Plotting two functions with different sample rate

Question

I want to plot two functions: sin(x) and a sampled and quantized sin(x). The script is simple

set xtic 1
set ytic 1
f1(x) = sin(x/16*2*pi)*8
round(x) = x - floor(x) < 0.5 ? floor(x) : ceil(x)
plot [0:16] [-8.5:8.5] f1(x) with lines,  round(f1(x)) with steps lt 2

The problem is, I want the sin(x) to be smooth and the sampled an quantized sin(x) sampled at intervals of 1. The problem is, I can't find any option to do so. Adding

set sample 21

nearly works, but the sin(x) does not look smooth enough. Is there any way to make it better?

Answer 1

Round the variable of f1() not f1() itself and use floor() instead of round()

plot [0:16] [-8.5:8.5] f1(x) with lines,  f1(floor(x)+0.0) with steps lt 2

also, set a lot of samples to keep the quantized plot properly aligned:

set samples 1000

If you use round() instead of floor the quantization steps are "0.5 steps" (0.5 to 1.5, 1.5 to 2.5 etc) instead of "1 steps".