Data signals consisting of arbitrarily modulated sequences of pulses are extensively used for processing and communication applications. The spectral extent of such signals is determined by the bandwidth of the individual pulses in the sequence, which imposes a fundamental limit to the maximum amount of information that can be transmitted or processed per time period. In this work, we propose and experimentally demonstrate that the frequency spectrum occupied by a data-modulated pulse sequence can be significantly compressed to well below the individual pulse bandwidth while still maintaining the temporal duration of the pulses in the sequence and without losing any of the information carried by the signal. The proposed method involves fully reversible linear transformations of the data signal along the time and frequency domains. We demonstrate successful pulse-shape-preserving spectral compression and subsequent full waveform and information recovery of a ～10Gb/s optical pulse sequence, modulated by an arbitrary data pattern, liberating over 60% of its bandwidth. These findings should prove useful for applications in signal processing, communications, and others.