# Frequency Domain

When we start in most engineering and physics topics, we look at things from a time perspective, because that is most familiar to most of us and most natural. However, as we work with audio, communication, or radio frequency signals, it makes more sense to view these signals as a function of the signal’s spectrum - its frequency components. In this chapter, Dr. Johnson goes over the way these spectrums are found via the Fourier transform and how this transform has been simplified into the powerful and ubiquitous fast Fourier transform, or FFT. The basic premise for this is that all signals can be represented by sinusoids of different frequencies that are superimposed. This creates both constructive and destructive interference and yields the original signal.

Once we learn about how we turn time-based signal into frequency-based signals, we go over those systems that treat input signals the same no matter when they’re input. Whether it’s now or 5 seconds or 5 years in the future, the output will be the same, just shifted an equal amount of the output, and has a linear output, meaning that if you sum the inputs or outputs of the system, they should be the same. These are linear time invariant systems and are both common and extremely important.

As a practical example and because speech recognition is becoming ubiquitous, Dr. Johnson devotes an entire chapter on how to model a speech signal, starting with going over how our own lungs and mouth works. Once we get a better understanding of how we make sounds as human beings, we learn about the energy levels and frequencies of each sound.

Meta-description:

In chapter 4, we learn about audio, communication, and radio frequency signals with Fourier transforms. Review linear time invariant (LTI) systems and speech recognition.