# What information do we lose when we increase whale songs to our hearing range?

TV documentaries on marine life often feature the evocative sounds of whales communicating with each other (apparently), over very long distances.

The frequency of baleen whale sounds ranges from 10 Hz to 31 kHz, whereas experiments have shown that a healthy young person hears sound frequencies from approximately 30 to 20,000 hertz.

So the film makers use the speeded up sound recordings provided to them by the whale research people to let us all hear whale song.

I would also like to ask this on a more general level than just whale sounds, as I think it's a related question.

I don't know anything about acoustics but I have a feeling there must be a tradeoff in the original information carried by a signal, acoustic or electromagnetic, when we alter it's frequency and I wonder is there a formal measure of this change in information content?

• Quality of sound is altered. Also, the speed of the song would have to be decreased. – Shubham Sep 19 '15 at 17:28

## 1 Answer

First, in the specific case of hearing, it has to be considered that the perceived loudness varies according to the frequency. So if the frequency scale of a sound is stretched, some parts of the sound may sound louder than others before stretching. For instance, if you want to focus on the bass line of a song, transpose it an octave above and it will be easier to ear because the bass will then be playing in frequency range emphasized by human ear.

Though, if you only consider the signal itself, theoretically, in the continuous time domain, it is just a change of scale. So nothing is lost, because you can apply the inverse transformation and get the original signal back.

In the discrete time domain, that's another story. Every transformation in that domain will involved some error in the signal, due to the limited sampling rate (time axis) and quantization (signal amplitude axis). Moreover, the algorithm used to do the transformation has to be mathematically right to be sure nothing unexpected is added to the signal. For instance, downsampling without low-passing to the target Nyquist frequency will add unexpected distortion to the signal.

• Well yes, but any decent A/D converter will produce a recording that's clean and accurate to many dB past human sensitivity. In this case, sampling has to be done at well over 62kHz -- and notice that speeding up the recording makes the low end audible, but you need to slow it down to hearthe upper end of the whale's spectrum. – Carl Witthoft Sep 19 '15 at 19:30