From 91e0e9f81cfb0ae9293429c714f5869d69c46bd1 Mon Sep 17 00:00:00 2001
From: Keerthanana212223060122 <keerthi.luv6@gmail.com>
Date: Mon, 24 Mar 2025 14:07:27 +0530
Subject: [PATCH] Update README.md

---
 README.md | 95 ++++++++++++++++++++++++++++++++++++++++++++++++++++---
 1 file changed, 90 insertions(+), 5 deletions(-)

diff --git a/README.md b/README.md
index 855ec9d..6879cfd 100644
--- a/README.md
+++ b/README.md
@@ -1,6 +1,91 @@
 # Pulse-Code-Modulation
-Aim
-Tools required
-Program
-Output Waveform
-Results
+Aim:
+To implement Pulse Code Modulation (PCM) for encoding and decoding a sinusoidal signal using quantization and to observe the output waveforms.
+
+
+Tools/Software Required:
+
+ 1. Python Software
+
+-> Numpy Library
+
+-> Matplotlib Library
+
+-> Scipy Library (for signal processing
+
+
+Program:
+
+import numpy as np
+
+import matplotlib.pyplot as plt
+
+def pcm_encode(signal, quantization_levels):
+   
+    min_val, max_val = np.min(signal), np.max(signal)
+    
+    quantized_signal = np.round((signal - min_val) / (max_val - min_val) * (quantization_levels - 1))
+    
+    return quantized_signal.astype(int)
+
+def pcm_decode(encoded_signal, quantization_levels, min_val, max_val):
+    
+    decoded_signal = encoded_signal / (quantization_levels - 1) * (max_val - min_val) + min_val
+   
+    return decoded_signal
+
+fs = 1000  # Sampling frequency
+
+t = np.linspace(0, 1, fs)
+
+original_signal = 0.5 * np.sin(2 * np.pi * 5 * t)  # 5 Hz sine wave
+
+quantization_levels = 16
+
+encoded_signal = pcm_encode(original_signal, quantization_levels)
+
+decoded_signal = pcm_decode(encoded_signal, quantization_levels, np.min(original_signal), np.max(original_signal))
+
+plt.figure(figsize=(12, 8))
+
+plt.subplot(3, 1, 1)
+
+plt.plot(t, original_signal, label='Original Signal')
+
+plt.title('Original Signal')
+
+plt.grid(True)
+
+plt.subplot(3, 1, 2)
+
+plt.step(t, encoded_signal, label='PCM Modulated Signal', color='r')
+
+plt.title('PCM Modulated Signal')
+
+plt.grid(True)
+
+plt.subplot(3, 1, 3)
+
+plt.plot(t, decoded_signal, label='Demodulated Signal', color='g')
+
+plt.title('PCM Demodulated Signal')
+
+plt.grid(True)
+
+plt.tight_layout()
+
+plt.show()
+
+Output Waveform:
+
+<img width="871" alt="image" src="https://github.com/user-attachments/assets/d78349ec-4e25-45a8-8e2e-f2b90004c576" />
+<img width="882" alt="image" src="https://github.com/user-attachments/assets/12550ba4-fd9a-4a8a-acb0-660c611a4e20" />
+<img width="873" alt="image" src="https://github.com/user-attachments/assets/8f0bc45f-b120-404c-9950-5c1f58173502" />
+
+Results:
+
+The PCM encoding process successfully quantized the original sine wave into 16 levels.
+
+The demodulated signal closely resembled the original signal with minor quantization noise.
+
+The output waveforms validated the functioning of PCM in digital communication systems.