This Lasionycteris noctivagans call exhibits a strong series of harmonic components, both real and aliased. The recording was made using a detector having a sampling rate of 300 kHz. According to digital sampling theory, this detector can only resolve real, i.e. non-aliased, sounds up to one half of its sampling rate, or 150 kHz. This limiting frequency is called the Nyquist frequency.

Alias harmonics represent real frequency content misinterpreted by too low a sampling frequency, or artifacts of signal content too loud for the microphone or recording hardware to interpret, analogous to overexposure in photography.

The frequency scale for this sonogram ends at the Nyquist frequency of 150 kHz and you would find no displayed frequency content above that. Any real frequency content above 150 kHz will render alias harmonics, as will artifactual frequency content interpreted from overloaded signals. These effects are known as aliases, because they are higher frequency signals aliasing as lower frequency signals. The multiple stacks of harmonics often seen in some recordings as shown here result from an artifactual effect of an overloaded recording. Also called a saturated or “clipped” recording because the upper an lower signal levels get clipped off leaving waveforms with flat tops an bottoms. Combining multiple harmonics can generate flat topped waves, and unfortunately digital signal processing cannot distinguish real from artifact harmonics.

Aliasing results from a direct effect of digital sampling and adds noise to recordings. Understanding aliasing helps to interpret digital sampling and processing of bat vocalizations.

Sounds are pressure density waves that travel through air (or other media). Microphones transduce these waves into fluctuating electrical waves. Originally these signals are continuous, or analog. But for a computer to work with such signals, they must be converted to a string of numbers that describe discrete positions of the wave. This digital representation can be thought of as a connect-the-dots model of the signal. To understand why aliasing occurs, it is important to realize that the dots are acquired as very quick “snap shots” of the signal, separated by the sampling interval.

Aliasing occurs when a signal fluctuates in between the snap shots; in other words, the frequency of the signal is greater than the frequency of the sampling snap shots. This leaves the computer ignorant that any additional fluctuation has occurred, and it thus interprets the signal at a lower frequency, or alias of the real signal waveform.

On a sonogram representaton of such a signal, the alias components fold down from the Nyquist frequency by the same amount that they are above it. Thus for this example with a Nyquist frequency of 150 kHz, a 160 kHz input signal would be represented as a 140 kHz signal; a 200 kHz signal would be represented as a 100 kHz signal and so on.