Update README.md

README.md

@@ -4,14 +4,60 @@ Write a simple Python program for the modulation and demodulation of PCM, and DM
 # Tools required
 # Program
 ```
-Attach the program
-```
-# Output Waveform
-```
-Attach the output waveform
+import numpy as np
+import matplotlib.pyplot as plt
+
+fs, f, T, L = 5000, 50, 0.1, 16
+t = np.linspace(0, T, int(fs*T), False)
+
+msg = np.sin(2*np.pi*f*t)
+clk = np.sign(np.sin(2*np.pi*200*t))
+
+step = (msg.max()-msg.min())/L
+q_msg = np.round(msg/step)*step
+
+plt.figure(figsize=(10,8))
+
+plt.subplot(4,1,1); plt.plot(t,msg); plt.title("Analog Message"); plt.grid()
+plt.subplot(4,1,2); plt.plot(t,clk); plt.title("Clock Signal"); plt.grid()
+plt.subplot(4,1,3); plt.step(t,q_msg); plt.title("PCM Signal"); plt.grid()
+plt.subplot(4,1,4); plt.plot(t,q_msg,'--'); plt.title("PCM Demodulation"); plt.grid()
+
+plt.tight_layout()
+plt.show()
+
+Delta Modulation
+
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.signal import butter, filtfilt
+
+fs, f, T, d = 10000, 10, 1, 0.1
+t = np.arange(0, T, 1/fs)
+msg = np.sin(2*np.pi*f*t)
+
+dm, bits = [0], []
+for s in msg:
+    step = d if s > dm[-1] else -d
+    bits.append(step > 0)
+    dm.append(dm[-1] + step)
+
+demod = np.cumsum([0] + [d if b else -d for b in bits])
+b, a = butter(4, 20/(0.5*fs))
+filt = filtfilt(b, a, demod)
+
+plt.figure(figsize=(10,6))
+plt.subplot(311); plt.plot(t,msg); plt.title("Original"); plt.grid()
+plt.subplot(312); plt.step(t,dm[:-1],where='mid'); plt.title("DM Signal"); plt.grid()
+plt.subplot(313); plt.plot(t,filt[:-1],'r:'); plt.title("Demodulated"); plt.grid()
+
+plt.tight_layout()
+plt.show()
+
 ```
 # Results
 ```
-Attach the output waveform
+Thus the Python program for the modulation and demodulation of PCM, and DM verified.
 ```
 # Hardware experiment output waveform.
+<img width="1189" height="1389" alt="image" src="https://github.com/user-attachments/assets/784fb191-eecd-4fb9-ad1b-be758a319af3" />