英文:
Why do we usually multiply an audio signal in log scale by 20?
问题
这是音频处理中相当基础的一个问题。
在信号被转换成对数刻度后，通常会乘以20。相反，为了在线性刻度中恢复一些增益，我们使用以下公式：
G_linear = 10 ** (0.05 * G_in_dB)
这是因为0.05等于1/20，所以这个20的因素从何而来呢？背后的理论是什么？
我阅读了一些关于信号处理的课程和代码，但没有找到任何对此的解释。
感谢您的帮助！
英文:
Here is a quite elementary question in audio processing.
After a signal is converted in log scale, it is usually multiplied by 20. Inversely, to recover some gain in linear scale, we use the formula
G_linear = 10 ** (0.05 * G_in_dB)
This makes sense because 0.05 is 1/20.
But where does this 20 factor comes from? What is the theory behind it?
I read some courses and code for signal processing, but have not found any explanation for this.
Thanks for your help!
答案1
得分: 0
根据定义，增益的分贝将信号的功率乘以10的1/10次方。
线性增益适用于振幅，而不是功率。
由于功率=振幅的2次方，增益的1分贝将信号的振幅乘以(10的1/10次方)的1/2次方=10的1/20次方。
英文:
By definition, a decibel of gain multiplies the signal power by a factor of 10<sup>1/10</sup>.
Linear gain applies to amplitude, not power, though.
Since power = amplitude<sup>2</sup>, a decibel of gain multiplies the signal amplitude by (10<sup>1/10</sup>)<sup>1/2</sup> = 10<sup>1/20</sup>
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