Multispectral imaging beyond the three RGB colors still remains a challenge, especially in portable inexpensive systems. In this paper, we describe the design and fabrication of broadband multichroic filters that have a sinusoidal transmission spectra to utilize a novel methodology based on the Fourier spectral reconstruction in the frequency domain. Since the spectral filters are posed as an optimal sampling of hyperspectral images, they also allow for the reconstruction of the full spectrum from subsequent demosaicking algorithms. Unlike conventional Color Filter Arrays (CFA) which utilizes absorption dyes embedded in a polymeric material, the sinusoidal multichroic filters require an all-dielectric interference filter design. However, the goal of most dielectric filter designs is to achieve sharp transitions with high-contrast. A smoothly varying sinusoidal transition is more difficult with conventional approaches. However, this can be achieved by trading off the contrast. Following the principles of a simple Fabry-Perot cavity, we have designed and built interference filters from 0.5 sinusoidal periods to 3 sinusoidal periods from 450nm to 900nm spectral range. Also, in order to maintain a uniform period across the entire spectrum, the material must have a very low dispersion. In this design, we have used ZnS as the cavity material. The six filters have been used in a multispectral imaging test bed.