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Signal Processing Word Cloud

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Description

This MicroSim displays 51 key terms from signal processing as a word cloud. In the embedded view each term is drawn at a font size equal to half its weight in pixels. The weights run from 18 to 80, so "Signal Processing" (weight 80) is drawn at 40 px and the smallest terms, such as "Notch Filter" (weight 18), are drawn at 9 px. In a larger window, such as fullscreen, every word is scaled up by the same factor so the cloud still fills the window. Each word has a 50% chance of being turned through 90 degrees and receives a random dark color, so every load gives a different arrangement while the size ordering never changes.

There are no sliders or buttons. The only interaction is to reload the page, which runs the placement algorithm again. The terms and weights are stored in words.json in this folder and are drawn with the wordcloud2.js library.

The cloud previews the vocabulary of the book: transforms (Fourier, Z, Laplace, wavelet, Hilbert), filters (lowpass, bandpass, notch, Butterworth, Chebyshev), sampling and rate conversion (aliasing, decimation, interpolation) and system properties (impulse response, causality, linear time-invariance). The weights are rough estimates of how often a term is mentioned in a typical college-level signal processing textbook. They were suggested by an AI assistant and were not counted from a real corpus, so read size as relative emphasis, not as a measured frequency.

The terms are introduced throughout the book, starting with Chapter 2: Introduction to Signals and Systems.

Lesson Plan

Learning Objectives

After using this MicroSim, students will be able to:

  1. Recall at least 15 of the 51 signal processing terms shown in the cloud.
  2. Classify the terms into families such as transforms, filters, and sampling and rate conversion.
  3. Relate a word's weight to its rendered font size and compare two words by that ratio.
  4. Evaluate what a word cloud does and does not show, separating how often a term is mentioned from how important it is.
  5. Predict the chapter of this book that introduces a given term.

Target Audience

College undergraduates in electrical engineering, computer science, data science or applied mathematics at the start of a signal processing course, or reviewing its vocabulary before an exam.

Prerequisites

None. Students do not need to know what any of the terms mean yet.

Activities

  1. Reload and compare (3 minutes). Reload the page three times. Positions, rotations and colors change each time, but "Signal Processing" is always the largest word (40 px) and "Filter" (35 px) is always the second largest. Which words are always among the smallest? "Notch Filter", "Phase Shift" and "Fast Fourier Transform (FFT)" share the lowest weight, 18, so they are drawn at 9 px.
  2. Sort into families (10 minutes). On paper, group the 51 terms into families. Count the terms containing the word "Transform" and the terms containing the word "Filter". Seven terms contain "Transform" and seven contain "Filter" (the plain term "Filter" included).
  3. Predict the chapter (10 minutes). For each of Convolution, Aliasing, Z-Transform, Butterworth Filter and Decimation, write down the chapter you expect to introduce it, then check the chapter pages. Convolution is in Chapter 4, Aliasing in Chapter 5, Z-Transform in Chapter 8, Butterworth Filter in Chapter 10 and Decimation in Chapter 13.
  4. Find the gaps (10 minutes). The cloud has "Lowpass Filter", "Bandpass Filter" and "Notch Filter" but no "Highpass Filter", "FIR Filter" or "IIR Filter". Which important terms would you add, and what weight would you give them? Chapter 9 lists High-Pass Filters, FIR Filters and IIR Filters as concepts; Chapter 14 lists Spectrogram. Weights are a judgment call, so justify yours.

Assessment

  1. Which term is drawn largest, and at what font size? "Signal Processing", weight 80, drawn at 40 px.
  2. "Sinc Function" and "Butterworth Filter" both have weight 30. How large is their text relative to "Signal Processing"? 30 / 80 = 0.375 of its size: 15 px against 40 px.
  3. "Sampling" has weight 60 and "Sampling Theorem" has weight 25. What font size does each get? 30 px and 12.5 px, because size is half the weight.
  4. Why do the positions change on every reload while the sizes do not? Placement and color are chosen at random each time the cloud is drawn; size comes only from the fixed weight in words.json.
  5. A classmate says that because "Noise" (65) is drawn larger than "Convolution" (60), noise is more important to learn. Respond. Size shows an estimate of how often a term is mentioned, not how much effort it takes to learn or how much later material depends on it. A term can be mentioned often and still be easy, or rarely and still be foundational.

Common Misconceptions

  1. "Bigger word means more important topic." Size here encodes an estimated frequency of mention. Reloading shows that size is fixed by weight alone, and Assessment question 5 asks students to separate frequency from importance.
  2. "Words that sit close together are related." Position is random. Reload and the same two words land in different places, so proximity carries no meaning in this cloud.

References

  1. Tag cloud - Wikipedia - background on word clouds and how font size encodes weight
  2. Signal processing - Wikipedia - overview of the field whose vocabulary the cloud shows
  3. Digital signal processing - Wikipedia - definitions of many of the digital terms in the cloud
  4. The Scientist and Engineer's Guide to Digital Signal Processing - S. W. Smith - free textbook that covers most of these terms
  5. wordcloud2.js - GitHub - the library that places the words
  6. Zipf's law - Wikipedia - why a few terms dominate word-frequency counts

Development Notes

The word list and weights were first generated with an AI assistant; the prompt and response are kept on the Wordcloud prompt page. Earlier experiments placed the words with vis-network text nodes; that page explains why wordcloud2.js, which places the words much better, is the library used here.