import matplotlib.pylab as plt
import numpy as np
# %matplotlib widget

Plot random waves and fourier tranform of the random waves

def get_wave(A, f, theta, phi):
    x = theta
    y = A*np.sin(2*np.pi*f*theta - phi)
#     plt.plot(x, y, alpha)
    return x, y

def plot_wave(time, data):
    A = data[0]
    f = data[1]
    phi = data[2]
    x, y = get_wave(A, f, time, phi)
    
    plt.figure(figsize = (13, 6))
    ax = plt.gca()
    plt.plot(x, y, color = 'blue')

    ax.set_xlabel('Time', fontsize = 20, color = 'red')
    ax.tick_params(axis='x', colors='red')
    ax.tick_params(axis='y', colors='red')

steps = 1000
theta = np.linspace(0, 2*np.pi, steps)
data = [2, 3, 0]
plot_wave(theta, data)

def plot_multiple_waves(time, data):
    no_of_plots = len(data)
    fig, axes = plt.subplots(no_of_plots, figsize = (16, 9))
    for i in range(no_of_plots):
        ax = axes[i]
        w_data = data[i] 
        A = w_data[0]
        f = w_data[1]
        phi = w_data[2]
        x, y = get_wave(A, f, time, phi)
        ax.plot(x, y, color = 'blue', alpha = 1)
        ax.set_ylabel(f'Wave {i + 1}', color = 'blue', fontsize = 15)

        fig.suptitle('Time', fontsize = 20, color = 'red')
        ax.tick_params(axis='x', colors='red')
        ax.tick_params(axis='y', colors='red')
        ax.set_ylim(-15, 15)

data = [
    [6, 1, 0],
    [5, 2, 0],
    [10, 6, -np.pi/3],
]
steps = 1000
theta = np.linspace(0, 2*np.pi, steps)
# time = theta
plot_multiple_waves(theta, data)

def plot_a_fourier_waves(data, time):
    no_of_plots = len(data)
#     fig, axes = plt.subplots(no_of_plots, figsize = (16, 9))
#     xs = np.zeros(len(time))
    ys = np.zeros(len(time))
    for i in range(no_of_plots):
#         ax = axes[i]
        w_data = data[i] 
        A = w_data[0]
        f = w_data[1]
        phi = w_data[2]
        x, y = get_wave(A, f, time, phi)
        ys += y
        
    fig = plt.figure(figsize = (16, 3))
    ax = plt.gca()
    plt.plot(x, ys, color = 'blue', alpha = 1)
#     ax.set_ylabel(f'Wave {i + 1}', color = 'blue', fontsize = 15)

    fig.suptitle('Time', fontsize = 20, color = 'red')
    ax.tick_params(axis='x', colors='red')
    ax.tick_params(axis='y', colors='red')
    lim = max(np.abs(ys))
    ax.set_ylim(-(lim+3), lim+3)

data = [
    [6, 1, 0],
    [5, 2, 0],
    [10, 6, -np.pi/3],
]
steps = 1000
theta = np.linspace(0, 2*np.pi, steps)
# time = theta
plot_a_fourier_waves(data, theta)

def plot_multiple_waves_fourier_wave(data, time, alpha = 1):
    no_of_plots = len(data) + 2
    fig, axes = plt.subplots(no_of_plots, figsize = (16, 9))
    xs = np.zeros(len(time))
    ys = np.zeros(len(time))
    for i in range(no_of_plots):
        ax = axes[i]
        if i < no_of_plots - 2:
            w_data = data[i] 
            A = w_data[0]
            f = w_data[1]
            phi = w_data[2]
            x, y = get_wave(A, f, time, phi)
            ax.plot(x, y, color = 'blue', alpha = alpha)
            xs += x
            ys += y
            
            
        elif i == no_of_plots - 2:
            for j in range(no_of_plots-2):
                w1_data = data[j]
                A = w1_data[0]
                f = w1_data[1]
                phi = w1_data[2]
                x1, y1 = get_wave(A, f, time, phi)
                ax.plot(x1, y1, color = 'green', alpha = alpha)
        else:
            ax.plot(xs, ys, color = 'red', alpha = alpha)
            
            
        fig.suptitle('Time', fontsize = 20, color = 'red')
        ax.tick_params(axis='x', colors='red')
        ax.tick_params(axis='y', colors='red')
        ax.set_xlim(min(time), max(time))
        ax.set_ylim(-20, 20)
        

data = [
    [6, 1, 0],
    [5, 2, 0],
    [10, 6, -np.pi/3],
    [1, 1, 0],
]
steps = 1000
theta = np.linspace(0, 2*np.pi, steps)
# time = theta
plot_multiple_waves_fourier_wave(data, theta)

