Role of sampling Effect of sampling

\( N \) discrete measurements (samples) of the ideal continuous wave.
Change \( N \); how does the information provided by the FFT \( Y(\omega) \) change?

DFT simulator

Questions

  1. The length of the sample is fixed at \( L=10 \) s. For \( N=4 \) samples (default setting), what is the minimum nonzero frequency that the FFT can resolve? State the theory and verify it in the FFT.
  2. For \( N=4 \) samples (default setting), what is the frequency resolution of the FFT? (i.e. what is the spacing between the zeroth and first or first and second frequency bins), and how does this compare with your answer in a?
  3. Does your answer in a, b change if you take more samples? Try increasing \( N \) and see.
  4. For \( N=4 \) samples (default setting), what is the highest frequency you can resolve with the FFT? Sketch the sampled waveform for the Nyquist frequency.
  5. What is the minimum number of samples needed to measure a frequency of \( 5 \) Hz? State the theory and verify on the plot.