D11 Spectral Analysis of Underwater Acoustic Signals

Topic

Spectral analysis of underwater acoustic signals characterizes the frequency content of sounds produced by fish—such as vocalizations, the stridulation of certain body structures, and swim bladder resonance—as well as ambient noise in marine or fresh water. This provides tools to identify the species producing a sound, assess fish reproductive behavior, and detect the impact of anthropogenic noise on them. Underwater acoustics operates on the same physical principle as acoustics in air—pressure waves propagating longitudinally through a fluid—but with significant differences: sound travels through water at a much higher speed than in air (approximately 1,500 meters per second compared to 340 meters per second); water is a much denser medium; and water lacks a reflection-free interface where sound could dissipate without bouncing back.

To analyze these sounds, spectral analysis transforms the recorded acoustic pressure signal from the time domain to the frequency domain using the Discrete Fourier Transform or its computationally more efficient version, the Fast Fourier Transform. The result of this transformation is the signal's power spectral density, which describes how the total signal power is distributed across its constituent frequencies.

For fish vocalization signals—typically brief pulses with frequencies between 100 and 1,000 Hertz—a spectrogram is calculated instead of a single power spectral density for the entire recording. This spectrogram is obtained via a Short-Time Fourier Transform applied to successive windows throughout the recording. It reveals how frequency content changes over time, making it possible to identify each vocalization pulse, its fundamental frequency, accompanying harmonics, and the vocalization's complete temporal structure. In addition to describing the frequencies at which a sound occurs, spectral analysis provides two standard indicators to quantify the sound's intensity: sound pressure level, which measures a signal's instantaneous intensity, and sound exposure level, which integrates that intensity over the entire duration of the exposure.

When more than one hydrophone is available, the coherence function between each pair of hydrophones in the array also makes it possible to estimate the direction of an incoming acoustic signal by applying the principle of beamforming; this principle combines—using varying weights—the signals captured by the array's multiple hydrophones to steer the system toward different spatial directions, thereby detecting the origin of each sound source.

Regarding ambient ocean noise, the expected behavior is for the power spectral density to follow the Wenz spectrum—which exhibits a steep decline of approximately twenty decibels per frequency decade—for both anthropogenic and biological noise. Against this declining background, fish vocalizations appear as spectral peaks rising above the noise floor; through the same spectral analysis described earlier, these peaks allow for the identification of the species that produced them.

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