Let's go through each question one by one:

Question 1: "I have a periodic signal with known period and I can determine An and Bn for the signal. This is sufficient to plot the spectrum of that signal."

• Answer: True
  • If you know the period of a periodic signal and can determine the Fourier coefficients $A_n$ and $B_n$, you can reconstruct the signal's Fourier series. This series essentially provides the frequency components (spectrum) of the signal, so you can plot its spectrum directly from this information.

Question 2: "The maximum frequency that can be displayed on the spectrum plot equals:"

• Answer: Half of the sampling frequency
  • This is the Nyquist-Shannon sampling theorem. When you sample a signal, the highest frequency that can be correctly represented (without aliasing) is half the sampling frequency. This is called the Nyquist frequency.

Question 3: "The frequency resolution for the spectral plot is solely determined by:"

• Answer: The number of data points acquired
  • The frequency resolution is determined by the total duration of the signal and the number of points in the Fourier Transform. The more data points you have (or the longer the signal duration), the better the frequency resolution in your spectrum.

Question 4: "Spectral leakage is (Choose the best answer only):"

• Answer: Associated with both amplitude ambiguity and signal energy leakage to other frequency bins.
  • Spectral leakage occurs when a signal that isn't perfectly periodic within the sampling window leads to energy spreading across multiple frequency bins, causing inaccuracies in the amplitude and frequency estimation. This is not just about amplitude ambiguity but also the energy distribution.

Question 5: "To improve the spectral variance:"

• Answer: Acquire and average multiple signal records
  • Averaging multiple signal records helps reduce the variance in the spectral estimate by mitigating random noise and fluctuations, improving the precision of the frequency spectrum.

Would you like further clarification on any of these answers? Or would you like to dive deeper into any of the topics?

Additional questions to consider:

1. How does the number of points in a Fast Fourier Transform (FFT) affect the frequency resolution?
2. What would happen if the sampling frequency is below twice the maximum frequency of the signal?
3. How does windowing affect spectral leakage?
4. How can you determine the signal's fundamental frequency from its spectrum?
5. Why is the Nyquist frequency important for signal sampling?

Tip: Always ensure your sampling rate is at least twice the highest frequency component of your signal to avoid aliasing and spectral inaccuracies.