## 3 Acquired Data  
### Signal Acquisition  
A wheel signature is a change of voltage signal u1 and u2 (sensor head signal) as a function of the position of the wheel on the rail in relation to the sensor (s). In fact, this signature does not depend only on the wheel profile (**W**), including its wear & tear but on its lateral position (p1) and may also depend on a rail profile and its condition (**R**).  
The wheel signature may be obtained automatically in the following way:  
* by means of recording the signals u1 and u2 for the wheel moving on the rail as a function of the position \(s\). This method gives directly the \"wheel signatures\" as a function **U** = f(s, **p**, **W**, **R**). This method is independent on the speed of the moving wheel, however it requires additional information about the position \(s\) (Figure 3).
* by means of recording the signals u1 and u2 for the wheel moving at constant speed along the rail as a function of time. This method gives the wheel signatures as a function **U** = f(t, **p**, **W**, **R**), that can be recalculated for the position of wheel (u = f(s)) as the speed is known and is constant. It does not require any additional signals to be measured. The center of a head may be used as a reference point where both signals u1 and u2 cross (Figure 3).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Wheel Profile** & **Position** & **Position** & **Position** \\
**W** & **p0 [mm]** & **p1 [mm]** & **p2 [mm]** \\ \hline k2 & 0 & 60 & 83 \\ k4 & 0 & 60 & 85 \\ k5 & 0 & 60 & 82 \\ k6 & 0 & 60 & 70 \\ k8 & 0 & 60 & 70 \\ k10 & 0 & 60 & 83 \\ k11 & 0 & 60 & 83 \\ k13 & 0 & 60 & 81 \\ k15 & 0 & 60 & 88 \\ k16 & 0 & 60 & 83 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The lateral position of wheel.  
The first method (a) gives a wheel signature directly. The number of samples for the wheel signature, while recorded with the density of one sample per millimeter, would be around 300 (for sensor sensitivity area equal to 30 cm). In the case of a wheel moving at 1 km/h and 10 kSps of the wheel detector sampling rate, 10,800 samples are acquired. It means that, to obtain the same resolution between each sample recorded using method (a), 36 new samples must be added.  
The second method (b), used during measurements does not require any additional signal except u1 and u2. To avoid the need for interpolation, the signals are recorded for wheel moving at a constant speed of 1 km/h and sampled exactly with the same frequency, like a wheel detector works (f\({}_{\mathrm{i}}\)).  
If the speed is different, then it is standardized to 1 km/h by a resampling method or by means of adjusting the sampling rate for gathering the signal (f\({}_{\mathrm{m}}\)) to the real speed of a moving wheel according to the formula:  
\[\mathrm{f_{m}[Hz]}=\mathrm{f_{i}[Hz]}.\frac{\mathrm{v[km/h]}}{1\mathrm{km/h}} \tag{1}\]  
where:  
f\({}_{\mathrm{m}}\)--sampling rate for signal recording,  
F\({}_{\mathrm{i}}\)--operating sampling rate of detector,  
v--speed of a moving wheel.  
Both methods provide the buffer of samples reflecting the signals recorded with the speed of 1 km/h and may be transformed to a different speed by means of a decimation method (down sampling).