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content/conference/2024.md

@@ -8,5 +8,5 @@ date: 2024-03-25
 * https://www.icecet.com/
 * http://www.icbibe.org/
 * http://www.icbeps.org/
-* https://www.icbbe.com/
+* https://www.icbbe.cICom/
 * https://www.ssip.org/

content/signal_processing/advanced_statistic/autocorrelation/autocorrelation.md

@@ -217,6 +217,11 @@ $$
 
 其傅里叶变换始终大于0
 
+
+# Application
+
+
+* [Period Detection by Autocorrelation](signal_processing/advanced_statistic/autocorrelation/period_detection.md)
 # Reference
 
 * https://pinkr1ver.notion.site/Autocorrelation-Analysis-Power-Spectral-Density-330755770347472989062c6b31f18a21?pvs=4

content/signal_processing/advanced_statistic/autocorrelation/period_detection.md

@@ -0,0 +1,38 @@
+---
+title: Period Detection by Autocorrelation
+tags:
+  - signal
+  - signal-processing
+---
+
+
+$$
+R_x(n,n+m) = E\{x(n)x(n+m)\}=\lim_{N\rightarrow\infty}\frac{1}{N}\sum_{k=1}^{N}x_k(n)x_k(n+m)
+$$
+
+$m=0$ 的时候肯定是autocorrelation最大的时候，即自己与自己最为相关；
+在$m \not = 0$的时候，在$m = \text{Period}$的时候，会得到第二大的值，即移动一个周期后做相关。
+
+
+# Demo Code
+
+```matlab
+for i = 1:length(signal_list) - 1
+    name = strsplit(matFiles(i).name, '.');
+    name = name{1};
+    [autocor, lag] = xcorr(signal_list{i}, 200);
+    figure;
+    plot(lag, autocor, 'LineWidth', 1);
+    xlabel('Lag');
+    ylabel('Auto-correlation');
+    title(['Auto-correlation for ', name]);
+    grid on;
+    grid minor;
+
+    [~, max_idx] = max(autocor);
+    disp(max_idx);
+    freq = 1 / (max_idx * 1 / fs);
+    disp(freq)
+    fprintf('Signal %s freq: %f\n', name, freq);
+end
+```

content/signal_processing/signal_processing_MOC.md

@@ -45,8 +45,7 @@ date: 2024-03-18
 ## Autocorrelation
 
 * [Autocorrelation in Signal Processing](signal_processing/advanced_statistic/autocorrelation/autocorrelation.md)
-* [Autocorrelation to Detect Period](signal_processing/advanced_statistic/autocorrelation/period_detect.md)
-
+* [Period Detection by Autocorrelation](signal_processing/advanced_statistic/autocorrelation/period_detection.md)
 # Software
 
 ## CST MWS