The QUIJOTE Experiment was developed to study the polarization in the Cosmic Microwave Background (CMB) over the frequency range of 10-50 GHz. Its first instrument, the Multi-Frequency-Instrument (MFI), measures in the range 10-20 GHz which coincides with one of the naturally transparent windows in the atmosphere. The Tenerife Microwave Spectrometer (TMS) has been designed to investigate the spectrum between 10-20 GHz in more detail. The MFI bands are 2 GHz wide whereas the TMS bands will be 250 MHz wide covering the complete 10-20 GHz range with one receiver chain and Fourier spectral filter bank. It is expected that the relative calibration between frequency bands will be better known than the MFI channels and that the higher resolution will provide essential information on narrow band interference and features such as ozone. The TMS will study the atmospheric spectra as well as provide key information on the viability of ground-based absolute spectral measurements. Here the novel Fourier transform spectrometer design is described showing its suitability to wide band measurement and √N advantage over the usual scanning techniques.