Update README.md

README.md

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-# Pulse-Code-Modulation
-Aim
-Tools required
-Program
-Output Waveform
-Results
+# Exp:3 Pulse Code Modulation (PCM) 
+
+## **Aim**
+To implement a **Pulse Code Modulation (PCM)** system that demonstrates:
+- **Analog signal generation** (Message signal)
+- **Sampling and quantization**
+- **PCM encoding**
+- **PCM demodulation (Reconstruction)**
+
+## **Tools Required**
+- Python 3.x
+- NumPy
+- Matplotlib
+
+## **Program**
+```
+# PCM import matplotlib.pyplot as plt
+import numpy as np
+
+# Parameters
+sampling_rate = 5000  # Sampling rate (samples per second)
+frequency = 50  # Frequency of the message signal (analog signal)
+duration = 0.1  # Duration of the signal in seconds
+quantization_levels = 16  # Number of quantization levels (PCM resolution)
+
+# Generate time vector
+t = np.linspace(0, duration, int(sampling_rate * duration), endpoint=False)
+
+# Generate message signal (analog signal)
+message_signal = np.sin(2 * np.pi * frequency * t)
+
+# Generate clock signal (sampling clock) with higher frequency than before
+clock_signal = np.sign(np.sin(2 * np.pi * 200 * t))  # Increased clock frequency to 200 Hz
+
+# Quantize the message signal
+quantization_step = (max(message_signal) - min(message_signal)) / quantization_levels
+quantized_signal = np.round(message_signal / quantization_step) * quantization_step
+
+# Simulate the PCM modulated signal (digital representation)
+pcm_signal = (quantized_signal - min(quantized_signal)) / quantization_step
+pcm_signal = pcm_signal.astype(int)
+
+# Plotting the results
+plt.figure(figsize=(12, 10))
+
+# Plot message signal
+plt.subplot(4, 1, 1)
+plt.plot(t, message_signal, label="Message Signal (Analog)", color='blue')
+plt.title("Message Signal (Analog)")
+plt.xlabel("Time [s]")
+plt.ylabel("Amplitude")
+plt.grid(True)
+
+# Plot clock signal (higher frequency)
+plt.subplot(4, 1, 2)
+plt.plot(t, clock_signal, label="Clock Signal (Increased Frequency)", color='green')
+plt.title("Clock Signal (Increased Frequency)")
+plt.xlabel("Time [s]")
+plt.ylabel("Amplitude")
+plt.grid(True)
+
+# Plot PCM modulated signal (quantized)
+plt.subplot(4, 1, 3)
+plt.step(t, quantized_signal, label="PCM Modulated Signal", color='red')
+plt.title("PCM Modulated Signal (Quantized)")
+plt.xlabel("Time [s]")
+plt.ylabel("Amplitude")
+plt.grid(True)
+
+# Plot 'PCM Demodulation'
+plt.subplot(4, 1, 4)
+plt.plot(t, quantized_signal, label="Signal Demodulation", color='purple', linestyle='--')
+plt.title("Signal Without Demodulation")
+plt.xlabel("Time [s]")
+plt.ylabel("Amplitude")
+plt.grid(True)
+
+plt.tight_layout()
+plt.show()
+```
+
+## **Explanation of Steps**
+1. **Message Signal Generation**  
+   - A **sine wave** represents the **analog signal** (message signal).
+   - Frequency: **50 Hz**  
+   - Sampling rate: **5000 samples per second**  
+
+2. **Clock Signal Generation**  
+   - A **square wave** acts as a **sampling clock**.
+   - Frequency set to **200 Hz** for increased precision.
+
+3. **Quantization Process**  
+   - The message signal is **quantized** using **16 levels**.
+   - Each sample is **rounded** to the nearest quantization level.
+
+4. **PCM Modulation (Encoding)**  
+   - The quantized values are converted into a **digital format**.
+
+5. **PCM Demodulation (Reconstruction)**  
+   - The quantized signal is **visualized** for reconstruction analysis.
+
+## **Output**
+![Screenshot 2025-03-26 095131](https://github.com/user-attachments/assets/33fd4695-b818-453d-a8dc-7d6d0b47c2aa)
+
+
+
+## **Result**
+This program successfully demonstrates the **Pulse Code Modulation (PCM) process**, including:
+- **Analog-to-digital conversion**
+- **Sampling and quantization**
+- **PCM encoding and signal transmission**
+- **Signal reconstruction without demodulation**
+