A time-stretched enhanced recording scope (TiSER) is described using time stretch analog-to-digital conversion in a real-time burst mode. A chirped optical signal is modulated in response to receiving segments of an input signal. The optical signal with its modulated input signal, is stretched through an optical medium and digitized to represent the waveform segment. TiSER provides ultra-fast real-time sampling within short segment bursts of the original input signal while providing an ability to detect non-repetitive events. Methods and apparatus are also described for providing real-time information about inter-symbol information (ISI), rapidly determining bit-error rates (BER), performing time-domain reflectometry (TDR), generating eye diagrams for serial data, facilitating digital correction of data, clock recovery, optical carrier phase recovery, and otherwise increasing the speed and/or accuracy of a diverse range of high-speed signal measurement and processing activities.