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Dynamic range (DR) audio is a difference between maximal and minimal signal levels. Read about methods of measurement and its difference.

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Introduction

DR may have 2 meanings: for audio device / software / format and audio signal.

DR of audio device is difference between maximal and minimal allowable levels of signal inside the device / software / format.
DR of audio signal is difference between maximal and minimal signal levels.

In this article we will discuss first meaning.

Dynamic range have multiple definitions. Because minimal and maximal levels may be measured various ways.

Read details about minimal and maximal level issues.

Dynamic range audio

Signal level definition

When a signal pass through audio unit/software (as digital as analog) its level is limited by minimal and maximal values.

Maximal level

Maximal level of audio signal

When signal achieve overload value it get non-linear distortions, that is shown at left part of the picture as red components.

Overload audio. It is output signal for input sine

Pure digital systems (as example, software) have sharp border between distorted and non-distorted signal.

Example:

16 bit signal have maximal value: 2¹⁵-1.
When signal achieve next level step 2¹⁵, it cause overload (mathematical overflow) and 2¹⁵ is transformed to -2¹⁵ (minimal allowable value).

Digital signal overload

Such transformation can cause loud click. To avoid the click, processing is performed in higher bit resolution. Before conversion to target (lower) bit resolution, signal is checked to overload. If there is overload, overloaded samples level is limited bay maximal allowable one. Such overload kind is same to traditional analog, that cause distortions without big "digital overload clicks".

Analog overload have smooth overload border. At the upper right opart of the picture input-output level characteristic is displayed.

Analog non-linear distortions. Input-output characteristic

When input signal level approaches to maximal limit, distortions grow too. Because the distortion intensity depend on level due non-linearity.

Input-output level characteristic display how to depend of output level on input one.

That characteristic may be linear (simple line) or non-linear, like one, displayed at the picture.

Let's look to highest levels. A-area at the characteristic impact to waveform in area B of output signal. So non-linearity kind in the A-area define distortions at output (B-area) when input signal level about maximal value. Other words different level of input signal generate various levels of distortion components at output.

For digital signal simple binary logic ("with" or "without" distortion) may be applied.

For analog signal we can estimate various distortion levels for different input signal levels. There is smooth overload border.

Therefore for analog signal, maximal level may be accepted as level that cause target distortion intensity.

As axample, as maximal level may be accepted levev where share of distortions in total energy more, than target value.

Minimal level

When signal level is decreased, it achieve noise floor and hide under it. It is fairly for both digital and analog signals.

Minimal level of audio signal

There is difference in noise nature. Analog noise is noise of electronic components. Pure digital noise is quantization noise. Captured digital signal have both kinds of noise: by electronic components and quantization. But it is not matter for minimal level estimation.

Therefore, minimal level has different sound quality for different level values.

For pure digital units and software, quality is defined by signal/noise ratio.

For analog systems, quality is also defined by non-linearity of input-output characteristic of measured device.

When we consider dynamic range as difference between noise floor and overload level, quality estimation is lost.

When signal "drowns" in noise we can't recognize it. So such way of dynamic range estimation is too optimistic.

We want to listen minimal level in given quality. The quality is defined by signal/noise ratio.

Analog system have different linearity for different level. The non-linearity generate distortions: spectral products, that correlate with original pure signal. So we must account the distortions as noise too. We can look to similar example with highest levels here.

Signal/noise ratio

Signal/noise ratio is ratio between energies of signal and noise.

Energy may be estimated as square of power spectrum.

Power is level².

Signal/noise ratio at the power spectrum

If we can localize signal spectrum, rest spectrum we can accept as noise and distortions.

It is reason, why we can't use music as test signal. Music have dense spectrum and it is almost impossibly to separate noise, distortions and original signal.

Also using of complex signals (multi-tones, as example) can cause issues of signal and noise separation.

We can step-by-step reduce noise level to achieve given signal/[noise and distortions] ratio. This level is accepted as minimal.

Signal energy (square) calculation is not matter. But band of the signal may be accepted differently for different methodics.

Also noise and signal energies may be calculated accounting psychoacoustics: equal-loudness contour.

Conclusions

Simplified dynamic range is difference between signal that cause overload and noise floor.
Estimation of audio dynamic range should take into account sound quality.
DR by goal #2 have lesser value than simplified definition by the goal #1.

Simplified dynamic range estimation