Nonstationary acoustic features provide essential cues for many auditory tasks, including sound localization, auditory stream analysis, and speech recognition. These features can best be characterized relative to a precise point in time, such as the onset of a sound or the beginning of a harmonic periodicity. Extracting these types of features is a difficult problem. Part of the difficulty is that with standard block-based signal analysis methods, the representation is sensitive to the arbitrary alignment of the blocks with respect to the signal. Convolutional techniques such as shift-invariant transformations can reduce this sensitivity, but these do not yield a code that is efficient, that is, one that forms a nonredundant representation of the underlying structure. Here, we develop a non-block-based method for signal representation that is both time relative and efficient. Signals are represented using a linear superposition of time-shiftable kernel functions, each with an associated magnitude and temporal position. Signal decomposition in this method is a non-linear process that consists of optimizing the kernel function scaling coefficients and temporal positions to form an efficient, shift-invariant representation. We demonstrate the properties of this representation for the purpose of characterizing structure in various types of nonstationary acoustic signals. The computational problem investigated here has direct relevance to the neural coding at the auditory nerve and the more general issue of how to encode complex, time-varying signals with a population of spiking neurons.