplication of two periodic signals and in the time domain corresponds to what operation on their Fourier series coefficients?

24 The plot of versus frequency (or index ) is known as the:

25 For a real-valued signal, the magnitude spectrum is:

26 For a real-valued signal, the phase spectrum is:

27 The Fourier series of an Impulse Train consists of:

28 If a signal is real and even, its exponential Fourier coefficients are:

29 If a signal is real and odd, its exponential Fourier coefficients are:

30 The frequency spectrum of a continuous time periodic signal is:

31 What happens to the Fourier coefficients if the signal is time-scaled to where ?

32 Which signal has Fourier coefficients that decay as ?

33 Which signal has Fourier coefficients that decay as ?

34 When simulating the frequency spectrum of a periodic signal using software, the spacing between spectral lines is determined by:

35 In a software simulation, calculating Fourier Series coefficients often involves numerical integration. Which method effectively implements this for discrete data?

36 The Power Spectral Density (PSD) of a periodic signal describes:

37 If , the exponential Fourier coefficients are:

38 If , the exponential Fourier coefficients are:

39 What is the Fourier Series representation of a constant signal ?

40 The linearity property of Fourier Series implies that if , then its coefficients are:

41 Frequency shifting: If the coefficients are shifted to , the time domain signal becomes:

42 The Fourier series expansion of a periodic square wave with zero DC value contains:

43 If a periodic signal is decomposed into even and odd parts , then generates:

44 The total power of a periodic signal is 10 W. If the DC component power is 2 W, what is the power contained in the AC components?

45 Why is the exponential form of Fourier series often preferred over the trigonometric form in software simulation and analysis?

46 For a periodic signal , if , the Fourier Series becomes:

47 Which mathematical tool is used to prove the orthogonality of the basis functions in Fourier Series?

48 If a periodic signal is time-shifted, which aspect of its spectrum changes?

49 In the context of software simulation, 'Aliasing' would occur if:

50 The RMS value of a periodic signal can be calculated from the Fourier coefficients as: