Plotting Signals in the Frequency Domain

Summary

When we look at signals in the frequency domain, we lose information about the time-domain. Previously this hadn’t been a problem because we were looking at signals whose frequency components did not change over time. They were stationary. However, most signals we deal with will not be stationary. In this case, it is better to visualize the frequency components of a signal over time using either a:

• Short-Time Fourier Transform
• Spectrogram

Notebook Review

If you wanted to interact with the notebook in the video, you can access it here in the repo /intro-to-dsp/walkthroughs/frequency-domain-plotting/ or in the workspace below.

New Vocabulary

• Frequency component: The Fourier transform explains a signal as a sum of sinusoids. Each of these sinusoids is a frequency component of the signal.
• Stationarity: A property of a signal where the statistics of a process generating a signal do not change in time. Generally, if the frequency components in a signal change in time, this signal is not stationary.

Exercise 4: Spectrograms

Instructions

1. Complete the Offline or Online instructions below.
2. Read through the whole .ipynb.
3. Complete all the code cells that contain ## Your Code Goes Here.
4. Complete all the markdown cells that contain TODO.

Offline

1. In the repo which you can access here in the repo /intro-to-dsp/exercises/4-spectrograms/ you should find the following files
   • 4_spectrograms.ipynb
   • exercise4.npz
2. Open up the python notebook and associated files in your desired editor.

Note: Instructions can be found in Introduction to Wearable Data's Concept Developer Workflow for how to set up your local environment.

Online

1. Go to the next concept and the 4_spectrograms.ipynb should be open and the workspace should already contain the appropriate exercise4.npz file.