Around 300 bat species are known to emit their ultrasonic biosonar pulses through the nostrils. This nasal emission coincides with the presence of intricately shaped baffle structures surrounding the nostrils. Some prior experimental evidence indicates that these "noseleaves" have an effect on the shape of the animals' radiation patterns. Here, we present a numerical acoustical analysis of the noseleaf of a horseshoe bat species. We show that all three distinctive parts of its noseleaf ("lancet," "sella," "anterior leaf") have an effect on the acoustic near field as well as on the directivity pattern. Furthermore, we show that furrows in one of the parts (the lancet) also exert such an influence. The underlying physical mechanisms suggested by the properties of the estimated near field are cavity resonance, as well as reflection and shadowing of the sound waves emitted by the nostrils. In their effects on the near field, the noseleaf parts showed a tendency toward spatial partitioning with the effects due to each part dominating a certain region. However, interactions between the acoustic effects of the parts were also evident, most notably, a synergism between two frequency-dependent effects (cavity resonance and shadowing) to produce an even stronger frequency selectivity.