import numpy as np
import matplotlib.pyplot as plt

N = int(input('Enter the length of the signal: '))

signal_types = [
    ('cos(2*pi*n)', lambda n: np.cos(2 * np.pi * n)),
    ('sin(pi*n)', lambda n: np.sin(np.pi * n)),
    ('3n^3 + 2n^2 + 5n + 2', lambda n: 3 * n**3 + 2 * n**2 + 5 * n + 2),
    ('Unit Ramp', lambda n: n),
    ('Unit Step', lambda n: np.ones_like(n))
]

for signal_name, signal_func in signal_types:
    n = np.arange(N)
    x = signal_func(n)

    W = np.exp(-1j * 2 * np.pi * np.outer(n, n.T) / N)

    X = np.dot(W, x)

    magnitude = np.abs(X)
    phase = np.angle(X)

    plt.figure()
    plt.subplot(2, 1, 1)
    plt.stem(magnitude)
    plt.xlabel('Frequency')
    plt.ylabel('Magnitude')
    plt.title(f'{signal_name} - Magnitude spectrum')

    plt.subplot(2, 1, 2)
    plt.stem(phase)
    plt.xlabel('Frequency')
    plt.ylabel('Phase')
    plt.title(f'{signal_name} - Phase spectrum')

    plt.tight_layout()


    print(f'Final complex output for {signal_name}:')
    print(X)

print(f'Twiddle factor:')
print(W)

plt.show()