Spectroscopic measurements are used in increasingly diverse areas of manufacturing, disease detection, food quality inspection, indoor lighting control, etc. Commonly used spectral decomposition methods utilize several discrete dispersive optical elements to split the incoming light into its frequency components and direct them onto a linear photodetector array. In our previous work, we demonstrated that such mechanically fragile systems can be replaced by thin film dielectric Fourier spectral filters. However, the main disadvantage of this technique is the need for multiple filters with varying dielectric Fabry-Perot cavity lengths, which requires extensive fabrication processes to lithographically pattern and etch. In this work, we demonstrate a novel fabrication of a continuously variable filter, using glancing angle deposition, that can produce 10× more Fourier filters in a single deposition run without the need for lithographic patterning. We apply this method to a commercial off-the-shelf 38-channel linear photodetector array and demonstrate the ability to quickly decompose the incoming signal using only half of the available channels. This novel technique has the potential to enable highly compact and highly robust spectrometers that could be integrated into many handheld devices