Learning Library · Signals and oscilloscopes · 2
Sample rate and aliasing
A digital oscilloscope does not see a continuous wave. It takes snapshots at a fixed rate and joins the dots. Sample fast enough and the dots trace the real signal. Sample too slowly and they trace a different, slower wave that is not there.
Faint grey: the real signal. Dots: the samples. Blue: the lowest-frequency sine that fits the dots (what a scope's sin(x)/x interpolation draws), or the dots joined by straight lines. The lower strip folds the signal frequency back below Nyquist.
The Nyquist limit
To pin down a sine wave you need more than two samples per cycle. Any signal above half the sample rate is indistinguishable, from the samples alone, from a signal below it. The scope cannot tell them apart, so it shows the lower one. That false frequency is an alias.
Try this
- Set the signal to 30 MHz and the sample rate to 250 MSa/s. With more than eight samples per cycle, the joined dots follow the signal closely.
- Slide the signal up to 240 MHz. It now aliases to 10 MHz: the blue wave runs 24 times slower than the real one.
- Set the signal to exactly the sample rate. Every sample lands on the same phase, the alias is 0 Hz, and the trace is a flat line.
How much sample rate is enough?
Nyquist is the theoretical floor, and it assumes the scope reconstructs with an ideal sin(x)/x filter. In practice, a sample rate of at least 2.5 times the scope's bandwidth is a common minimum with sin(x)/x interpolation, and 4 to 5 times gives cleaner edges and more trustworthy timing measurements.
Watch for one trap: on many scopes the sample rate is shared between channels, and it also drops automatically at slow time-base settings when the record fills memory. The memory depth explainer shows why.
A quick check for aliasing: change the time base. A real signal keeps its frequency reading as you zoom. An alias jumps to a different frequency, because the sample rate changed underneath it.
Sample fast enough to trust what you see. Digital oscilloscopes with the sample rate on every spec sheet.
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