Ask Lemmy

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

def generate_damped_signal():
    # 1. Setup Parameters
    fs = 50                 # 50Hz Sampling frequency
    t_max = 6.0             # Run for 6 seconds to clearly visualize it hitting 0 at 5s
    freq = 2.0              # Oscillation frequency in Hz
    
    # 2. Generate Independent Time Axis
    # 50 samples per second from 0 to t_max
    time = np.arange(0, t_max, 1/fs)
    
    # 3. Generate Dependent Damped Signal Axis
    # Using an exponential decay constant of 1.0 ensures that at t=5 seconds,
    # e^(-5) drops down to ~0.006, effectively decaying the signal to zero.
    amplitude = np.exp(-time) * np.cos(2 * np.pi * freq * time)
    
    # 4. Create Pandas DataFrame
    df = pd.DataFrame({
        'Time_Seconds': time,
        'Signal_Amplitude': amplitude
    })
    
    # 5. Export DataFrame to CSV File
    csv_filename = "damped_signal.csv"
    df.to_csv(csv_filename, index=False)
    print(f"Successfully generated DataFrame and saved to '{csv_filename}'")
    
    # 6. Plot the Data Using Matplotlib
    plt.figure(figsize=(10, 5))
    plt.plot(df['Time_Seconds'], df['Signal_Amplitude'], label='Damped Signal', color='cyan', linewidth=2)
    
    # Visual Anchors for the 5-second decay mark
    plt.axvline(x=5.0, color='red', linestyle='--', alpha=0.7, label='5-Second Decay Target')
    plt.axhline(y=0.0, color='gray', linestyle='-', alpha=0.5)
    
    # Labeling and Grid Configuration
    plt.title('Damped Signal Decay Over Time (50Hz Sampling Rate)')
    plt.xlabel('Time (Independent Axis - Seconds)')
    plt.ylabel('Signal (Dependent Axis - Amplitude)')
    plt.grid(True, linestyle=':', alpha=0.6)
    plt.legend()
    
    # Display the Plot Window
    plt.show()

if __name__ == "__main__":
    generate_damped_signal()