import numpy as np

# Calculate the signal to noise ratio given a signal and a noisy approximation
def snr(signal, noisy_signal):
    noise = noisy_signal - signal       # Extract just the noise

    P_signal = np.sum(signal**2)        # Calculate the signal power
    P_noise = np.sum(noise**2)          # Calculate the noise power

    return P_signal/P_noise


# Calculate the mean squared error given a signal and a noisy approximation
def mse(signal, noisy_signal):
    squared_difference = (signal - noisy_signal)**2
    return np.sum(squared_difference)/signal.size


# Calculate the peak signal to noise ratio for a signal and a noisy approximation
def psnr(signal, noisy_signal):
    max_i = 255
    return max_i**2 / mse(signal, noisy_signal)