The simulation of complex light effects such as depth-of-field, motion blur or scattering in participating media requires a tremendous amount of computation. But the resulting pictures are often blurry. We claim that those regions should be computed sparsely to reduce their cost. To do so, we propose a method covariance tracing that estimates the local variations of a signal. This method is based on a extended frequency analysis of light transport and permits to build efficient algorithms that distribute the cost of low frequency parts of the simulation of light transport. This thesis presents an improvement over the frequency analysis of local light-fields introduced by Durand et al. [2005]. We add into this analysis of light transport operations such as rough refractions, motion and participating media effects. We further improve the analysis of previously defined operations to handle non-planar occlusions of light, anisotropic BRDFs and multiple lenses. We present covariance tracing, a method to evaluate the covariance matrix of the local light-field spectrum on a per light-path basis. We show that covariance analysis is defined for all the defined Fourier operators. Furthermore, covariance analysis is compatible with Monte Carlo integration making it practical to study distributed effects. We show the use of covariance tracing with various applications ranging from motion blur and depth-of-field adaptive sampling and filtering, photon mapping kernel size estimation and adaptive sampling of volumetric effects.