Signal Sampling

#import "@preview/cetz:0.5.3": canvas, draw
#import draw: circle, content, line

#set page(width: auto, height: auto, margin: 8pt, fill: none)
#set text(size: 12pt)

#let signal(t) = calc.sin(2 * calc.pi * t / 13)
#let scale-x = .74
#let scale-y = 2.6
#let pt(t) = (t * scale-x, signal(t) * scale-y)
#let (duration, n-samples) = (15, 12)
#let sample-period = duration / (n-samples - 1)

#canvas({
  let arrow = (mark: (end: "stealth", fill: black, scale: .8), stroke: 1.4pt)

  // axes (axis lines = middle)
  line((0, -1.1 * scale-y), (0, 1.5 * scale-y), ..arrow, name: "y-axis")
  line((0, 0), ((duration + 1) * scale-x, 0), ..arrow, name: "x-axis")
  content("y-axis.end", [signal $x(t)$], anchor: "north-west", padding: (left: 4pt))
  content("x-axis.end", [time $t$], anchor: "north-east", padding: (top: 4pt))

  // continuous signal
  line(..range(301).map(idx => pt(idx * duration / 300)), stroke: 1.1pt)

  // sampled stems with dots
  for idx in range(n-samples) {
    let t = idx * sample-period
    line((t * scale-x, 0), pt(t), stroke: 1.1pt)
    circle(
      pt(t),
      radius: .09,
      fill: red.darken(25%),
      stroke: red.darken(60%) + .6pt,
    )
  }

  // label the lowest sample
  let lowest = pt(7 * sample-period)
  content(
    (rel: (0, -.2), to: lowest),
    text(fill: red.darken(25%))[samples $x(n \/ f_s)$],
    anchor: "north",
  )

  // sample-time tick labels on a shared baseline
  for (idx, label) in ((1, $1 \/ f_s$), (2, $2 \/ f_s$), (3, $3 \/ f_s$), (4, $dots$)) {
    content((idx * sample-period * scale-x, -.55), label, anchor: "base")
  }
  content((2.5 * sample-period * scale-x, -1.0), [$f_s$: sampling frequency], anchor: "north")
})