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A wide-band FFT spectrum analyzer, which we call FX, has been in operation since 1983 at the Nobeyama Radio Observatory for spectroscopy of radio waves from interstellar molecules. It processes an input of six 320-MHz-bandwidth data streams to produce the output of fifteen cross-power spectra of 1024 frequency channels each. Its highly parallel pipeline architecture made it possible to achieve the above speed, 1010butterfly operations per second, which is 105times that of usual mainframe computers. The FX incorporates about 4500 newly developed CMOS LSI chips. They are designed using CAD (computer-aided design) and have 3900 or 2000 gates/chip, operate at a clock rate of 10 MHz, and consume 100 mW/chip or less. For 80-MHz bandwidth signal at an optimum input level, the SNR (signal-power to noise-power ratio) of the FX is better than 10 dB, which is adequate for astronomical use.