19. Exercise 4: Solution

Key Takeaways

• We need to use the STFT or spectrogram to visualize a non-stationary signal in the frequency domain effectively.
• We can also use a spectrogram to visualize the effect of a bandpass filter on our signal.
• Again, matplotlib and numpy are our friends here.

Further Resources

Plotting a spectrogram or visualizing the short-time Fourier transform are ways of balancing the trade-off between time resolution and frequency resolution.

Surprisingly, this trade-off is related to the quantum uncertainty principle. If you would like to know more about Quantum Uncertainty Principle, you can watch 3Blue1Brown's video The more general uncertainty principle, beyond quantum.

This tutorial is a great explanation of this trade-off as well as a description of the wavelet transform, which is another solution to this problem.