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## A Matched Filter System for Muon Detection with Tilecal

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**IX International Workshop ACAT**A Matched Filter System for Muon Detection with Tilecal R. R. Ramos1, J. M. de Seixas2 and A. S. Cerqueira3 1,2 Signal Processing Laboratory EP/COPPE – Federal University of Rio de Janeiro 3 Federal University of Juiz de Fora**Topics**• The Hadronic Calorimeter (Tilecal) • The Muon Signal • The Matched Filter System • Results • Conclusions A Matched Filter System for Muon Detection with Tilecal**The Hadronic Calorimeter (Tilecal)**ATLAS • Tilecal is the hadronic calorimeter of ATLAS. • Tilecal comprises 192 modules. • Each module is segmented into three layers of cells. • The last layer may be used by the LVL1 trigger envisaging muon detection. Tilecal Barrel Extended Barrels A Matched Filter System for Muon Detection with Tilecal**The Tilecal and the Muon Signal**• Tilecal cells geometry: • The Level 1 trigger (LVL1) requiresanalogue signal summation along the three sampling layers (up to six calorimeter redout channels) of the calorimeter, forming the so called trigger tower signals. • Each adder circuit also fanouts the • information corresponding to the third layer of the calorimeter, which is used for muon detection. • As muons deposit very small energy levels in the calorimeter, muon output signal exhibits low signal-to-noise ratio. Tilecal layers: 1st - (A# cells) 2nd - (B#, C# cells) 3rd - (D# cells) Tilecal electronic readout: A Matched Filter System for Muon Detection with Tilecal**The Muon Signal (1)**• July, 2003 testbeam setup: Physics events (signal) Superposition • 16 samples/event (Fast ADC – 40MHz). • Muon signal severely corrupted by background noise. • Online detection is critical. • Adding the muon outputs corresponding to a given D_cell may improve the signal-to-noise ratio. • Projective data at η = 0.45 (D2 cell) was analysed. Mean Pedestal events (noise) ??? Superposition Mean • FADC problems. Only 14 samples were considered in analysis. A Matched Filter System for Muon Detection with Tilecal**The Muon Signal (2)**• Discriminating signal from noise: Peak sample histograms • An usual technique consists of a simple peak detector. • An efficiency above 88.0% is obtained for a false alarm probability of 10.0%, considering the summation of the two signals of the same D_cell. • Using a single muon output results in an efficiency higher than 70.0% for the same 10.0% false alarm probability. • Adding the two signals improves the detection efficiency and is considered in the matched filter system development. Receiver Operating Characteristic (ROC) A Matched Filter System for Muon Detection with Tilecal**The Matched Filter System (1)**• The detection problem can be modeled as the classical decision rule between two hypothesis, where n[k] is considered a zero-mean additive white gaussian noise with variance N0/2 and s[k] is the signal to be detected. H1: r[k] = s[k] + n[k] , k = 1,…,K H0: r[k] = n[k] • We make use of the orthonormal expansion of s[k], the well-known Karhunen-Löeve Series. Considering Ks the auto-correlation matrix of s[k], we have Ks.Q = Q.λ, Ks = E[s.sT] Q – matrix of orthonormal eigenvectors qi λ – matrix of diagonal eigenvalues λi A = QT.s , A – 1,…,Kprojections • Using the new orthonormal basis spanned by Q, the signal sM[k] can be reconstructed by truncating the series in the M-ary term. sM[k] = Q.A , A – 1,…,M projections Q – 1,…,M eigenvectors or principal components (PCAs) A Matched Filter System for Muon Detection with Tilecal**The Matched Filter System (2)**• Both signal s[k] and noise n[k] processes are considered multivariate Gaussians so that the classical matched filtering algorithm for random processes can be adapted to this problem. • Instead of using the signal s[k] (not available), we use r[k] under the hypothesis H1. The algorithm is derived by computing the following likelihood ratio: • The detection is made by comparing this ratio result with a threshold η (Neyman-Pearson rule). • We can take the natural logarithm of the likelihood ratio, resulting in an optimal receiver The Øi are the eigenvectors qi. M = 14. K = 1,…,14. A Matched Filter System for Muon Detection with Tilecal**Results (1)**• The covariance matrix Kn of the background noise n[k] shows that it´s not white. Kn before whitening filter • The matched filter is considered optimal in the sense of the signal-to-noise ratio if the signal to be matched is corrupted by white noise. Kn after whitening filter (training set) • At this point, a whitening filter for proper treatment of the background noise is necessary. • That is made by an orthogonal transformation equivalent to the following Kn after whitening filter (testing set) (similarity transformation) A Matched Filter System for Muon Detection with Tilecal**Results (2)**ROCs with whitening filter • The development of the matched filter is normally performed considering the new signal r*[k] (after whitening). • The overall performance of the detector grows as we decrease the number of PCAs in both cases (with or without whitening filter). ROCs without whitening filter • The efficiency with the whitening filter is better, reaching 93.5%, when compared to peak detector (89.0%), for a fixed 10.0% false alarm probability. A Matched Filter System for Muon Detection with Tilecal**Results (3)**• We considered a deterministic approach by designing a matched filter that uses the mean signal of hypothesis H1 (muon signal) as the signal to be matched. Overall Performance Comparison • At this point, we have three approaches to be compared: the peak detector, and both stochastic and deterministic matched filters. • The stochastic matched filter has the best performance of the three approaches. A Matched Filter System for Muon Detection with Tilecal**Conclusions**• We developed a matched filter system that reached an efficiency of 93.5% (for 10.0% false alarm probability). A whitening filter was also designed as part of the system. • The matched filter system using whitening filter outperforms a peak detector based system that is being considered by the Tilecal collaboration. • The development of an online system is being considered to be part of the ATLAS experiment. • The use of neural networks is also being considered. Preliminary results are promising. A Matched Filter System for Muon Detection with Tilecal