Skip
# seeing whale songs

Fourier Series translates a signal into a set of sinusoids, not the Fourier Transform.

posted by dongolier at 1:48 PM on January 29, 2010

The article actually said why these are useful, they aid in identifying different species' songs:

Post

# seeing whale songs

January 29, 2010 8:50 AM Subscribe

Visualizing Whale Songs "Mark Fischer, an expert in marine acoustics, has come up with another way to illustrate whale song. He uses a more obscure method, known as the wavelet transform, which represents the sound in terms of components known as wavelets: short, discrete waves that are better at capturing cetacean song."

These look really cool, and I see how they are different per species, but are they different per

posted by OmieWise at 9:23 AM on January 29, 2010

*individual*?posted by OmieWise at 9:23 AM on January 29, 2010

From what I understand of whalesongs, not very. But they're different per

posted by clarknova at 9:59 AM on January 29, 2010

*group*, and per*year*.posted by clarknova at 9:59 AM on January 29, 2010

These kind of look cool, but how is this really "visualizing" the whale songs? It doesn't really tell you much about what they sound like, unlike an FFT or something.

posted by delmoi at 11:35 AM on January 29, 2010

posted by delmoi at 11:35 AM on January 29, 2010

thanks to New Scientist for again leaving out most of the science and math and instead just showing some (admittedly beautiful) handwaving.

wavelet transforms are indeed beautiful mathematically, and efficient computationally, but, what possible advantage do they have over the standard linguistic model: language as a sequence of phonemes (intervals that exhibit similar spectral traits) and their larger scale usage patterns (ie. syllables, words, phrases, sentences.... or, in music: melodic voices, harmonic chord changes, rhythmic patterns).

this Fischer guy is more about (selling his) art than science.

posted by dongolier at 1:35 PM on January 29, 2010

wavelet transforms are indeed beautiful mathematically, and efficient computationally, but, what possible advantage do they have over the standard linguistic model: language as a sequence of phonemes (intervals that exhibit similar spectral traits) and their larger scale usage patterns (ie. syllables, words, phrases, sentences.... or, in music: melodic voices, harmonic chord changes, rhythmic patterns).

this Fischer guy is more about (selling his) art than science.

posted by dongolier at 1:35 PM on January 29, 2010

*Spectrograms are created using a mathematical process called the Fourier transform (FT), which can convert raw sound into a set of sinusoidal waves.*

Fourier Series translates a signal into a set of sinusoids, not the Fourier Transform.

posted by dongolier at 1:48 PM on January 29, 2010

*It doesn't really tell you much about what they sound like, unlike an FFT or something.*

*this Fischer guy is more about (selling his) art than science.*

The article actually said why these are useful, they aid in identifying different species' songs:

On a spectrogram it can be difficult to distinguish between similar-sounding species, particularly if the animal clicks very rapidly, because these get smeared out in an FT. With the wavelet method, the clicks show up as precise spikes.posted by OmieWise at 2:25 PM on January 29, 2010

It's nice looking art.. but I'd be more impressed if it was animated.

posted by jmnugent at 2:57 PM on January 29, 2010

posted by jmnugent at 2:57 PM on January 29, 2010

okay, okay.... i think i see the wavelet advantage. you dont have to fuss with picking the right time-interval window: with FFT if you pick too narrow you lose low freqs; too wide and the signal is nonstationary ("smeared out" might describe it). and from wikipedia it looks like everybody is dumping the FFT for wavelet method's---maybe we'll even get JPEG2000 browser support in ... wait for it... 2010!

also interesting though: wikipedia has the same error as the article, "the Fourier Transform... expresses a signal as a sum of sinusoids."

someone at NewScientist was negligently lazy on the olde wikipedia-factcheck....

posted by dongolier at 4:18 PM on January 29, 2010

also interesting though: wikipedia has the same error as the article, "the Fourier Transform... expresses a signal as a sum of sinusoids."

someone at NewScientist was negligently lazy on the olde wikipedia-factcheck....

posted by dongolier at 4:18 PM on January 29, 2010

dongolier, the Fourier transform is an algorithm for switching from an arbitrary function to an equivalent Fourier series. What's wrong with the statement you quoted?

posted by fantabulous timewaster at 12:42 AM on January 30, 2010

posted by fantabulous timewaster at 12:42 AM on January 30, 2010

Joseph Fourier is responsible for giving use both the Fourier Series expansion of a function as well as all of Fourier Analysis which includes the Transform.

Fourier Series is an expansion of a

Fourier Transform (really, a special case of the Laplace Transform) transforms a periodic function of

FFT is a Discrete Fourier Transform, an adaptation of the above for

the Fourier Series gives an approximation to an input function. the FFT gives you the spectrum of that function.

posted by dongolier at 3:25 AM on January 31, 2010

Fourier Series is an expansion of a

*continuous*periodic function into sinusoidal components of*integer*multiples of the original functions periodic frequency. (ie. at a 1 sec period you get a weighted sum of 0Hz, 1Hz, 2Hz, ... terms---which is different from a continuous "spectrum")Fourier Transform (really, a special case of the Laplace Transform) transforms a periodic function of

*continuous*time (or data over an interval) into a function of frequency, where frequency is a*continuous*variable from zero to infinity (more precisely: negative infinity to positive infinity).FFT is a Discrete Fourier Transform, an adaptation of the above for

*discrete*time. it is useful as it transforms arbitrary data samples equally spaced in time into a spectrum showing relative power at discrete frequencies---if the interval is 1 sec and their are 1024 samples in it, the FFT gives you a spectrum with values at 0Hz,1Hz, 2Hz,...511Hz.the Fourier Series gives an approximation to an input function. the FFT gives you the spectrum of that function.

posted by dongolier at 3:25 AM on January 31, 2010

Well, the sum of the series gives an approximation to the input function. The terms in the series (that is, the weights associated with each frequency term in the sum) are what's usually meant by the spectrum.

I really don't see the hair that you're splitting. The sentence you quoted is one of the least wrong things I've ever read in New Scientist.

posted by fantabulous timewaster at 3:52 PM on January 31, 2010

I really don't see the hair that you're splitting. The sentence you quoted is one of the least wrong things I've ever read in New Scientist.

posted by fantabulous timewaster at 3:52 PM on January 31, 2010

« Older 200 Motels | I have one in my pillow fort. Newer »

This thread has been archived and is closed to new comments

posted by demiurge at 8:57 AM on January 29, 2010