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2.2 Spectrogram for chirp signals: sampling issues In Lab Assignment 4 you plotted the spectrogram of a linear FM chirp signal. In this assignment you will con- sider how sampling affects a chirp signal. Specifically, you will explore what happens when the instantaneous frequency of the chirp exceeds the sampling frequency. 1. Determine the parameters associated with a chirp signal that starts at 1000 Hz when t = 0 and chirps up to 11,000 Hz at t = 4 s. Include a short explanation of how you derived these parameters in your report. 2. Generate this chirp signal in MATLAB using a sample rate of 4000 Hz. Compute and plot the spectro- gram for this signal. Note that you will need to determine the number of samples in the time window (nwin) to use for your spectrogram plot. You should chose a window length that allows you to check whether the starting/ending frequencies of your chirp are correct. What is the equivalent length of your time window in seconds (Twin)? 3. Explain why the instantaneous frequency seen in the spectrogram is goes up and down between zero and fs/2, i.e., it does not chirp up to 11,000 Hz. There are two effects that should be accounted for in your explanation. 4. Listen to the signal you created using the soundsc command. Does the audio signal agree with the spectrogram plot? Why or why not?

          2.2 Spectrogram for chirp signals: sampling issues
In Lab Assignment 4 you plotted the spectrogram of a linear FM chirp signal. In this assignment you will con-
sider how sampling affects a chirp signal. Specifically, you will explore what happens when the instantaneous
frequency of the chirp exceeds the sampling frequency.
1. Determine the parameters associated with a chirp signal that starts at 1000 Hz when t = 0 and chirps up
to 11,000 Hz at t = 4 s. Include a short explanation of how you derived these parameters in your report.
2. Generate this chirp signal in MATLAB using a sample rate of 4000 Hz. Compute and plot the spectro-
gram for this signal. Note that you will need to determine the number of samples in the time window
(nwin) to use for your spectrogram plot. You should chose a window length that allows you to check
whether the starting/ending frequencies of your chirp are correct. What is the equivalent length of your
time window in seconds (Twin)?
3. Explain why the instantaneous frequency seen in the spectrogram is goes up and down between zero and
fs/2, i.e., it does not chirp up to 11,000 Hz. There are two effects that should be accounted for in your
explanation.
4. Listen to the signal you created using the soundsc command. Does the audio signal agree with the
spectrogram plot? Why or why not?

2.2 Spectrogram for chirp signals: sampling issues
In Lab Assignment 4 you plotted the spectrogram of a linear FM chirp signal. In this assignment you will con-
sider how sampling affects a chirp signal. Specifically, you will explore what happens when the instantaneous
frequency of the chirp exceeds the sampling frequency.
1. Determine the parameters associated with a chirp signal that starts at 1000 Hz when t = 0 and chirps up
to 11,000 Hz at t = 4 s. Include a short explanation of how you derived these parameters in your report.
2. Generate this chirp signal in MATLAB using a sample rate of 4000 Hz. Compute and plot the spectro-
gram for this signal. Note that you will need to determine the number of samples in the time window
(nwin) to use for your spectrogram plot. You should chose a window length that allows you to check
whether the starting/ending frequencies of your chirp are correct. What is the equivalent length of your
time window in seconds (Twin)?
3. Explain why the instantaneous frequency seen in the spectrogram is goes up and down between zero and
fs/2, i.e., it does not chirp up to 11,000 Hz. There are two effects that should be accounted for in your
explanation.
4. Listen to the signal you created using the soundsc command. Does the audio signal agree with the
spectrogram plot? Why or why not?

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