A new spectral representation called the composite model is proposed. Its key point is to decompose all spectra into a smooth background and a collection of spikes. The smooth part can be represented by Fourier coefficients and a spike by its location and height. In this paper, the sufficiency of a low-dimensional representation is shown analytically based on the characteristics of human perception. A re-sampling technique is also proposed to improve performance. The composite model demonstrates advantages in all identified representation criteria including accuracy, compactness, computational efficiency, portability and flexibility. Its applications in areas of realistic image synthesis, image understanding, storage and communication of spectral images, and deriving natural spectra are discussed.