You will be able to
- Calculate sample spacing and record duration.
- Distinguish sample rate from signal frequency.
A clock for measurements
Uniform sampling measures x(t) at times n/fₛ. The interval Δt=1/fₛ belongs to the measurement clock, not the signal. A 5 Hz tone can be measured at 100 samples/s: 20 samples per cycle. Increasing the sample rate supplies more observations per second, not a faster physical oscillation.
The record is finite
N samples allocate N/fₛ seconds of record time, with last sample at (N−1)/fₛ when the first is at zero. A finite record does not reveal everything before or after it. Missing samples, irregular timestamps and sensor bandwidth complicate the uniform model, so record timestamps and acquisition settings.
Worked example
At 1,000 samples/s, neighbouring samples are 1 ms apart. A 100 Hz sinusoid has 10 samples per cycle. A 2,000-sample record occupies 2 s.
A common trap
Sample rate and frequency are both measured per second but describe different things: observation rate and oscillation rate.
Predict, then experiment
For a fixed 3 Hz source, how does doubling the sampling rate change the sample markers? Before touching the controls, say or write your prediction.
Interactive experiment
Frequency folding
When does a sampled sinusoid become indistinguishable from a slower one?
Blue is the source, dashed amber is the apparent sinusoid, and circles are samples shared by both. The display covers two seconds.
Your experiment
Set source to 3 Hz. Compare sample rates 10 and 20 Hz over the same two-second plot. Explain why the underlying source completes the same number of cycles.
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.
Reference answers (after your attempt)
- halves time between samples — Correct: Δt=1/fₛ.
- 2.5ms — 1/400 s = 0.0025 s = 2.5 ms.
Apply it: Specify an acquisition
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.
- Design a 3-second, 200-samples/s record.
- Calculate N and the last timestamp.
- State what sensor units and clock assumptions you need.
Reference solution & review criteria
N=600 and last timestamp=599/200=2.995 s. Include amplitude units/calibration, a uniform clock and any analogue filtering before conversion.
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.
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.