Signals to learning / 1. Read the signal

Lesson 1 of 40 · Beginner · About 15 minutes

What is a signal?

What does a waveform actually tell you?

You will be able to

  • Identify the independent variable and the measured quantity.
  • Distinguish a sample index from physical time.

A measurement that varies

A signal assigns a value to an input such as time or position. A microphone measures pressure variation; a thermometer measures temperature; an image measures brightness over two spatial coordinates. The curve is not the phenomenon itself: it is a representation of a measurement, with units, a sensor and assumptions.

Read the axes before the shape

Write x(t) for a continuous-time quantity and x[n] for a sequence indexed by integer n. Brackets do not tell you the sample rate. Without the rate, an array tells you sample order but not elapsed seconds. A tensor adds axes such as channels and batches; those axes also need meanings.

tₙ = n / fₛ (n starts at 0; fₛ is samples per second)

Worked example

At 100 samples/s, sample 25 is at 0.25 s. A 100-sample record runs from 0 to 0.99 s; the interval allocated to that record is 1 s. Distinguish the last timestamp from N/fₛ.

A common trap

A smooth line drawn between samples does not prove that the original physical signal followed that line.

Predict, then experiment

If you double amplitude, does the number of oscillations change? Before touching the controls, say or write your prediction.

Interactive experiment

Harmonic composer

How do amplitude, frequency and phase appear in a discrete spectrum?

The waveform is the sample-wise sum; its vertical scale is automatic and labelled. The spectrum view shows 0–16 Hz of the available 0–32 Hz band. Bars use the left amplitude scale; phase points use the right −π to +π radian scale. Phase is omitted below amplitude 0.03.

Your experiment

Set Tone B amplitude to 0. Compare Tone A amplitude 0.5 and 1 at 3 Hz. Count cycles over the one-second record, then explain what changed and what stayed fixed.

Change one parameter at a time. Compare what you observed with your prediction and record an explanation in your notes.

Check your understanding

Try from memory first. Hints and feedback are part of learning, not a penalty. These checks are for self-study, not a graded qualification.

1. Which information is needed to convert an array index into seconds?
Give me a hint

Which quantity says how often measurements are taken?

2. At 200 samples/s, what is the time of sample 50? Enter seconds.

Accepted absolute tolerance: ±0.001 s.

Give me a hint

Divide index by sample rate.

Reference answers (after your attempt)
  1. The sample rate — Correct: seconds per sample is 1/fₛ.
  2. 0.25s — 50/200 = 0.25 s.

Apply it: Annotate a real measurement

Use paper, your notes, or a local notebook/editor. Code examples are Python 3 starting points to run yourself; this page does not execute code or automatically assess the practical task.

  1. Choose a temperature, audio or image signal.
  2. Name each axis, its units and what one value means.
  3. State one sensor or sampling limitation.
Reference solution & review criteria

For mono audio: index n, rate fₛ in samples/s, amplitude in calibrated pressure units or explicitly uncalibrated digital units. Clipping, noise or unknown calibration limits interpretation.

Your notebook

Notes and progress stay in this browser. They are not sent to the server; ordinary web-server request logs still operate. Export a backup from the course page.

Review list

Completion requires both correct checks and your practical-task acknowledgement.

Go deeper

Sources support further study; the worked examples and questions here are original. Browser experiments are small, disclosed models—not evidence of production-model quality or hardware performance.