Practice Discrete Fourier Transform (dft) (11.11) - Fourier Transform and Properties

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6 sample questions

Question 1.
What does DFT stand for?
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Focus on the process of transforming discrete signals.
Question 2.
True or False: The Fast Fourier Transform (FFT) is slower than DFT.
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Think about the computational efficiency of FFT.
3Question 3.
What does the DFT transform?
- Time-domain samples into frequency-domain
- Frequency-domain into time-domain
- Both
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Consider what signals are transformed through DFT.
4Question 4.
True or False: Inverse DFT reconstructs the original signal from its frequency representation.
- True
- False
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Think about the cyclical nature of the transformation.
Question 5.
Consider a signal consisting of five samples with values [1,2,3,4,5]. Calculate the DFT using the definition. What are the resulting frequency components?
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Detail each step of the formula for clarity.
Question 6.
Discuss the limitations of DFT when applied to non-periodic signals and the importance of windowing.
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Think about the implications of discontinuities in signals.

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