<p>While with additional information, the three measurement can be related, there are three typical situations for these measures</p>
<p>rms: long signal that are best characterized by their  energy or intensity
(example: ambient noise)</p>
<p>p2p: short transients, where waveforms are asymmetric and no further processing is done
(example: explosions)</p>
<p>peak: short transients, where processing is done to obtain the signal amplitude
(example: amplitude function of cetacean echolocation clicks)</p>

CC BY-SA 4.0
2022-06-25T06:06:18.010Z
2022-06-25T06:06:18.010Z
WMXZ
<p>The three measurements are typically inter-convertible, though strictly speaking the inter-convertibility holds for sinusoidal sounds only (not always applicable to real-data). If we have a waveform <code>X</code>  then</p>
<pre><code>rms(X) = peak(X)/sqrt(2)
# 'rms' is the root-mean-square of all samples in X.
# 'peak' is the absolute maximum sample value of X.
</code></pre>
<p>and</p>
<pre><code>peak-to-peak(X) = 2 x peak(X)
# peak-to-peak is the difference between the highest and lowest samples. 
</code></pre>
<p>However, the actual choice of measurement to report depends on both the properties of the sound, and the field convention. For very short sounds that occupy that span only a few samples, it may not make sense to report an rms reading for example - where a peak measurement may be more representative. On the other hand, if you have longer sounds with occasional blips due to unavoidable background noise, an rms reading may provide a more stable readout of sound level.</p>
<p>Even if there is no broad convention, it may make sense to report the measurement/s of the papers that you'd like to compare your results with.</p>

CC BY-SA 4.0
2022-06-23T22:43:45.390Z
Thanks Thejasvi! what is "peak()" exactly doing?
Marcelo Araya-Salas
CC BY-SA 4.0
2022-06-24T05:47:19.203Z
Added short comments to explain peak, peak-to-peak, and rms!
Thejasvi
CC BY-SA 4.0
2022-06-24T23:18:09.427Z
Are these definitions all assuming X is a perfect sinusoid? I think it might be helpful to more explicitly state "the following are only true for a perfect sinusoid X, for most real data we cannot convert between them easily"
Taiki Sakai
CC BY-SA 4.0
2022-06-23T10:59:44.193Z
2022-07-02T17:04:34.443Z
2022-07-02T17:04:34.443Z
Thejasvi
<p>I've seen papers report source/received levels of animal vocalisation using three measures: rms, peak and peak-to-peak.
Even within a field there doesn't always seem to be a single convention, and papers will report different measures for the same sound type (e.g. bat calls report with rms in one paper, and peak in another).</p>
<p>Can I convert between the measures, and how valid are these conversions?</p>

<loudness><source-level><received-level><measurement>
Which method to report source/received level (p2p, rms, peak) of recorded sounds?
# Which method to report source/received level (p2p, rms, peak) of recorded sounds?

(Asked by: username_0 on 2022-06-23)

I've seen papers report source/received levels of animal vocalisation using three measures: rms, peak and peak-to-peak.
Even within a field there doesn't always seem to be a single convention, and papers will report different measures for the same sound type (e.g. bat calls report with rms in one paper, and peak in another).

Can I convert between the measures, and how valid are these conversions?

**Tags:** loudness, source-level, received-level, measurement


---

## 2 answers

### Answer by username_1 on 2022-06-25. Score: 5

While with additional information, the three measurement can be related, there are three typical situations for these measures

rms: long signal that are best characterized by their energy or intensity
(example: ambient noise)

p2p: short transients, where waveforms are asymmetric and no further processing is done
(example: explosions)

peak: short transients, where processing is done to obtain the signal amplitude
(example: amplitude function of cetacean echolocation clicks)


---

### Answer by username_0 on 2022-06-23. Score: 4

The three measurements are typically inter-convertible, though strictly speaking the inter-convertibility holds for sinusoidal sounds only (not always applicable to real-data). If we have a waveform `X` then

```
rms(X) = peak(X)/sqrt(2)
# 'rms' is the root-mean-square of all samples in X.
# 'peak' is the absolute maximum sample value of X.

```

and

```
peak-to-peak(X) = 2 x peak(X)
# peak-to-peak is the difference between the highest and lowest samples. 

```

However, the actual choice of measurement to report depends on both the properties of the sound, and the field convention. For very short sounds that occupy that span only a few samples, it may not make sense to report an rms reading for example - where a peak measurement may be more representative. On the other hand, if you have longer sounds with occasional blips due to unavoidable background noise, an rms reading may provide a more stable readout of sound level.

Even if there is no broad convention, it may make sense to report the measurement/s of the papers that you'd like to compare your results with.

> **Comments:**
> **username_2**: Thanks username_0! what is "peak()" exactly doing?  
> **username_0**: Added short comments to explain peak, peak-to-peak, and rms!  
> **username_3**: Are these definitions all assuming X is a perfect sinusoid? I think it might be helpful to more explicitly state "the following are only true for a perfect sinusoid X, for most real data we cannot convert between them easily"  

---

