7. Example Problems and Applications

Try these first

1. 1.

   What is the purpose of a notch filter?

   Hint

   Think of a frequency that often causes issues in measuring devices.

2. 2.

   Define leakage in frequency analysis.

   Hint

   It relates to how accurately we can read a signal's peaks.

3. 3.

   What do digital filters do in signal processing?

   • Allow all frequencies
   • Remove unwanted frequencies
   • Amplify all frequencies

   Hint

   Consider the functionalities of filters discussed in class.

4. 4.

   True or False: Leakage can enhance the clarity of frequency analysis.

   • True
   • False

   Hint

   Think about how misalignment affects data.

5. 5.

   You have a sampling rate of 1000 Hz and want to analyze a signal with 2048 data points. Calculate the frequency resolution and discuss its implications for distinguishing between two close frequencies of 50 Hz and 51 Hz.

   Hint

   Use the frequency resolution formula.

6. 6.

   Describe a scenario where applying a Hamming window might improve the clarity of frequency analysis over a rectangular window. What effect does the windowing function have on leakage?

   Hint

   Consider what happens to edges in your data.