A fundamental question in sensory neuroscience is how information is encoded in spike trains. The question often takes the form of distinguishing between rate codes, in which information is encoded in terms of the number of spikes within an encoding window, and temporal codes, in which the position of spikes within an encoding window carries information beyond that available from the number of spikes in the window 
. Temporal codes are usually associated with nonlinear relations between the Fourier components of a stimulus and a neuronal response 
, i.e. correlations between a particular frequency component of a stimulus and higher-frequency components of the response. These nonlinear relations provide information about the stimulus beyond that provided by linear correlations within the frequency band of the stimulus. In contrast, rate coding can be nonlinear, but it is characterized by a lack of correlation between Fourier components of the stimulus and higher-frequency components of the response, or by the fact that such nonlinear correlations, when present, do not provide any additional information about the stimulus. The pioneering work of Adrian 
provided clear evidence that cutaneous sensory afferents use firing rate to encode stimulus intensity (a concise history of this work and related issues is in 
). More recent work on a number of sensory systems has provided equally compelling evidence that precise spike timing can carry information beyond that available from measures of firing rate (e.g., 
among many others).
An additional consideration is that primary afferent neurons in a variety of sensory systems exhibit an ongoing background discharge. Examples include vestibular afferents 
, and electroreceptor afferents in several aquatic species 
. Such background firing can arise from a variety of mechanisms including intrinsic oscillators, intrinsic noise, or random synaptic events. The resulting discharges span the spectrum from highly periodic to completely random spike sequences. Several studies have attempted to relate the properties of this background discharge to the stimulus encoding properties of afferents, by stimulating a system with time-varying Gaussian noise, and assessing information transmission based on various information metrics calculated from their responses (reviewed in 
To assess the relative importance of firing rate versus precise spike timing in stimulus encoding, a computational procedure is often used in which the time of each spike is “jittered” by the addition of a variable time offset, chosen randomly from a zero-mean distribution 
. The jittering produces a surrogate data set for which information metrics can be computed and compared to the same metrics computed from the original data. If the addition of jitter significantly decreases the information transmission and/or encoding efficiency of the afferent, as happens, for example, for some vestibular afferents 
, then the existence of a temporal encoding scheme is inferred.
However, the distinction between a rate code and a timing code can be problematic for a number of reasons. First, as discussed by Theunissen and Miller 
, the use of spike timing to encode transient or high frequency components of a stimulus can be consistent with a rate coding scheme, e.g. 
. Nor does the use of a temporal encoding scheme require high spike timing precision. Even in the case of a highly periodic spontaneously firing neuron, which like all self-sustained oscillators is inherently nonlinear, the response magnitude at different points in the neuron's cycle (its phase response curve) can be closely related to its linear response function 
. Weak stimuli can be linearly encoded in the instantaneous firing rate of a periodically firing neuron, and this encoding can be accounted for within the framework of linear response theory 
. Thus, the intrinsic timing precision of a periodically firing neuron is not necessarily indicative of a temporal code as understood in the current neuroscience literature.
Second, the linear stimulus reconstruction technique 
that is typically used in conjunction with the jitter procedure treats a neuron as a linear
“black box” whose transfer function is tuned to minimize the mean square error of stimulus estimation. This technique essentially assumes a rate code, since the stimulus is estimated by convolving a spike train with the response function of the optimal linear
filter. Adding external noise in the form of jitter is equivalent to a distortion of the transfer function of the optimal filter. Thus, conclusions about the existence of a nonlinear time code drawn solely from application of a linear stimulus reconstruction technique may be questionable.
Third, the rationale for jitter analysis is based on the assumption that the standard deviation (SD) of the jitter distribution is small relative to the duration of an “encoding window”, so that the number of spikes within the window is unaffected, and only their temporal position within the window is altered. Thus, the SD of the jitter is normally chosen to be much smaller than the characteristic time scale of the stimulus on the assumption that this will be less than the duration of the encoding window. However, since the duration of the encoding window itself is never determined, this assumption cannot be validated, and so the results of artificial jittering should be interpreted with caution.
Here, we develop an analytical framework that provides a detailed, quantitative assessment of the effects of artificial jitter on spike train metrics commonly used to analyze sensory encoding: coefficient of variation, serial correlations, power spectral density, transfer functions, and coherence functions. This theoretical analysis allows us to specify precisely the relationships between these metrics as calculated for original and jittered spike trains. Using this framework, we show that jitter alters the higher order statistics of spike trains by introducing spurious serial correlations among interspike intervals. This can alter encoding properties. More importantly, we show that for weak stimuli and linear responses, jitter merely increases the noise in the background discharge. This occurs independently of any applied lower-frequency stimulus, and with minimal effects on stimulus-response gain. The additional noise from jitter results in suppression of the stimulus-response coherence (or the linear reconstruction kernel), and consequently of the mutual information rate, as estimated with the linear reconstruction technique. We illustrate these theoretical results by applying them to a model neuron with gamma-distributed interspike intervals, to a phase model of a periodically firing neuron, and to experimental data from vestibular and electroreceptor afferents. Although we focus on spontaneously active neurons, the theory, results, and conclusions we develop have broad applicability to analyses of sensory encoding.