Looking at a function of time with a single component of frequency.

When you drag the slider, the “blip” in the spectrum goes up in frequency. So you expect the function of time to go up in frequency too. What you see is that f[τ] has both a real and imaginary part.

ℱ→

𝜈=0 𝜈=32

Slider for setting frequency

The simple sine function turns out to be the complex sine function. In other words, a single “component” of frequency contributes to a complex function of time. And it is the same in the other direction. Now, in the real world you only see real values. The spectra of any real real-time function will necessarily be complex. The next page lets you construct real sine waves from a complex spectrum.

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