A dual representation of spectral functions called the composite model is proposed. Its key point is to decompose all spectra into a smooth background and a collection of spikes. This duality not only reflects the physical emission and light-material interaction, but also provides a mathematical basis to effectively handle the opposing characteristics of spectra?frequency space is effective for smooth components, but wavelength space for spikes. In this paper, we represent the smooth part through Fourier coefficients, and spikes through delta functions. We show the sufficiency of a low-dimensional representation analytically through evaluating errors based on CIE color space and approximating the CIE color-matching functions in terms of Gaussian functions. To improve performance, we propose resampling smooth functions that are reconstructed from Fourier coefficients, and as a result spectral multiplications are greatly reduced in complexity. Overall, our composite model eliminates the drawbacks of previous one-fashion representations and is able to satisfy all identified representation criteria with aspect to accuracy, compactness, computational efficiency, portability, and flexibility. This new model has been demonstrated to be crucial for realistic image synthesis, especially for rendering spectral optical phenomena such as light dispersion and diffraction, and has promise in other research areas such as image analysis and color science.