Echolocating bats perceive objects as acoustic images derived from echoes of the ultrasonic sounds they emit. They can detect, track, identify, and intercept flying insects using sonar. Many species, such as the big brown bat, Eptesicus fuscus, emit frequency-modulated sonar sounds and perceive the distance to targets, or target range, from the delay of echoes. For Eptesicus, a point-target's image has a sharpness along the range axis that is determined by the acuity of echo-delay perception, which is about 10 ns under favorable conditions. The image as a whole has a fine range structure that corresponds to the cross-correlation function between emissions and echoes. A complex target- which has reflecting points, called "glints", located at slightly different distances and reflects echoes containing overlapping components with slightly different delays--is perceived in terms of its range profile. The separation of the glints along the range dimension is encoded by the shape of the echo spectrum created by interference between overlapping echo components. However, Eptesicus transforms the echo spectrum back into an estimate of the original delay separation of echo components. The bat thus converts spectral cues into elements of an image expressed in terms of range. The absolute range of the nearest glint is encoded by the arrival time of the earliest echo component, and the spectrally encoded range separation of additional glints is referred to this time-encoded reference range for the image as a whole. Each individual glint is represented by a cross-correlation function for its own echo component, the nearest of which is computed directly from arrival-time measurements while further ones are computed by transformation of the echo spectrum. The bat then sums the cross-correlation functions for multiple glints to form the entire image of the complex target. Range and shape are two distinct features of targets that are separately encoded by the bat's auditory system, but the bat perceives unitary images that require fusion of these features to create a synthetic psychological dimension of range. The bat's use of cross-correlation-like images reveals neural computations that achieve fusion of stimulus features and offers an example of high-level operations involved in the formation of perceptual "wholes".