Decibels

Tags

speech-processing

The logarithmic ratio between the sound-pressure of a given sound-wave and a reference value $p_{r}ef$.

Sound pressure is commonly measured using [see page 4, Pascals]. The range of human hearing ranges from around $20/1\ast {10}^6$ pascals upto ear-splitting at $20$ Pascals. This huge range is really inconvenient to work with so we commonly use decibels instead.

$0dB$ is commonly [see page 6, scaled] to be the threshold of human hearing, with $140dB$ being the threshold of pain.

Technically it's wrong to say x is 50 dB loud because dB is a ratio and a ratio
always needs a reference value.

The formula for converting the power/amplitude of a wave to Decibels is: $x{\log }_{1}0(p1/p_{r}ef)$ where $x$ is some multiplier we choose to scale the range of decibel values. Observe that this means at:

• $p1 = $p_{r}ef$ the power is exactly $0$
• $p1 = 10 $p_{r}ef$ the power is $x$
• $p1 = $\frac{p_{r}ef}{2}$ the power becomes negative
• $p1 = $p_{r}ef\ast 2$ the power becomes positive

Power vs. Amplitude

For power we normally set $x=10$ and for amplitude we set it to $x=20$ (because we square $\frac{p1}{p_{r}ef}$ by expanding it out of the log).