Unit 4: The Continuous Time Fourier Transform and Sampling - Practice Quiz

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

2 The inverse Continuous Time Fourier Transform is given by:

3 The Fourier Transform is primarily used to represent a signal in which domain?

4 The Fourier Transform of a periodic signal consists of:

5 The Fourier Transform of is:

6 The linearity property of the Fourier Transform states that if and , then :

7 According to the time-shifting property, if , then transforms to:

8 Convolution in the time domain corresponds to what operation in the frequency domain?

9 The Fourier Transform of the impulse function is:

10 Parseval's relation for the Fourier Transform relates the energy of a signal in the time domain to its energy in the:

11 The frequency-shifting (modulation) property states that multiplying by causes its spectrum to be:

12 Sampling is the process of converting a:

13 According to the sampling theorem, to reconstruct a signal with maximum frequency , the sampling frequency must satisfy:

14 The minimum sampling rate equal to twice the maximum signal frequency is called the:

15 If the highest frequency in a signal is 4 kHz, the Nyquist rate is:

16 Ideal reconstruction of a band-limited signal from its samples is performed using which filter?

17 The interpolation function used in ideal reconstruction from samples is the:

18 Aliasing occurs when a signal is sampled at a rate that is:

19 The main effect of aliasing on a sampled signal is that:

20 In software, the algorithm commonly used to compute the frequency spectrum of a sampled real-world signal is the:

21 The continuous-time Fourier transform of with is:

22 The Fourier transform of a rectangular pulse of unit height and width centered at the origin is:

23 The Fourier transform of a periodic signal consists of:

24 The Fourier transform of is:

25 If , then the Fourier transform of is:

26 According to the convolution property of the CTFT, convolution in time corresponds to which operation in frequency?

27 Using the scaling property, the Fourier transform of for is:

28 Parseval's relation for the CTFT states that the total energy of equals:

29 The duality property implies that if a rectangular pulse in time gives a sinc in frequency, then a sinc in time gives:

30 For a real-valued signal , its Fourier transform satisfies:

31 The differentiation-in-time property gives the Fourier transform of as:

32 A signal band-limited to must be sampled at a minimum rate of:

33 The sampling theorem states that a band-limited signal can be perfectly reconstructed if the sampling frequency satisfies:

34 Ideal impulse-train sampling of with period produces a spectrum that is:

35 Ideal reconstruction of a band-limited signal from its samples uses interpolation with which kernel?

36 A zero-order hold reconstruction produces a staircase output. Its frequency response distortion is best corrected by:

37 A sinusoid is sampled at . The apparent (aliased) frequency observed is:

38 Aliasing occurs when:

39 To prevent aliasing before sampling, a system typically uses:

40 In a software simulation, a sine wave sampled at will appear as a wave of frequency:

41 The continuous-time Fourier transform of for is:

42 If , what is the Fourier transform of ?

43 For a periodic signal with Fourier series coefficients and fundamental frequency , the continuous-time Fourier transform is:

44 A signal is bandlimited to Hz. It is multiplied by before sampling. What is the minimum sampling rate to avoid aliasing of the product?

45 A sinusoid at kHz is sampled at kHz. What apparent (aliased) frequency appears in the baseband kHz?

46 By Parseval's relation, if , then equals:

47 The Fourier transform of the unit step is:

48 In ideal band-limited reconstruction, the interpolation kernel used to reconstruct from samples spaced apart is:

49 If is the transform of , the transform of is:

50 A signal has spectrum nonzero only for Hz (bandpass). What is the theoretical minimum uniform sampling rate exploiting bandpass sampling?

51 Two continuous sinusoids at Hz and Hz are sampled at Hz. After sampling, they become indistinguishable because both alias to:

52 The inverse Fourier transform of (height 1 over ) is:

53 The duality property implies that if , then (function of ) transforms to:

54 The Fourier transform of an impulse train is:

55 When computing the spectrum of a finite-length real-world signal using the DFT/FFT, a rectangular window causes spectral leakage primarily because:

56 A zero-order hold (ZOH) reconstruction filter has frequency response magnitude proportional to:

57 If is real and even, then its Fourier transform is:

58 A signal bandlimited to Hz is sampled at . In the sampled spectrum, aliasing distortion appears in the band:

59 In a simulation, a Hz sine is sampled at Hz and reconstructed. The observed reconstructed frequency is:

60 The Fourier transform of for is: