Biomedical Engineering Reference
In-Depth Information
temporal evolution in frequency, and is perceived as becoming progressively
higher, lower, etc. For this reason, if we were to restrict ourselves to analyzing
the spectral content of a syllable as if it was a simple note, we would miss
much of the richness of the song. Therefore we use another strategy.
1.4.2 Building a Sonogram
In Fig. 1.7a, we have a signal corresponding to a syllable. We have already
worked with it in Fig. 1.2. We shall not look at the complete syllable, but just
at a small fraction of it around a given time
t
. We call this our time window,
and we center it around the time
t
. Let us proceed to analyze the spectral
content of this small fragment, and choose the aspects of the spectrum that
we find most relevant. We could, for example, concentrate only on the fun-
damental frequency, forgetting about the harmonics discussed earlier. In this
way, we can plot a diagram of fundamental frequency as a function of time,
plotting a dot for the fundamental frequency found in the window centered
at time
t
, at that time. For successive times, we proceed in the same way.
What we obtain with this procedure is a smooth curve that describes the
time evolution of the fundamental frequency within the syllable. This way
of analyzing small fragments of a song is a useful procedure for sounds that
change rapidly in frequency, and is available as part of almost any computer
sound package.
(a)
(b)
1.0
3000
-1.0
0.0
0.0
time (s)
1.0
0.0
time (s)
1.0
Fig. 1.7.
Building a sonogram. (
a
) We start by plotting the sound wave (actually,
at this scale, one cannot see the actual oscillation, just the envelope). Now we focus
on a very narrow
time window
at the beginning of the recording and calculate
the spectral content only for the part of the sound in that narrow window. Next,
we slightly shift our time window and repeat the procedure time after time, until
we reach the end of the recording. By gathering together all the results we have
obtained with the time-windowing procedure, we finally obtain (
b
), the sonogram,
which tells us how the sound frequency (and, in general, the spectral content)
evolves in time. In this case, the syllable is a note with an almost constant 2 kHz
frequency
