Wideband Spectroscopy: The Design and Implementation of a 3 GHz Bandwidth, 8192 Channel, Polyphase Digital SpectrometerA family of state-of-the-art digital Fourier transform spectrometers has been developed, with a combination of high bandwidth and fine resolution unavailable elsewhere. Analog signals consisting of radiation emitted by constituents in planetary atmospheres or galactic sources are downconverted and subsequently digitized by a pair of interleaved Analog-to-Digital Converters, (ADC). This 6 Gsps (giga-sample per second) digital representation of the analog signal is then processed through an FPGA-based streaming Fast Fourier Transform (FFT), the key development described below. Digital spectrometers have many advantages over previously used analog spectrometers, especially in terms of accuracy and resolution, both of which are particularly important for the type of scientific questions to be addressed with next-generation radiometers. the implementation, results and underlying math for this spectrometer, as well as, potential for future extension to even higher bandwidth, resolution and channel orthogonality, needed to support proposed future advanced atmospheric science and radioastronomy, are discussed.