11.11. Discrete Fourier Transform (DFT)

Try these first

1. 1.

   What does DFT stand for?

   Hint

   Focus on the process of transforming discrete signals.

2. 2.

   True or False: The Fast Fourier Transform (FFT) is slower than DFT.

   Hint

   Think about the computational efficiency of FFT.

3. 3.

   What does the DFT transform?

   • Time-domain samples into frequency-domain
   • Frequency-domain into time-domain
   • Both

   Hint

   Consider what signals are transformed through DFT.

4. 4.

   True or False: Inverse DFT reconstructs the original signal from its frequency representation.

   • True
   • False

   Hint

   Think about the cyclical nature of the transformation.

5. 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?

   Hint

   Detail each step of the formula for clarity.

6. 6.

   Discuss the limitations of DFT when applied to non-periodic signals and the importance of windowing.

   Hint

   Think about the implications of discontinuities in signals.