We describe what we believe to be novel methods for waveform synthesis and detection relying on longitudinal spectral decomposition of subpicosecond optical pulses. Optical processing is performed in both all-fiber and mixed fiber-free-space systems. Demonstrated applications include ultrafast optical waveform synthesis, microwave spectrum analysis, and high-speed electrical arbitrary waveform generation. The techniques have the potential for time-bandwidth products of >=10~(4) due to exclusive reliance on time-domain processing. We introduce the principles of operation and subsequently support these with results from our experimental systems. Both theory and experiments suggest third-order dispersion as the principle limitation to large time-bandwidth products. Chirped-fiber Bragg gratings offer a route to increasing the number of resolvable spots for use in high-speed signal processing applications.
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