A MOCK-SAD FACE

1560 4D

I decided to visit the Archives. I went to a local outlet not far from Tyrae and latched in.

“Welcome, Deng Bai-Xin. What would you like to find?” The ainon who greeted me gave me that dazzling female smile. As usual she wore very little. I never understood why distracting Archive visitors seemed to be such a priority.

“Tell me what a transform is.”

“There are a lot of them. They’re just maps from one domain to another, sometimes back into the same domain. Translations are transforms. So are mathematical functions.”

“Could you give me an example of a mathematical transform?”

She nodded. “Two of the most familiar examples are the Laplace transform and the Fourier transform.” The names from ancient Earth seemed to come awkwardly to her, but I had no way of knowing how they should actually sound. “The first one maps a real-number domain to an exponential domain to simplify solving differential equations. The second one maps between time domains and frequency domains, and allows the simplified characterization of periodic waveforms.”

That made me ask, “Waveforms? Like oscillations?”

“Yes.”

“Like the lines on the City street walls and floors?”

“I’m sorry. That is a protected region of the Archives. You will need special permission to access that region.” She made a mock-sad face. “Would you like to see illustrations of waveform analysis using Fourier transforms?”

“All right,” I said, disappointed. “Show me your demos.”

She smiled like the sun far above.

When she was finished, my head rattled and spun. One diagram from her presentation stood out in my mind:

One the left, a set of waveforms. On the right, the transformed counterparts of each of those waveforms. I noted how each undulating line on the left – a waveform – corresponded to a set of vertical lines on the right – a set of frequencies making up the frequency spectrum of each line. The height of each vertical line was an amplitude. I studied the diagram on my datasheet. At last, somewhere in my brain, a light switched on.