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Data-processing techniques in spectroscopy are fundamental and powerful analytical tools for lots of practical applications. In the age of big data, high-speed data-processing in spectroscopy is in urgent need, especially for the real-time analysis/feedback of data stream of spectroscopy or the capture of non-repetitive/rare phenomena in fast dynamic process. So far, intensive researches focus on high-speed processing of light signal in time/spatial domain but few people find a way to do it in spectral domain. Here, we report an optical computing technology for high-speed optical spectrum processing with features of real time, multiple functions, all-fiber configuration and immunity to electromagnetic interference. The software-controlled system could perform as, but not limited to, the first-order (or arbitrary fractional-order) differentiator/integrator/Hilbert transformer and tunable band-pass filter, respectively, to handle spectral data rapidly. High-speed processing of optical spectrum at a rate of 10,000,000 times per second is demonstrated.