6.2. Discrete Fourier Transform (DFT) and FFT

Try these first

1. 1.

   What does DFT stand for?

   Hint

   Think about what it means to analyze a discrete signal.

2. 2.

   What is the primary purpose of FFT?

   Hint

   Consider its speed advantage over DFT.

3. 3.

   What does the DFT allow us to do?

   • A. Identify time-domain characteristics
   • B. Analyze frequency components of signals
   • C. Reduce data size

   Hint

   Think about the main function of DFT in signal analysis.

4. 4.

   True or False: The FFT is a slower method for computing the DFT.

   • True
   • False

   Hint

   Recall the speed advantage of FFT.

5. 5.

   Analyze a time signal with irregular intervals and compute its DFT. How would you ensure accurate frequency representation?

   Hint

   Consider how time samples affect frequency resolution.

6. 6.

   Given a sampled signal of 2048 points at 2000 Hz, calculate its frequency resolution and explain its significance.

   Hint

   Apply the resolution formula discussed.