To increase the percentage of time that an input signal is actively monitored, a digital oscilloscope has an acquisition system (100) that includes an analog-to-digital converter (15), an acquisition memory (40), an acquisition rasterizer (50), and a raster acquisition memory (60). The rasterizer contains circuitry (52) for concurrently rasterizing and combining the results of several acquisitions together and with a stored composite raster image to produce a new composite raster image, while additional acquisition records are being created and stored in the acquisition memory. A display system (220) takes the composite raster images after they contain the results of many acquisitions and overlays these single-bit raster images on a multi-bit raster image that is then decremented to produce a simulated persistence effect. The number of new pixels turned on as a result of each acquisition can be counted during the combining process and used to stop acquisitions, signal the operator, or specially treat that particular acquisition when the number of new pixels created by a particular acquisition exceeds a predetermined value. Acquisition circuitry for multiple channels can be used on one channel to further increase the percentage of time that the signal is monitored.