From d0ba9cfac9af2cb239e1aa52294623344ed6ad51 Mon Sep 17 00:00:00 2001
From: HariharanGanesh <144553215+HariharanGanesh@users.noreply.github.com>
Date: Sun, 30 Mar 2025 21:34:53 +0530
Subject: [PATCH] Update README.md

---
 README.md | 99 +++++++++++++++++++++++++++++++++++++++++++++++++++----
 1 file changed, 93 insertions(+), 6 deletions(-)

diff --git a/README.md b/README.md
index 466bd15..097afe6 100644
--- a/README.md
+++ b/README.md
@@ -1,6 +1,93 @@
-# Delta-Modulation
-Aim
-Tools required
-Program
-Output Waveform
-Results
+Delta-Modulation
+
+Aim:
+To implement Delta Modulation (DM) for efficiently encoding a message signal. To analyze the stepwise modulation process and observe quantization effects.
+
+Tools required:
+Python IDE (Numpy)
+Program:
+#DELTA MODULATION 
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.signal import butter, filtfilt
+
+# Parameters
+fs = 10000  # Sampling frequency
+f = 10  # Signal frequency
+T = 1  # Duration in seconds
+delta = 0.1  # Step size
+
+t = np.arange(0, T, 1/fs)
+message_signal = np.sin(2 * np.pi * f * t)  # Sine wave as input signal
+
+# Delta Modulation Encoding
+encoded_signal = []
+dm_output = [0]  # Initial value of the modulated signal
+prev_sample = 0
+
+for sample in message_signal:
+    if sample > prev_sample:
+        encoded_signal.append(1)
+        dm_output.append(prev_sample + delta)
+    else:
+        encoded_signal.append(0)
+        dm_output.append(prev_sample - delta)
+    prev_sample = dm_output[-1]
+
+# Delta Demodulation (Reconstruction)
+demodulated_signal = [0]
+for bit in encoded_signal:
+    if bit == 1:
+        demodulated_signal.append(demodulated_signal[-1] + delta)
+    else:
+        demodulated_signal.append(demodulated_signal[-1] - delta)
+
+# Convert to numpy array
+demodulated_signal = np.array(demodulated_signal)
+
+# Apply a low-pass Butterworth filter
+def low_pass_filter(signal, cutoff_freq, fs, order=4):
+    nyquist = 0.5 * fs
+    normal_cutoff = cutoff_freq / nyquist
+    b, a = butter(order, normal_cutoff, btype='low', analog=False)
+    return filtfilt(b, a, signal)
+
+filtered_signal = low_pass_filter(demodulated_signal, cutoff_freq=20, fs=fs)
+
+# Plotting the Results
+plt.figure(figsize=(12, 6))
+
+plt.subplot(3, 1, 1)
+plt.plot(t, message_signal, label='Original Signal', linewidth=1)
+plt.title("Message Signal")
+plt.xlabel("Time (s)")
+plt.ylabel("Amplitude")
+plt.legend()
+plt.grid()
+
+plt.subplot(3, 1, 2)
+plt.step(t, dm_output[:-1], label='Delta Modulated Signal', where='mid')
+plt.title("Delta Modulation Output")
+plt.xlabel("Time (s)")
+plt.ylabel("Amplitude")
+plt.legend()
+plt.grid()
+
+plt.subplot(3, 1, 3)
+plt.plot(t, filtered_signal[:-1], label='Demodulated & Filtered Signal', linestyle='dotted', linewidth=1, color='r')
+plt.xlabel("Time (s)")
+plt.ylabel("Amplitude")
+plt.title("Reconstruction from Delta Modulation")
+plt.legend()
+plt.grid()
+
+plt.tight_layout()
+plt.show()
+Output Waveform:
+![image](https://github.com/user-attachments/assets/9c2a5757-a942-4a50-ae68-a3c793ef672a)
+![image](https://github.com/user-attachments/assets/20b3a920-2760-45dd-95b5-9a37353b532a)
+
+
+
+Results:
+Delta Modulation (DM) was successfully implemented, encoding the message signal into a stepwise waveform. The reconstructed signal closely follows the original, with minor quantization noise.