All signal processing techniques exploit signal structure; when the signals are random, we want to understand the probabilistic structure of irregular, ill-formed signals. Such signals can be either be bothersome (noise) or information-bearing (discharges of single neurons). Our research is predicated on the notion that a deep understanding of a signal’s structure will result in signal processing algorithms that can either suppress bothersome signals or enhance information-bearing ones. Current research ranges from fundamental studies of non-Gaussian signals and how systems extract and represent information to applying these theories to the analysis of neural data and modeling of how neural structures process information.

Stationary non-Gaussian signals occur frequently in practical situations. For example, the amplitude distributions of ambient underwater sounds and of background electromagnetic signals have been found to deviate strongly from a Gaussian characterization.

Neural discharges are modeled as stochastic point processes, which have no waveform, thereby disallowing Gaussian models.

Combined discharges of neural populations and DNA sequences represent examples of *symbolic* data, which have amplitudes selected from a finite set: the signal takes on values drawn from the alphabet representing base pairs {A, C, G, T}. These signals are particularly interesting since amplitudes have **no** mathematical operations defined for them: No field or group can be meaningfully defined for them. We have found ways of computing the Fourier and wavelet transforms of symbolic signals.