Application to biomedical signals - Practical Biomedical Signal Analysis Using MATLAB - page 143

“noise” as an uncorrelated signal is also a great simplification and it is necessary
to take into account the statistical characteristics of the ongoing activity as will be
shown in the next paragraph. In any case, it is always suggested to include some
pre-stimulus time in the EEG epochs to be averaged to obtain some estimate of the
mean and variability of the ongoing activity.

4.1.7.1.2 Influence of noise correlation In quantification of EP, the main issue is
to increase the signal-to-noise ratio so as to minimize the contamination of EP by the
background EEG activity. Equation 4.10 shows that the ratio of signal variance to the
noise variance for N repetitions of the stimulus is N . This result holds for the noise
samples that are uncorrelated. This however, often is not true, e.g., in the presence of
strong rhythmic background activity like for example alpha rhythm. In such a case
subsequent samples of n are not independent. The degree of dependence of noise

samples is given by its autocorrelation function, which in this case has the following
form [Niedermayer and Lopes da Silva, 2004, chap. 50]:

( t )

σ 2 exp R xx ( τ )= ( − β | τ | ) cos ( 2π f 0 τ ) (4.12)

where σ 2 is the variance of noise, f 0 is the mean frequency of rhythmic activity, β π

is the corresponding bandwidth, and τ is the delay parameter. In this case the EP
variance takes another form [Spekreijse et al., 1976]:

/

σ 2
N

1 − exp ( − 2β T )

σ x ( t ) = (4.13)

1 − 2exp ( − β T ) cos ( 2π f 0 T )+ exp ( − 2β T )

where T is the inter-stimulus period. It is important to note that rhythmicity in the
background activity will influence the signal-to-noise ratio. It can be seen from the
above equation that the variance ratio tends to σ 2

N as β T becomes large. A related
problem is whether the stimulus should be periodic or aperiodic. Aperiodic stim-
ulation can lead to reduced EP variance [Ten Hoopen, 1975]. Periodic stimulation
can result in generation of a rhythmic activity with frequency corresponding to the
repetition rate of the stimulus.

4.1.7.1.3 Variations in latency One of the forms of randomness in single trial
response is the variation in latency. The latency jitter may lead to a distortion of the
averaged EP. The distortion may result in an underestimation of the averaged EP peak
amplitude and its greater spread over time. In more severe cases it may render the
EP undetectable. A possible consequence of this fact is that a significant difference
in amplitude of an average EP recorded in two experimental conditions can come
from a difference in latency jitter between conditions. Moreover, if the distribution
of latency jitter is skewed, the difference in latency jitter between conditions will also
lead to a difference in the latency of the deflections of the average ERP. The extent
to which latency jitter affects ERPs averaged in the time domain varies as a function
of the duration of the ERP deflection. Indeed, for the same latency variance, a long-
lasting deflection will be relatively more repeatable across trials than a short-lasting