Unit 4 - Practice Quiz

1 The Continuous Time Fourier Transform (CTFT) of an aperiodic signal is defined as:

2 Which of the following conditions guarantees the convergence of the Fourier Transform (Dirichlet conditions)?

3 The inverse Fourier transform is given by:

4 What is the Fourier Transform of the impulse signal ?

5 The Fourier transform of the signal for is:

6 What is the Fourier Transform of a constant signal ?

7 The Fourier Transform of a rectangular pulse is a:

8 In the context of periodic signals, the Fourier Transform consists of:

9 What is the Fourier Transform of ?

10 If is real and even, its Fourier Transform is:

11 If , then the linearity property states that transforms to:

12 The time-shifting property states that if , then transforms to:

13 The frequency-shifting property implies that multiplying by results in:

14 Regarding the time-scaling property, if , then transforms to:

15 What is the Fourier Transform of the derivative ?

16 The convolution property states that convolution in the time domain corresponds to what in the frequency domain?

17 Parseval's relation for aperiodic signals states that the total energy in the time domain equals:

18 The multiplication property states that corresponds to:

19 What is the duality property of the Fourier Transform?

20 The integration property results in:

21 When simulating the frequency spectrum of a real-world signal using software, which algorithm is typically used?

22 In a software simulation, plotting versus yields the:

23 The process of converting a continuous-time signal into a discrete-time signal by selecting values at specific time instants is called:

24 Mathematically, ideal sampling can be represented as multiplying the continuous signal by:

25 The Sampling Theorem (Nyquist-Shannon) states that a signal can be perfectly reconstructed if the sampling frequency satisfies:

26 The minimum sampling rate required to avoid aliasing is called the:

27 What is the Nyquist interval for a signal with maximum frequency ?

28 If a signal is sampled, what is the Nyquist rate?

29 The spectrum of a sampled signal consists of:

30 Undersampling occurs when:

31 The phenomenon where high-frequency components of a signal appear as lower frequencies in the sampled version is known as:

32 To recover the continuous signal from its samples , we pass the sampled signal through a:

33 The ideal interpolation formula for reconstructing a band-limited signal is based on which function?

34 In the frequency domain, the ideal reconstruction filter should have a gain of and a cut-off frequency of:

35 Which of the following is an example of a practical (non-ideal) reconstruction method?

36 If a signal with max frequency 10 kHz is sampled at 15 kHz, what will happen?

37 An anti-aliasing filter is placed:

38 In software simulation of undersampling, if a 90 Hz sine wave is sampled at 100 Hz, it will appear as a sine wave of what frequency?

39 The 'wagon wheel effect' in movies, where wheels appear to rotate backwards, is a visual example of:

40 If is the spectrum of , and is real-valued, then is:

41 What happens to the spectrum if a signal is compressed in time ()?

42 What is the value of (the DC component)?

43 The Fourier Transform of the unit step function involves:

44 Which property explains why sharp transitions in time (like a square wave) result in high-frequency components in the spectrum?

45 In the context of sampling, the 'Guard Band' is:

46 If a signal is band-limited to Hz, its energy is:

47 The First-Order Hold (FOH) interpolation connects sample points with:

48 The Energy Spectral Density (ESD) is defined as:

49 When sampling at exactly the Nyquist rate (), reconstruction can be problematic if:

50 Which of the following signals cannot be sampled without aliasing (conceptually)?