Sampling & Aliasing
Your ADC takes snapshots. Take them too slowly and the signal doesn't just blur — it lies, confidently, about its own frequency.
Builds on: 11.2 Reading the Analog World5.1 Alternating Current
From continuous to snapshots
Lesson 11.2 chopped voltage into steps; this lesson is about chopping time. An ADC doesn’t watch a signal — it glances at it, fs times per second, and between glances it knows nothing. The question that founded digital audio, digital radio and digital everything: how often must you glance to truly know the signal?
Sample at least twice per cycle and — remarkably — the samples contain everything: the original wave can be reconstructed perfectly, not approximately. That’s why 44.1 kHz became the CD standard: comfortably twice the 20 kHz edge of human hearing.
Aliasing: the confident lie
Break the rule and something worse than blur happens. A 900 Hz wave sampled at 1000 Hz produces samples that fall exactly on a 100 Hz sine. Not noise — a clean, plausible, completely fictional signal. This is aliasing, and you’ve seen it all your life: wagon wheels spinning backwards on film (24 frames/s undersampling the spokes), helicopter rotors frozen on video. The apparent frequency folds down like a reflection:
The vicious part: once aliased, the damage is undetectable and irreversible — the 100 Hz phantom is indistinguishable from a real 100 Hz signal. The defence must happen before sampling: an analog anti-alias low-pass filter (Lesson 5.3, promoted to guard duty) removes everything above fs/2 so there is nothing left to fold. Every serious ADC input has one.
Your Pico oscilloscope will sample at a rate you choose. Point it at the 1.4 kHz PWM dimmer with fs too low and you will meet a slow, stately phantom wave that isn’t there. Now you’ll know its name.
⚡ Lab — The Wagon Wheel
A signal, a sample rate, and the wave the samples believe in.
- Keep fs above 2f: the reconstruction (green) sits on the truth.
- Set f = 900 Hz, fs = 1000 Hz: a 100 Hz phantom, drawn in red.
- Find the eeriest setting: f exactly equal to fs — the samples see DC.