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Whales and Wavelets

From The Interspecies Newsletter

wavelet blainvilleWavelets and Whales

Sound possesses attributes of energy (volume or gain) frequency, harmonics, timbre, rhythm, and time. These attributes allow audio signals to be graphed in various ways. Acousticians rely heavily on spectral analysis based on Fourier transforms, to examine the component frequencies and amplitude of a sound over a set period of time. Phoneme graphs are able to illustrate the complex sound patterns we string together to form words, sentences...language. There is a biologist studying beluga calls in Russia who claims to have graphed 24 discrete phonemes of the local whale vernacular. He describes it as the 24 letters of beluga alphabet.

Some acousticians are also starting to use wavelet transforms to research whale communication. This offers an especially detailed graphic technique for examining sounds that display very little frequency modulation over very short time periods. Think drum hits. And echolocation clicks. The image to the right shows, in exquisite detail, one Blainville's Beaked Whale click of about 1/100th of second interval. Graphing that same click via spectrogram would show a very thin straight line displaying the click's frequency bandwidth and little else.

The first mention of the term "wavelet" occurred in a thesis by Alfred Haar in 1909. Unlike sines and cosines which have infinite extent, wavelets are finite. Suffice it to say that wavelets display sound in in much more of an integral, three-dimensional fashion. A discrete sound displays edges as if it were a stand-alone object rather than the zigzag waveform we see in a spectrograph.

For detailed info, read "Wavelets and Filter Banks" by Gilbert Strang and Truong Nguyen. Or go

Mark Fischer has been working closely with for over 10 years, to refine wavelets as a graphing technique to study whale communication. He has rendered hundreds of discrete cetacean calls into wavelet-based images and movies. AFor most of tthe time of our relationship, he was primarily interested in the striking beauty of the format, which seems to display whale calls as pure energy. But he always keeps an eye firmly focused on the possibility that the object-rendering capabilities of the wavelets might shed light on the speculation that toothed whales (belugas, orcas, cachalot, dolphins) may use sound to communicate an echolocated object-oriented vocabulary.

Toothed whales perceive their world via sonar. A series of specific echoed clicks gets interpreted by their brains as a fish, a rock, a boat. Since several of these cetacean species also use clicks in a social context, researchers speculate the obvious: that these species may possess a language comprised of all the objects (and the dynamic movement of objects) within their realm.

We at Interspecies joke that eventually, one of Mark's wavelets is going to show up on the screen as a perfectly articulated fish. Actually, looking closely at the cachalot (sperm whale) wavelet below, it is easy to spot a resemblance to a squid, which is this whale's primary food. Is it just a coincidence, a serendipitous function of the transform? Mark is clearly a pioneer. His wavelet studies will eventually be recognized as an important new direction in the study of cetacean acoustic behavior.

Mark writes:
"What motivated me to try this form of analysis is simple. The range of frequencies involved in cetacean sounds is extraordinary, from a low of 5-9Hz in the large mysticetes up to 150 kHz in some of the odontocetes. Standard, off-the-shelf spectral analysis software simply buckles under these demands.

I am no longer interested in this as solely an art form. We are now using wavelets quite effectively to extract just those parts of a complex audio signal that constitute a whale call. This makes it all very useful for graphing, researching, and identifying many species just by their clicks. This is impossible to do with other audio graphing techniques. In other words, after years of development, we are well on our way to practical applications that help identify species just by their clicks. But it all started with the art which allowed the work to develop, without being "evaluated", or "measured". In the beginning, that was the only way progress could be made.

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