Synthetic aperture sonars (SAS) or radars (SAR) that transmit narrow‐band signals are sampled arrays and therefore must satisfy sampling requirements to avoid aliasing. The sampling requirements for a narrow‐band SAS or SAR may be relaxed if a broadband signal is used. From a beamforming view, broadband transmit signals result in a mainlobe that always points in the same direction and has a width that varies as the transmit signal sweeps through the broadband, but having aliasing lobes that change in both width and direction. A composite broadband beam pattern would show constructive mainlobes but smeared aliasing lobes. Broadband undersampled synthetic aperture images similarly show a target image having the samex–yimage space position for all frequencies, but alias target images that have azimuth positions that vary with frequency. A synthetic aperture image uses the entire transmit band, and so, targets appear sharp and aliases become smeared. An approximate relation for the level of smearing of the alias targets may be shown, which depends on the signal bandwidth, the platform speed, the sonar along‐track length, center frequency, and the pulse rate. This allows the design of broadband undersampled synthetic aperture sonars with higher speeds and greater mapping rates. [Work supported by the Charles Stark Draper Laboratory, Cambridge, MA.]