A waveform display apparatus and method displays one or more waveforms of a signal under test at high throughput while acquiring digital data of the signal under test in a large acquisition memory. A user sets a time interval of user's interest when viewing a signal under test and sets trigger criteria through a user interface. An ADC converts the signal under test into digital data that is stored in a large acquisition memory. A trigger unit detects and produces trigger events, based on a trigger, as trigger event information during one acquisition process. A trigger event eliminator may discard some of the trigger events based on pre-trigger and post-conditions set through the interface by a user. The trigger events are recorded in a trigger list as the trigger event information. A control unit locates the digital data in the acquisition memory corresponding to the trigger events in the trigger list and displays a waveform associated with the trigger event for the time interval on a display device.