Look once every millisecond
Start with ideal instantaneous sampling at one thousand samples per second. Give sinusoids at and the same starting phase. Between observations, the slow signal advances one tenth of a cycle. The fast one advances a whole cycle and another tenth. At every clock tick they arrive at the same phase.
The extra turn fits entirely between samples. Join the recorded points and the fast signal can look like the slow one. This merging of different frequencies in a sampled record is aliasing. The apparent wave can be clean and repeatable because the ambiguity repeats with the clock.
A trigger gives the edge a repeatable position
Draw a repeating pulse from a different starting point each time and it slides across the display. A trigger selects a shared event, such as voltage rising through a chosen level. Putting that event at the same horizontal position makes the edge stand still.
One digital implementation finds the crossing among the numerical voltage samples already acquired. Sampling continues before the trigger, and a buffer preserves the preceding part of the stream. That is how a record can show events before its trigger point. If no qualifying edge arrives, normal mode retains the previous record; auto mode can save an untriggered segment after a timeout.
An aliased slow wave can repeatedly cross that level too. Steadiness shows that these samples align consistently. Distinguishing the fast input from the slow one requires information about sampling as well.
Sources: [1]
The edge can change before sampling begins
Voltage passes through the probe and analog input before it reaches the sampling clock. The probe adds a load to the source, and the input responds imperfectly to rapid changes. A sharp pulse can emerge lower and rounder. Bandwidth describes how that analog path responds to different frequencies.
A resistor and capacitor provide a simple teaching front end: voltage on the capacitor approaches a changed input gradually. With a bandwidth of , an ideal step takes about to rise from ten to ninety percent. That is less than one fifty-thousandth of a second. The number follows from this response shape and is not a universal oscilloscope specification.
A faster clock records the rounded edge in more detail. It does not restore the sharp edge that entered the analog path. Conversely, a fast analog input can pass changes that a slow clock still fails to distinguish.
Measurements must follow the recorded points
The converter stores each voltage as an integer code within a finite range. Observing zero and a known voltage supplies a voltage scale; counting clock ticks during a known interval checks the time scale. The connecting line is a display built from those discrete readings.
For example, dividing a full span of into the two hundred and fifty-six codes available with eight bits gives steps of about . Twelve bits provide four thousand and ninety-six codes, with steps of about . Finer voltage steps reduce rounding error. Recording the motion between clock ticks still requires a sufficiently fast clock.
The record must also last long enough. A hundred-hertz wave fits less than half a cycle into a four-millisecond window. A forty-millisecond window spans roughly four cycles, allowing several same-direction crossings to be compared. A longer record supplies more repetitions while leaving the spacing between samples set by the clock.
Several crossings in the same direction can supply a period. Sampled ten- and ninety-percent crossings can supply an edge time. A short record or an edge represented by only a few sparse samples can leave those estimates poorly determined. If a peak exceeds the code range and clips, its original height is absent from the samples.
The earlier eleven-hundred-hertz input leaves more of its oscillations visible under a faster sampling clock. Keeping both sets of raw codes, their ranges and their trigger positions lets you investigate how the slow trace arose.