Here we show the actual continuous position of the object (converted to encoder counts), and the quantized position indicated by the encoder output. Quantized? Yes, both incremental and absolute encoders aredigital and have a quantizing effect. A quadrature encoder advertised as "256 lines" or "256 ppr" (pulses per revolution) measures 1024 counts per revolution: quadrature encoders yield 4 counts per cycle, and each cycle corresponds to a "line" (dark mark in an optical encoder) or a pulse measured on an oscilloscope.
In any case, we have lots of choices to obtain velocity from the position count.
The simplest approach is to estimate velocity = Δpos/Δt: measure the change in position and divide by the change in time. There are two classic options here:
execute code at fixed time increments (constant Δt), measure position, and take Δpos = the difference between two successive position measurements
execute code triggered by changes in encoder count (constant Δpos), measure elapsed time, and take Δt = the difference between two successive time measurements
The usual explanation is that the first approach (constant Δt) is better for moderate speeds and the second approach (constant Δpos) is better for low speeds. Texas Instruments has a user's guide (SPRUG05A) discussing this in detail: