Biomedical Engineering Reference
In-Depth Information
The values of the amplitudes are
T
1
T
a
0
=
f
(
t
)
dt ,
0
T
2
T
a
n
=
f
(
t
)cos(
nω
1
t
)
dt ,
0
T
2
T
b
n
=
f
(
t
) sin(
nω
1
t
)
dt .
0
This set of coe
cients constitutes what we call the spectral content of
the signal. They prescribe the specific waves for all the harmonic functions
that we have to add in order to reconstruct a particular signal
f
(
t
). For the
moment, it is enough to say that in order to represent a note, we have several
elements available: its frequency, its amplitude and its spectral content.
However, there is still some way to go in order to have a useful set of
descriptive concepts to study birdsong. If all a bird could produce were simple
notes, we would not feel so attracted to the phenomenon. The structure of
a song is, typically, a succession of syllables, each one displaying a dynamic
structure in terms of frequencies. A syllable can be a sound that rapidly
increases its frequency, decreases it, etc. How can we characterize such a
dynamic sweep of frequency range?
1.4 Sonograms
1.4.1 Onomatopoeias
Readers of this topic have probably had in their hands, at some point, or-
nithological guides in which a song is described in a more or less onomatopoeic
way. Maybe they have also experienced the frustration of noticing, once the
song has been identified, that the author's description has little or no simi-
larity to the description that they would have come up with. Can we advance
further in the description of a bird's song with the elements that we have
described so far? We shall show a way to generate “notes”, i.e., a graphical
representation of the acoustic features of the song. We shall do so by defining
the
sonogram
, a conventional mathematical tool used by researchers in the
field, which, with little ambiguity, allows us to describe, read and reproduce
a song.
The song of a bird is typically built up from brief vocalizations separated
by pauses, which we shall call syllables. In many cases, a bird can produce
these vocalizations very rapidly, several per second. In these cases the pauses
are so brief that the song appears to be a continuous succession of sounds.
But one of the aspects that makes birdsong so rich is that even within a
syllable, the bird does not restrict itself to producing a note. On the contrary,
each syllable is a sound that, even within its brief duration, displays a rich
