SSBSC-Using-Python

Aim

To implement and analyze (SSBSC) using Python's NumPy and Matplotlib libraries.

Apparatus Required

1.Software: Python with NumPy and Matplotlib libraries

2.Hardware: Personal Computer

Theory

SSB-SC (Single Sideband Suppressed Carrier) is a bandwidth-efficient form of amplitude modulation in which only one sideband (either the upper or the lower) is transmitted, and the carrier is suppressed. This reduces both bandwidth and power usage compared to standard AM and DSB-SC.

The SSB-SC signal is generated by removing one of the sidebands from the DSB-SC signal, typically using filters or mathematical methods (like the Hilbert transform).

The general expression (conceptually) for an SSB-SC signal is:

Algorithm

1.Initialize Parameters: Set the values for carrier frequency, message frequency and sampling frequency.

2.Generate Time Axis: Create a time vector for the signal duration.

3.Generate Message Signal: Define the message signal as a cosine wave.

4.Compute the Integral of the Message Signal: Calculate the integral of the message signal over time.

5.Generate AM Signal: Apply the SSBSC modulation formula to obtain the modulated signal.

6.Plot the Signals: Use Matplotlib to plot the message signal, carrier signal, and modulated signal.

Program

import numpy as np
import matplotlib.pyplot as plt

Am = 7.2
Fm = 569
Fs = 56900
Ac = 14.4
Fc = 5690
t = np.arange(0, 2/Fm, 1/Fs)
m1 = Am * np.cos(2 * np.pi * Fm * t)
plt.subplot(4,1,1)
plt.plot(t,m1)
c1 = Ac * np.cos(2 * np.pi * Fc * t)
plt.subplot(4,1,2)
plt.plot(t,c1)
m2 = Am * np.cos(1.57 - 2 * np.pi * Fm * t)
c2 = Ac * np.cos(1.57 - 2 * np.pi * Fc * t)
A = m1 * c1
B = m2 * c2
C = A + B
plt.subplot(4,1,3)
plt.plot(t,C)
D = A - B
plt.subplot(4,1,4)
plt.plot(t,D)

Output Waveform

Tabular Column

Calculation

Result

The message signal, carrier signal, and amplitude modulated (AM) signal will be displayed in separate plots. The modulated signal will show frequency variations corresponding to the amplitude of the message signal.