The Short Time Fourier Transform and the Spectrogram

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Question 1 of 3

1. Question
Select the purpose of the short-time Fourier transform (STFT).
- The STFT is used to find the DFT of signals with very few data samples.
- The STFT is used to determine how the spectral content of a signal changes with time.
- The STFT is used when you are short on time finishing a project and need a Fourier transform that runs very fast.
- The STFT is used to speed up, or shorten, time in a signal so that it plays back faster than it was recorded.
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Question 2 of 3

2. Question
Which of the following statements describe the method for computing the short-time Fourier transform of a signal with $N$ samples?
- Take the DFT of all $N$ samples, then apply different windows in the frequency domain to obtain the spectral components for different time windows.
- Break the $N$ samples up into shorter segments that possibly overlap, then take separate DFTs of each segment and display the DFT coefficients as a function of time.
- Apply the $N$ samples as the input to a time-varying filter that scans for short bursts of sinusoids display the sinusoid frequency as a function of time.
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Question 3 of 3

3. Question
What factors should be considered in choosing the segment length $L$ when computing the short-time Fourier transform?
- $L$ determines temporal resolution for analyzing any changes in the signal spectral content; as $L$ increases, evidence of changes in spectral content becomes blurred over a larger temporal interval.
- $L$ determines frequency resolution; as $L$ increases, we can more easily separate closely spaced frequency components.
- $L$ determines frequency resolution; as $L$ decreases, we can more easily separate closely spaced frequency components.
- $L$ determines the frequency band represented in the STFT; when $L$ is small, we can only see low frequencies and high frequencies are not represented.
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The Short Time Fourier Transform and the Spectrogram

The Short Time Fourier Transform and the Spectrogram

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