Compressive sensing (CS) is an approach for efficient signal acquisition based on the compressibility of the data and allowing the reconstruction signals below the Shannon-Nyquist sampling rate. Besides imaging, compressive sensing can be exploited in spectrometer design. Here we have constructed and compared a broadband, high resolution Echelle spectrometer against a potentially higher resolution, narrower band Sagnac Fourier spectrometer that also has larger signal intensity. The goal of each is a field-deployable Raman gas isotope system. The initial demonstration will have hardware resolution and algorithms specific to oxygen isotope identification. The end goal is also detection and recognition directly on the compressive measurements without needing to first reconstruct the entire spectrum. Towards that end, we have also combined the mathematics of manifold secants in multiple network structures to construct a detection and classification algorithm useful for spectra, as well as images. Combining this with dynamic-rate training scheme, we reach higher classification accuracy and need only a few measurement rates for training for the chosen dataset with a single neural network, rather than training a unique neural network for each rate.