# Log Scale Unit in Audio
###### tags: `Tutorial`

* Why use log scale?
* 簡化運算 (multiplication -> addition + lookup table)
* We perceive sound logarithmically
* frequency
* loudness
* Overview
* 1. Bel and dB
* 2. Perception

## 1. Bel and dB (decibel)
### 1.1 Definition
* Bel is **relative unit** of measurement
* 1 dB = 0.1 Bel
* dB is the most common unit

**DEF**
logarithm of the ratio of power or root-power type quantity

* power quantity: **power**, energy density, acoustic intensity, and luminous intensity.
<img src="https://i.imgur.com/MhCws79.png" alt="drawing" width="150"/>

* root-power quantity: **amplitude**, voltage, current, **sound pressure**, electric field strength, speed, or charge density. The square of which, in linear systems, is proportional to power.
<img src="https://i.imgur.com/jK1eYI4.png" alt="drawing" width="150"/>

**Proof**

<img src="https://i.imgur.com/hxbOo06.png" alt="drawing" width="350"/>

## 1.2 Common Unit

| Unit | Quantity | Reference | Scenario |
|:----:|:----:|:----:|:----:|
| dBu | voltage (root power) | 0.775 Vrms | audio spec
| dBV | voltage (root power) | 1 Vpeak |
| dBFS | amplitude (root power) | digital limit | DAW
| dBSPL | pascal (root power) | 2 x 10^-5 Pa | 日常生活最常見的音量單位

*SPL: Sound Pressure Level*

## 1.3 dBFS: dB Full-Scale
dBFS is a unit of measurement for **amplitude levels** in digital systems, such as pulse-code modulation (PCM), which have a defined maximum peak level.

<img src="https://i.imgur.com/fzmPgYH.png" alt="drawing" width="300"/>

* \> 0 dB: digital clpping
* dB and linear scale conversion

<img src="https://i.imgur.com/oH6cdQV.png" alt="drawing" width="200"/>

</br> </br>
* 常見對照
* -0.9 dB = 0.9
* -6 dB = 0.5
* -20 dB = 0.1
* -40 dB = 0.01
* -60 dB = 0.001
* -80 dB = 0.0001

## 2. Perception

1. Specturm
* x: frequency, y: loundess
<img src="https://i.imgur.com/YvUWeui.png" alt="drawing" width="450"/>
2. A-weighting, 等音量曲線
* loudness standards, EX: LUFS...

## Reference
https://corychu.medium.com/%E9%8C%84%E9%9F%B3%E7%AD%86%E8%A8%98-%E6%95%B8%E4%BD%8D%E9%9F%B3%E9%87%8F%E6%A8%99%E6%BA%96-dbfs-dbtp-lufs-c47ca4646b7f