The spectrogram correlation and transformation (SCAT) model of the sonar receiver in the big brown bat (Eptesicus fuscus) consists of a cochlear component for encoding the bat's frequency modulated (FM) sonar transmissions and multiple FM echoes in a spectrogram format, followed by two parallel pathways for processing temporal and spectral information in sonar echoes to reconstruct the absolute range and fine range structure of multiple targets from echo spectrograms. The outputs of computations taking place along these parallel pathways converge to be displayed along a computed image dimension of echo delay or target range. The resulting image depicts the location of various reflecting sources in different targets along the range axis. This series of transforms is equivalent to simultaneous, parallel forward and inverse transforms on sonar echoes, yielding the impulse responses of targets by deconvolution of the spectrograms. The performance of the model accurately reproduces the images perceived by Eptesicus in a variety of behavioral experiments on two-glint resolution in range, echo phase sensitivity, amplitude-latency trading of range estimates, dissociation of time- and frequency-domain image components, and ranging accuracy in noise.