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Laboratory molecular spectroscopy provides the basis for interpretation of atmospheric, planetary, and astrophysical data gathered by remote sensing. Laboratory studies of atomic and molecular signatures across the electromagnetic spectrum provide high-precision, quantitative data used to interpret the observed environment from remote measurements. Historically, the region of the spectrum above 500 GHz has been relatively unexplored due to atmospheric absorption and technical difficulties generating and detecting radiation. Laboratory spectroscopy at these frequencies has traditionally involved measurement of one or two absorption features and relied on fitting of models to the limited data. We report a new spectrometer built around a computer-controlled commercial synthesizer and millimeter-wave module driving a series of amplifiers followed by a series of wide-bandwidth frequency doublers and triplers. The spectrometer provides the ability to rapidly measure large pieces of frequency space with higher resolution, accuracy, and sensitivity than with Fourier transform infrared techniques. The approach is simple, modular, and requires no custom-built electronics or high voltage and facilitates the use of infrared data analysis techniques on complex submillimeter spectra.