diff --git a/QAM/out b/QAM/out
index 632d3a0..0a31e53 100755
Binary files a/QAM/out and b/QAM/out differ
diff --git a/QAM/qam.c b/QAM/qam.c
index ed2f6ef..e2b0fc6 100644
--- a/QAM/qam.c
+++ b/QAM/qam.c
@@ -352,7 +352,7 @@ void pll(qam_system* qam, double complex* s_with_preamble, double complex* r_cor
         phase_est += Kp * filtered_error + integrator;
 
         if (fp_error) {
-            fprintf(fp_error, "%d % .8f\n", k, 100 * filtered_error);
+            fprintf(fp_error, "%d % .8f\n", k, 5 * filtered_error);
             fflush(fp_error);
         }
 
@@ -413,7 +413,7 @@ void muller_muller_sync(qam_system* qam, double complex* s_data, int nb_symbols,
         d_k_minus_1 = d_k;
 
         if (fp_error) {
-            fprintf(fp_error, "%d % .8f\n", k, 5 * timing_offset);
+            fprintf(fp_error, "%d % .8f\n", k, 3 * timing_offset);
             fflush(fp_error);
         }
     }
@@ -466,6 +466,41 @@ void demodulate_carrier(qam_system* qam, double complex* s_input, double complex
     }
 }
 
+// Réponse impulsionnelle du filtre RRC
+void rrc_impulse_response(qam_system* qam, int N_taps, double alpha, double* rrc_taps) {
+    double Ts_symbol = qam->N / qam->Fs;
+    double t;
+    int k;
+
+    for (int i = 0; i < N_taps; i++) {
+        t = ((double)i - (N_taps - 1.0) / 2.0) / qam->Fs;
+        k = i;
+
+        double t_norm = t / Ts_symbol;
+
+        if (fabs(t) < 1e-9) { // t = 0
+            rrc_taps[k] = (1.0 / Ts_symbol) * (1.0 + alpha * (4.0 / M_PI) * (1.0 / 4.0));
+        } else if (fabs(fabs(t_norm) - 1.0 / (4.0 * alpha)) < 1e-9) { 
+            rrc_taps[k] = (1.0 / Ts_symbol) * (alpha / M_PI) * ( (M_PI / 4.0) * (1.0 / alpha) + 1.0) * sin(M_PI / (4.0 * alpha)) + (1.0 / Ts_symbol) * (alpha / M_PI) * ( (M_PI / 4.0) * (1.0 / alpha) - 1.0) * cos(M_PI / (4.0 * alpha));
+        } else {
+            double num = sin(M_PI * t_norm * (1.0 - alpha)) + (4.0 * alpha * t_norm) * cos(M_PI * t_norm * (1.0 + alpha));
+            double den = (M_PI * t_norm * (1.0 - (4.0 * alpha * t_norm) * (4.0 * alpha * t_norm)));
+            rrc_taps[k] = (1.0 / Ts_symbol) * num / den;
+        }
+    }
+}
+
+// Séquence d'impulsions de Dirac en base band 
+void generate_baseband_pulses(qam_system* qam, double complex* symbols, int L_symbols, double complex* s_pulses) {
+    int total_samples = L_symbols * qam->N;
+    memset(s_pulses, 0, total_samples * sizeof(double complex)); 
+
+    for (int k = 0; k < L_symbols; k++) {
+        int idx = k * qam->N;
+        s_pulses[idx] = symbols[k]; 
+    }
+}
+
 int main () {
     // Initialisation du system qam
     qam_system qam;
@@ -538,7 +573,7 @@ int main () {
     demodulate_carrier(&qam, s_corrected + L * qam.N, s_bande_base, nb_symbols * qam.N);
     
     double complex* r_mm_out = malloc(sizeof(double complex) * nb_symbols);
-    double Kp_mm = 0.5; 
+    double Kp_mm = 0.6; 
     double Ki_mm = 0.01;
     FILE *fp_mm_error = fopen("mm_timing_error.dat", "w");
     muller_muller_sync(&qam, s_bande_base, nb_symbols, Kp_mm, Ki_mm, r_mm_out, fp_mm_error);
@@ -571,6 +606,5 @@ int main () {
     free(s_with_preamble);
     free(texte_recup);
     free_constellation(&qam);
-
     return 0;
 }