Discrete time spectrum, finding possible continuous-time signals.

In summary, the discrete-time spectrum of a sampled continuous-time signal x(t) is shown in the figure above, with values of A = 9.8exp(-j0.06π), B = 0.51π, C = -0.27π, and D = 1.9exp(-j0.41π). The sampling frequency is 4928 and the question asks for a possible solution for x(t) from the given options. This is a multiple choice problem and the correct answer is option D.
  • #1
Jd303
35
0
The discrete-time spectrum of a sampled continuous-time signal x(t) is shown in the figure above,
where (A = 9.8exp(-j0.06π), B = 0.51π, C = -0.27π, and D = 1.9exp(-j0.41π) ).
If the sampling frequency is 4928, which of the following continous-time signals is a possible solution for x(t).

The following question is with respect to the diagram attached. I really struggle with these spectrum drawings. Can anyone break this problem down for me, and put me in the right direction?
 

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  • #2
For more context, this is multiple choice with the following values:
A. 9.80cos(1330.56πt + 0.06π) + 1.90cos(2513.28πt - 0.41π)
B. 9.80cos(1064.45πt - 0.06π) + 1.90cos(5026.56πt - 0.41π)
C. 9.80cos(2661.12πt - 0.06π) - 1.90cos(1759.30πt + 0.41π)
D. 9.80cos(1330.56πt - 0.06π) + 1.90cos(2513.28πt + 0.41π)
 

Related to Discrete time spectrum, finding possible continuous-time signals.

1. What is a discrete time spectrum?

A discrete time spectrum is a mathematical representation of a signal in the time domain. It is a sequence of values that represent the amplitude of a signal at different discrete time intervals.

2. How is a discrete time spectrum calculated?

A discrete time spectrum is calculated by taking the Fourier transform of a discrete time signal. This involves converting the signal from the time domain to the frequency domain.

3. What is the difference between a discrete time spectrum and a continuous-time spectrum?

A discrete time spectrum represents a signal that is sampled at discrete time intervals, while a continuous-time spectrum represents a signal that is measured continuously over time. The main difference lies in the way the signal is sampled or measured.

4. How can a discrete time spectrum be used to find possible continuous-time signals?

A discrete time spectrum can be used to find possible continuous-time signals by analyzing the frequency components of the discrete signal. By identifying the dominant frequencies in the spectrum, one can infer the type of continuous-time signal that could have produced it.

5. What are some applications of discrete time spectra?

Discrete time spectra have various applications in signal processing, such as in digital signal processing, communication systems, and system identification. They are also used in fields such as audio and image processing, where signals are typically represented and analyzed in the frequency domain.

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