## 4 Video Rate Identification
Such noise-induced errors are of three kinds: (i) a transmission value, which is theoretically out of PBG bandwidth, gets lower than the PBG threshold (horizontal black dashed line): the PBG bandwidth is badly estimated as much as the frequency assignment of the channels, (ii) a defect peak is not taken into account as it keeps below the decision threshold (horizontal black continuous line): a channel is then not activated whereas it should be and (iii) a \"noise peak\" is detected as its amplitude becomes higher than the decision threshold, leading to the activation of a non-expected channel. Of course, the impact of the noise can be optimized by adjusting the two thresholds, especially the decision one that directly controls the unwanted activation, or inactivation of channels by the noise. In order to better understand the influence of the decision threshold, we plot in Figure 7a the behaviour of the BER versus this parameter for different acquisition times. First of all, Let noticed that the BER goes up to 100% when the decision threshold becomes higher than \(-8\) dB, despite the acquisition duration. This threshold value corresponds to the magnitude of the peak centered at 0.345 THz (see Figure 6). Indeed, in such a case, the peak can never be detected and thereby used to activate a channel, since the decision threshold is too high: the binary code cannot be retrieved and the BER tends to 100%. This behaviour is less drastic with short acquisition time since additional noise can potentially activate the expected channel, even if the decision threshold is higher than the peak magnitude (as illustrated by case (iii)) in Figure 6.  
On the other hand, when the decision is chosen lower, BER decreases to 0%, corresponding to an effective reliability of a reading smaller than 1%, before increasing again. This is obviously explained by the fact that the find-peak algorithm is more robust to the noise induced errors of kind ii and iii as long as the threshold decision remains in between the noise level and peaks magnitudes. Therefore, for each measurement time duration there is an optimal decision threshold position to obtain a minimum BER. We can notice in Figure 7b that this optimal threshold is roughly constant around \(-11\) dB, despite the acquisition time. Note that this optimal threshold is then located 3 dB below the magnitude of the lowest peak (here cantered at 0.345 THz). This decision threshold value can be  
Figure 6: Example of a tag signature obtained using an acquisition time of 8 ms (blue dots and dashed curve), compared to the reference one (red continuous curve). The grey dashed curve is the transfer function obtained by averaging one hundred 8-ms measurements (error bars are given by the standard deviation). The horizontal lines represent the decision thresholds used to automat-tically define the PBG bandwidth limits (dashed line), and the peaks presence (solid line). consequently used to determine the best value of the BER for all the different acquisition duration (Figure 8). As expected, the BER becomes greater when acquisition time decreases. Considering the TAS7500 SP system, it appears that the tag is accurately identified as long as the acquisition time remains longer than 64 ms. In this case, the effective BER drops down below 1%, which corresponds to the minimum achievable limit of this study, as each set of measurements is based on one hundred tag signatures. Obviously, such a result depends on the other intrinsic performances of the THz system (dynamics, bandwidth, and spectral resolution), but also on the tag response (magnitude of the defect peaks, rejection level and bandwidth of the PBG). Moreover, the electromagnetic response of such a multi-layered structure, i.e., the PBG width and peak positions, also closely depend on the incident angle of measurement \(\theta\) (see insert of Figure 9). Indeed, under non normal incidence, the effective optical thickness of each layer is then increased, tending to a high frequency shift of the spectral signature.