Plot the given circular waves and fourier transform of the given circular waves

def get_circle(A, f, theta, phi):
    x = A*np.cos(2*np.pi*f*theta - phi)
    y = A*np.sin(2*np.pi*f*theta - phi)
#     ax.plot(x, y, color = color, alpha = alpha)
    return x, y

def plot_circles_fourier(data, time, alpha = 1):
    x = 0
    y = 0
    for A, f, phi in data:
        x_temp, y_temp = get_circle(A, f, time, phi)
        x += x_temp
        y += y_temp
    fig = plt.figure(figsize = (6, 6))
    ax = plt.gca()
    plt.plot(x, y, alpha, color = 'blue')
    
    ax.tick_params(axis='x', colors='red')
    ax.tick_params(axis='y', colors='red')

data = [
    [8, 1, 0],
    [5, 2, 0],
#     [50, 6, -np.pi/3],
]
steps = 1000
theta = np.linspace(0, 2*np.pi, steps)

plot_circles_fourier(data, theta)
plt.gca().set_aspect('equal')

def plot_circular_wave(data, time):
    A = data[0]
    f = data[1]
    phi = data[2]
    x, y = get_circle(A, f, time, phi)
    
    plt.figure(figsize = (13, 6))
    ax = plt.gca()
    plt.plot(x, y, color = 'blue')

    ax.set_xlabel('Time', fontsize = 20, color = 'red')
    ax.tick_params(axis='x', colors='red')
    ax.tick_params(axis='y', colors='red')
    ax.set_aspect('equal')    

data = [2, 3, 0]

steps = 1000
theta = np.linspace(0, 2*np.pi, steps)

plot_circular_wave(data, theta)

def plot_circles_fourier(data, time, alpha = 1):
    no_of_plots = len(data) + 2
    fig, axes = plt.subplots(ncols = no_of_plots, figsize = (16, 9))
    xs = np.zeros(len(time))
    ys = np.zeros(len(time))
    for i in range(no_of_plots):
        ax = axes[i]
        if i < no_of_plots - 2:
            w_data = data[i] 
            A = w_data[0]
            f = w_data[1]
            phi = w_data[2]
            x, y = get_circle(A, f, time, phi)
            ax.plot(x, y, color = 'blue', alpha = alpha)
            xs += x
            ys += y
        elif i == no_of_plots - 2:
            for j in range(no_of_plots-2):
                w1_data = data[j]
                A = w1_data[0]
                f = w1_data[1]
                phi = w1_data[2]
                x1, y1 = get_circle(A, f, time, phi)
                ax.plot(x1, y1, color = 'green', alpha = alpha)
        else:
            ax.plot(xs, ys, color = 'red', alpha = alpha)
            
            
        ax.set_xlim(-12, 12)
        ax.set_ylim(-12, 12)
        ax.set_aspect('equal')

data = [
    [6, 4, 0],
    [2, 9, 0],
#     [50, 6, -np.pi/3],
]
plot_circles_fourier(data, theta)

def plot_multiple_circular_waves(data, time):
    no_of_plots = len(data)
    fig, axes = plt.subplots(ncols = no_of_plots, figsize = (16, 9))
    for i in range(no_of_plots):
        ax = axes[i]
        w_data = data[i] 
        A = w_data[0]
        f = w_data[1]
        phi = w_data[2]
        x, y = get_circle(A, f, time, phi)
        ax.plot(x, y, color = 'blue')           
            
        ax.set_xlim(-12, 12)
        ax.set_ylim(-12, 12)
        ax.set_aspect('equal')

        ax.set_title(f'Wave {i + 1}', fontsize = 20, color = 'red')
        ax.tick_params(axis='x', colors='red')
        ax.tick_params(axis='y', colors='red')

data = [
    [8, 1, 0],
    [5, 2, 0],
#     [50, 6, -np.pi/3],
]
steps = 1000
theta = np.linspace(0, 2*np.pi, steps)

plot_multiple_circular_waves(data, theta)