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resolve 256 (= 28) different amplitude values; a 16-bit converter can resolve 65,536 (= 216) values.

      For the echolocation recordings in this book, the sampling rate (250 or 500 kHz) was always more than twice the highest frequency contained in the original bat signal, and the sample size was 16-bit.

      Any acoustic signal can be graphically or mathematically represented in two ways: time domain and frequency domain. A time-domain graph shows how a signal changes over time, while a frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies. A pure tone is called a sinusoid because its amplitude is a sine function in the time domain. In the frequency domain, it is a vertical line. Any continuous sound, no matter how complex, can be represented as the sum of sinusoidal components, because each pure tone has a particular amplitude and time relationship relative to the other pure tone components.

      Spectrum analysis is the process of converting the time-domain signal to a frequency-domain signal, showing how different frequency components contribute to the sound. Fourier transformation is the mathematical function that is often used to convert the time-domain form to a frequency-domain representation or spectrum. An individual spectrum contains no information about temporal changes in frequency composition of the spectrum. A spectrogram shows how the frequency composition of a signal changes over time. The spectrograms in this book are based on a Fast Fourier Transform algorithm. A Hanning window was used to eliminate the effects of background noise (Figure 38).

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      The transformation of ultrasound into a signal audible to human ears requires the use of specialised bat detectors, of which there are three main types. Advances in digital technology have completely revolutionised the means available to study bat sonar today, even compared to three decades ago. Thus, the pioneering work by M. B. Fenton and colleagues in southern Africa (e.g. Fenton et al. 1977, Fenton and Bell 1981) required heavy, expensive analog equipment, particularly to record ultrasonic calls (Kunz 1988). While the best of the modern digital bat detectors, coupled with powerful laptop computers, are still relatively costly, they are much more affordable to researchers. More compact digital ultrasonic detectors have radically lowered the costs of functional bat detectors, which has opened up their affordability to non-specialist enthusiasts to survey bats.

      Heterodyne detectors convert bat calls into electronic signals, which are then compared to an internal signal of a particular frequency. The internal frequencies of detectors are ‘tunable’ so that the bat’s actual peak frequency can be estimated within a limited band of frequencies, usually 10 kHz. Two disadvantages of this system are that bat passes can be missed because the full range of possible echolocation frequencies used by bats (e.g. between 10 and 214 kHz in southern Africa) has to be scanned ∼10 kHz at a time, and bandwidth information is lost. Advantages of heterodyne detectors are that they work in real time, are easy to use, and are the least expensive. In fact, in Europe, heterodyne detectors such as the Magenta, Maplin, and Batbox III are very popular among the public and scientists for basic field identification of species and the monitoring of bat activity, because calls of local species are increasingly well known.

      Frequency division detectors digitally scale down the entire ultrasonic frequency range of a bat call into the human hearing range. This is done by converting the call into a square wave, called a zero-crossing signal. The square wave is divided by a constant factor, usually 10, meaning that a frequency of 50 kHz will be converted to 5 kHz. In other words, frequency division detectors count the number of cycles of the ultrasonic signal (N), and effectively divide the frequency by N, where N is usually 10. Frequency division detectors are only capable of tracking one frequency (harmonic) at a time. Usually this is the fundamental frequency. Consequently, it is difficult to perform a harmonic analysis from a frequency division signal. Advantages of frequency division detectors are that they are reasonably priced, work in real time and cover a broad bandwidth, in other words, all of the ultrasonic frequencies of co-existing bats are recorded, without missing frequencies of species because of tuning choices. Because some scientists use the ANABAT frequency division bat detector (Titley Electronics, Australia) to identify bat species and monitor bat activity (but see Fenton et al. 2001), echolocation data of southern African bat species that were recorded by the authors with the ANABAT system are presented in Table 3.

      TABLE 3.

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SPECIES N FMAX FMIN FC FK DUR TC TK
HIPPOSIDERIDAE
Hipposideros caffer 6 143.8±1.1 125.5±13.2 142.6±1.2 142.3±1.5 4.5±0.5 3.2±0.3 0.9±0.5
Hipposideros ruber 4 136.6±2.7 106.9±21.2 136.3±2.9 135.8±2.9 4.8±0.5 3.9±0.8 1.1±1.5
Macronycteris vittatus 2 65.3±1.9 57.9±0.4 64.5±1.7 64.9±2.1 9.5±1.3 7.6±1.8 0.4±0.07
RHINONYCTERIDAE
Cloeotis percivali 4 103.2±0.7 99.4±4.3 102.4±0.7 103.1±0.8 1.9±0.6 1.6±0.3 0