## 3 Results
### The Detection of PCRRf Patterns
#### 3.2.1 The Extraction of the PCRRf1 Patterns
As can be clearly seen in window 1, all harmonics of the fundamental component (with period \(T_{p1a}\)) are practically represented, which means that the analytical description of the pattern from Equation (6) can theoretically be raised over \(r=15\). The dominant sinusoidal component (previously identified by curve fitting and described in the first row of Table 2) is also well represented here (with frequency and amplitude by the highest peak in window 1). However, here and for all other sinusoidal components shown in the spectrum, the phase angle at the time origin is missing (not provided by FFT). Similarly to window 1 in Figure 20, curve 1 in Figure 21 shows a zoomed-in portion of the FFT spectrum of the extended analytical PCRRf1a (in the frequency range \(0\div 550\) Hz). As expected, there are only 15 peaks in this spectrum, corresponding to the 15 components identified before by curve fitting (and described in Table 2). Figure 20: The partial FFT spectrum of the synthetic PCRRf1a extended pattern (10 periods); 2—a zoomed-in area A; 3—a zoomed-in area B. It is important to note that both PCRRf1a patterns (synthetic and analytical) are affected by the action of BMAF (which previously allowed the definition of IAEPf from IEP) in the sense that practically the amplitudes of all sinusoidal components of these patterns are attenuated (and some of them are eliminated) on the one hand (i.e., depending on their frequency, their real amplitudes are found at the output of the filter multiplied by the transmissibility _Tr(f)_ of the filter, with _Tr(f)_\(<1\)), and on the other hand, their phases at the time origin are modified (a phase angle is introduced by filtering). The frequencies of the sinusoidal components remain unchanged. The variation of this transmissibility _Tr(f)_, depending on frequency, has already been shown (as an example) in Figure 5 (BMAF with \(h\) = 2000) for PCRRf1a; in particular, \(h\) = 2001. This question now arises: is it possible to obtain the real pattern unaffected by these two deficiencies (as the PCRR1a pattern)? Since the description of the main components of the analytical PCRRf1a is fully known (Table 2), there is a simple way to find the real amplitudes (as \(A_{ai}\)) of the sinusoidal components: amplify the amplitudes (\(A_{ai}\)) with the inverse of the BMAF transmissibility (1/_Tr(f)_) at frequencies \(f\) = \(B_{fai}\), so \(A_{ai}\) = \(A_{ai}\)/_Tr(\(B_{fai}\))_. As a consequence, because _Tr(f)_\(<1\), all the amplitudes \(A_{ai}\) increase (\(A_{ai}\) > \(A_{ai}\)). The variation of the inverse of the transmissibility with the frequency (within \(0\div 550\) Hz range) was shown before in Figure 21 (the red curve, 2). On the 1/_Tr(f)_ curve (with an upper limit at 200), there are some peaks (with infinite amplitudes) corresponding to _Tr(f)_ = 0 and the regions labelled R1, R2,..., R11 in between. It is easy to prove that only in the even regions (R2, R4,..., R10) is a phase shift of \(\pi\) radians introduced by BMAF so that the real phase angles at the origin of time (as \(C_{ai}\)) should be rewritten as \(C_{ai}\) = \(C_{fai}\) +\(\pi\). Only the components \(i\) = \(4\div 6\) fulfil this condition, such as when placed in R2. Using these amplitude and phase correction approaches, the description of the sinusoidal components of the real analytical pattern PCRR1a is given in Table 3.  
Unexpectedly, the amplitude \(A_{a7}\) is huge. A simple reason explains this fact: within the IEP, there is a huge dominant component of 100 Hz (1164 W, as shown in Figure 5). Because of the sampling, new sinusoidal components are artificially created (due to a phenomenon known as spectral leakage) and are very close (in frequency) to this dominant component. This component is not completely removed by the BMAF. It is obvious that this component must be compulsarily neglected in the analytical patterns PCRRf1a and PCRR1a.