How to plot sine wave in Python with sudden amplitude change?

Question

Posted: 7/4/2020

I was wondering if anyone knows how to plot a sine wave with let\'s say amplitude of 0.1 as a start and then continuing on as usual. Until at one point,

Answer 1

You could plot a piece-wise sin function where the second part defines the surge happening and you can change the amplitude there.

For instance:

import numpy as np
import matplotlib.pyplot as plt
import math

surge_point = 50
amplitudeAfterSurge = 4
T = 50
x_normal = np.linspace(0, surge_point, 1000)
x_surge = np.linspace(surge_point, 150, 1000)

y_normal = [math.sin(2*math.pi*i/T) for i in x_normal] # first part of the function

# second part ,note `amplitudeAfterSurge` multiplying the function
y_surge = [amplitudeAfterSurge * math.sin(2*math.pi*i/T) for i in x_surge] 

plt.plot(x_normal, y_normal , 'r')
plt.plot(x_surge, y_surge , 'r')

plt.show()

And you will get:

Answer 2

I have converted the code to period time:

import matplotlib.pyplot as plt
import math


# ------------------------------------------------------------------------
# uses the list amplitude_changes to get the amplitude for time t
def get_amplitude(t):
    for amplitude_change in amplitude_changes:
        if t >= amplitude_change['t']:
            amplitude = amplitude_change['amplitude']

    return amplitude


# --------------------------------------------------------------------------
def y_func(time, period_time, amplitude):
    return amplitude * math.sin((time / period_time) * 2 * math.pi)

# --------------------------------------------------------------------------


t_values = []
amplitude_values = []

signal1Frequency = 50
period_time = 1 / signal1Frequency
sampling_frequency = 1500

delta_t = 1 / sampling_frequency


amplitude_changes = [
                        {'t': 0, 'amplitude': 1},
                        {'t': period_time * 0.9, 'amplitude': 1.5},
                        {'t': period_time * 0.95, 'amplitude': 1},
                        {'t': period_time * 1.2, 'amplitude': 0.8},
                        {'t': period_time * 1.25, 'amplitude': 1},
                    ]

max_t = period_time * 3                     # plot 3 periods
t = 0
while t <= max_t:
    t_values.append(t)
    amplitude = get_amplitude(t)
    amplitude_values.append(y_func(t, period_time, amplitude))
    t += delta_t


plt.plot(t_values, amplitude_values)
plt.title(f'f = {signal1Frequency} Hz (T = {period_time}) - Sampling frequency = {sampling_frequency} Hz')
plt.show()

Result

Answer 3

Just like a sine wave in reality if the amplitude changes. You connect the dots of the amplitude just before and just after the change. It's not different from plotting the sine wave itself. How it looks, sharps edges for example, depends only of the moment the change happens.

This is a very basic way of calculating the points and plotting the lines between them.

At x=5 I double the amplitude.

import matplotlib.pyplot as plt
import math

def y_func(x):
    return math.sin(x)

x_values = []
y_values = []

x = 0

amplitude = 1
while x < 5:
    x_values.append(x)
    y_values.append(amplitude * y_func(x))
    x += 0.1

amplitude = 2
while x < 10:
    x_values.append(x)
    y_values.append(amplitude * y_func(x))
    x += 0.1

plt.plot(x_values, y_values)

plt.title('test')
plt.show()

After structuring it some more and putting the desired amplitude changes in a list, it's easy to produces nice spikes.

import matplotlib.pyplot as plt
import math


# ------------------------------------------------------------------------
def get_amplitude(x):
    for amplitude_change in amplitude_changes:
        if x >= amplitude_change['x']:
            amplitude = amplitude_change['amplitude']

    return amplitude


# --------------------------------------------------------------------------
def y_func(x, amplitude):
    return amplitude * math.sin(x)

# --------------------------------------------------------------------------

amplitude_changes = [
                        {'x': -1, 'amplitude': 1},
                        {'x': 6.5, 'amplitude': 2.2},
                        {'x': 6.7, 'amplitude': 1},
                        {'x': 9.1, 'amplitude': 0.5},
                        {'x': 9.2, 'amplitude': 1.2},
                        {'x': 9.4, 'amplitude': 1},
                    ]

x_values = []
y_values = []

x = 0
max_x = 10
step = 0.1

while x <= max_x:
    x_values.append(x)
    amplitude = get_amplitude(x)
    y_values.append(y_func(x, amplitude))
    x += step

plt.plot(x_values, y_values)
plt.title('test')
plt.show()