EXP 1: Ideal-Sampling

##AIM:

To demonstrate the process of ideal sampling, where a continuous sinusoidal signal is sampled at a
sufficient rate and accurately reconstructed without loss of information.

##Tools required

. Python
. NumPy
. Matplotlib
. SciPy

###Program

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import resample
# Define parameters
fs = 100 # Sampling frequency
t = np.arange(0, 1, 1/fs) # Time vector
f = 5 # Frequency of the sine wave
# Generate continuous signal
signal = np.sin(2 * np.pi * f * t)
plt.figure(figsize=(10, 4))
plt.plot(t, signal, label='Continuous Signal')
plt.title('Continuous Signal (fs = 100 Hz)')
plt.xlabel('Time [s]')
plt.ylabel('Amplitude')
plt.grid(True)
plt.legend()
plt.show()
# Sampling process
t_sampled = np.arange(0, 1, 1/fs)
signal_sampled = np.sin(2 * np.pi * f * t_sampled)
plt.figure(figsize=(10, 4))
plt.plot(t, signal, label='Continuous Signal', alpha=0.7)
plt.stem(t_sampled, signal_sampled, linefmt='r-', markerfmt='ro', basefmt='r-', label='S
plt.title('Sampling of Continuous Signal (fs = 100 Hz)')
plt.xlabel('Time [s]')
plt.ylabel('Amplitude')
plt.grid(True)
plt.legend()
plt.show()
# Reconstruction process
reconstructed_signal = resample(signal_sampled, len(t))
plt.figure(figsize=(10, 4))
plt.plot(t, signal, label='Continuous Signal', alpha=0.7)
plt.plot(t, reconstructed_signal, 'r--', label='Reconstructed Signal (fs = 100 Hz)')
plt.title('Reconstruction of Sampled Signal (fs = 100 Hz)')
plt.xlabel('Time [s]')
plt.ylabel('Amplitude')
plt.grid(True)
plt.legend()
plt.show()`

###Output Waveform

Results

The original continuous sine wave was successfully sampled at 100 Hz. The sampled signal was plotted using discrete red markers. The signal was reconstructed using resampling techniques.