their mathematical expectations follow the

their mathematical expectations follow the expressions
According to the CLT for independent random variables , for N → ∞  the expression tends to a standardized Gaussian random variable. Therefore for N ≫ 1 we have the following approximate equalities: where θ0, , are the standardized Gaussian random variables. From here we obtain that the partial sum of the series (2) containing a constant component and a sum of the first kmax harmonics (that satisfy the inequality (6)) would take the form where for the Fourier-series expansion of the normal fluctuation interferences on the [–T/2, T/2] interval. To obtain the protein phosphatase inhibitor spectrum S(w) of the interference (1) in the frequency range, where , it is necessary to square the expression (10) and to average the result over the implementation ensemble. It is seen from Eqs. (10) and (11) that the discrete energy spectrum is non-uniform: for the spectral component of the energy spectrum at a zero frequency decreases twofold; for the case when , the spectral component at this frequency increases significantly. This result was missing in Ref. [2]. We may assume that when a finite (and not very large) number of points N is chosen, a ‘pedestal’ will form in the vicinity of the zero frequency. For the energy spectrum we obtain from Eq. (10): where N is the mean value of pulses during time T. With an increase of T the discrete spectrum becomes practically continuous.
A canonical decomposition of Gaussian narrowband fluctuation interferences Now let us discuss the situation when there are numerous interferences in the [–T/2, T/2] interval: where is a Gaussian stationary narrowband random process with a zero mathematical expectation and variance σ2; is the point in time at which the lth interference lasting for the time period ≪ Tappears (Fig. 2). Let us set the each interference as a periodic (in the root-mean-square average [6]) random process with the autocorrelation-function period τ by using the canonical Walsh analysis: where the lower index (m( ± )n) is defined by m, n designations in binary notation with a subsequent taking the modulo 2 sum of their bits [7]. Before we start discussing the formalism of delta functions, notice that we may roughly assume based on Eq. (13) that over a sufficiently short interval the function takes the value which is a random variable that is a linear combination of random variables with their factors equaling either +1 or –1:
Case 1. Let , i.e. period τ (Fig. 2(a)) of the first harmonic of the canonical decomposition is no less than the length of the carrier of any interference . In this case the fluctuation interferences (12), which we are going to subject to harmonic analysis over an interval of T length, may be given mathematically using the delta functions: where the form of random variables  is given by Eq. (14). Let all interferences be characterized by a zero mathematical expectation and variance σ2. The mathematical expectations of random variables equal zero (since the mathematical expectation of the initial process equals zero), while the variance of a random variable , based on Eq. (14), equals the sum of variances of uncorrelated random variables ; therefore, it equals the variance of the interference (13) σ2. Then, by using the CLT (as in the previous section), we obtain a decomposition of a random process (15) during time T:
Case 2. Let us now examine the situation where the carrier of each interference ( is a natural number larger than or equal to 2), so that the sum of the series
In this case it makes sense to split each interval into non-intersecting subintervals of length τ (Fig. 2(b)).For each subinterval let us write a canonical representation of interference in the form (13). Let us assume that the interferences are characterized by a zero mathematical expectation and a total σ2 on each subinterval of length τ.