Page 32 - Summer 2006

A signal resulting from a pair of brown ghost fish (Apteronotus leptorhynchus) interacting can display at least two such components, and the fish have been described as abruptly moving the frequencies of their signals quite con- siderably in response to one another. Recent analysis per- formed by the first author in collaboration with John Lewis and Ginette Hupe of the University of Ottawa, however, reveals that these interactive modulations may instead involve only a slight adjustment of signal frequencies to induce different beat frequencies in the resulting combina- tion tone. The auditory impression of a brief change in beat- ing is often that of a chirp or abrupt change in fundamental frequency. Without the precision of the reassigned spectro- gram, the resolution and measurement of closely aligned and beating gymnotid signals has been a serious challenge in the past. Figure 6 shows both a long and a short frame analysis of the same brown ghost signals; the long frame resolves the closely spaced line components, but does not have sufficient time resolution to show the beating between them, while the short frame fails to resolve the multiple components, but gains the ability to show the individual beats as impulse-like signal elements.
Sound modeling
Additive sound models represent sounds as a collection of amplitude- and frequency-modulated sinusoids. The time- varying frequencies and amplitudes are estimated from peaks in the spectrogram. These models have the very desirable property of easy and intuitive manipulability. Their parame- ters are easy to understand and deformations of the model data yield predictable results. Unfortunately, for many kinds of sounds, it is extremely difficult, using conventional tech- niques, to obtain a robust sinusoidal model that preserves all relevant characteristics of the original sound without intro- ducing artifacts.
For example, an acoustic bass pluck is difficult to model because it requires very high temporal resolution to represent the abrupt attack without smearing. In fact, in order to cap- ture the transient behavior of the pluck using a conventional spectrogram, a window much shorter than a single period of the waveform (which is approximately 13.6 ms in the exam- ple shown in Fig. 7) is needed. Any window that achieves the desired temporal resolution in a conventional approach will fail to resolve the harmonic components.
An additive model constructed by following ridges on a
reassigned spectrogram yields greater precision in time and
frequency than is possible using conventional additive tech-
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It is useful to emphasize that the single attack transient in the bass pluck has been located in time to a high level of pre- cision using long analysis windows which resolve the har- monics, a feat that is not possible with the conventional spec- trogram. This is not to suggest that two closely spaced tran- sients could be resolved if they both fell within a single analy- sis window.
Improving on the improved
In spite of the obvious gains in clarity of the locations and movements of line components in these reassigned spec- trograms, as well as the improved time localization of impul- sive events, the images can be cluttered with meaningless random points. This is mainly because the algorithm employed to locate the AM/FM components in the signal has a meaningful output only in the neighborhood of a compo- nent. Where there is no component of significant amplitude, the time-frequency locations of the points to be plotted can become random.
We next describe a technique theoretically outlined by Doug Nelson of the National Security Administration at Fort Meade, which has the potential to “denoise” our spectro- grams, and also to permit quasistationary (low FM rate) components to be isolated in a display, or alternatively to per- mit highly time-localized points (impulses) to be isolated.
From the reassigned spectral data shown in Fig. 7, we can construct a robust model of the bass pluck that cap- tures both the harmonic components in the decay and the transient behavior of the abrupt attack. Sounds reconstruct- ed from a reassigned additive model preserve the temporal envelope of the original signal. Time-warping, pitch shifting, and sound morphing operations can all be performed on the model data while retaining the character of the original sound.
niques.
Fig. 6. Brown ghost fish signals interacting; upper panel analyzed with 200 ms frames, lower panel with 10 ms frames. The long frame reveals the small changes in fundamental frequencies of closely spaced components, while the short frame is unable to resolve the multiple components but shows the beats as quasi-impulsive amplitude modulations.
30 Acoustics Today, July 2006