We experimentally demonstrate the first instrument for compressing the time-bandwidth product of analog signals in real-time. By performing self-adaptive stretch, this technology enables digitizers to capture waveforms beyond their bandwidth with digital data size being reduced at the same time. The compression is achieved through a transformation of the signal’s complex field, performed in the analog domain prior to digitization. For proof of concept experiments, we compress the modulation bandwidth of an optical signal by 500 times. At the same time, we reduce its modulation time-bandwidth product (i.e., the record length) by 2.73 times while achieving 16 dB power efficiency improvement in comparison to the case of using conventional dispersive Fourier transform. Dispersive data compression addresses the big data problem in real-time instruments and in optical communications.