Skip to content

Dynamic Range Ladder

Run the Dynamic Range Ladder MicroSim Fullscreen

You can include this MicroSim on your website using the following iframe:

1
2
<iframe src="https://dmccreary.github.io/fft-benchmarking/sims/dynamic-range-ladder/main.html"
        height="502px" width="100%" scrolling="no"></iframe>

About This MicroSim

Clipping, headroom, dynamic range, and noise floor usually arrive as four separate vocabulary items. They are not four things. They are four positions on one scale, and once you can see them stacked up, the relationships between them become almost obvious.

Reading top to bottom:

  • Clipping zone — above full scale. Nothing can be represented here, so anything that lands here gets flattened to full scale.
  • Full scale (0 dBFS) — the largest value your bit depth can express.
  • Headroom — deliberately unused space. Insurance against transients.
  • Typical signal level — where you actually want to be.
  • Noise floor — the level of noise present even in silence.
  • Below the noise floor — indistinguishable from nothing.

Click any band to read what it means and what happens to a signal there.

What One More Bit Buys

Check Add 1 bit of depth and watch carefully. Full scale does not move. The clipping zone does not move. What moves is the noise floor, which drops about 6 dB, and the usable range grows into the space it vacated.

That is the whole content of the "6 dB per bit" rule. More bits do not let you record anything louder — they let you record something quieter without it being swallowed by noise.

How to Use

  1. Click each band in turn, top to bottom, and note the consequence line for each.
  2. Before toggling the extra bit, predict which boundary will move: full scale, or the noise floor?
  3. Toggle Add 1 bit of depth and check your prediction against the ladder and the dB figures in the subtitle.
  4. Consider the trade: headroom protects against clipping but pushes your signal closer to the noise floor. Where would you sit a quiet signal you cannot re-record?

Lesson Plan

Grade Level

Undergraduate (college junior/senior)

Duration

8-10 minutes

Prerequisites

  • A sample is stored as a fixed-width integer
  • Familiarity with the idea of a decibel as a ratio

Learning Objective

Students will be able to interpret a vertical amplitude scale showing where full scale, headroom, typical signal level, noise floor, and the clipping zone sit relative to one another, and explain what happens to a signal in each zone.

Activities

  1. Zone tour (4 min): Students click each band and summarize each in their own words.
  2. Predict the shift (3 min): Students predict which boundary moves when a bit is added, then verify.
  3. Place a signal (3 min): Given a quiet source, students decide where on the ladder they would aim to sit and justify the headroom they leave.

Assessment

Ask: "Two recordings clip identically at full scale, but one used 16-bit and one used 24-bit. What is different about them, and which zone accounts for the difference?"

References

  1. Dynamic range — the ratio between the largest and smallest representable signal.
  2. dBFS — the decibels-relative-to-full-scale convention used on the left of the ladder.
  3. Quantization (signal processing) — where the roughly 6 dB per bit figure comes from.