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

问题

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, the amplitude change to 1.0. Like a sudden surge of change in amplitude. It's like I was an oscillatory system that was stable, and becoming unstable at one point. The plot that I am expecting is as follow:

Regards, Anis

回答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:

回答2:

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()

来源：https://stackoverflow.com/questions/61081943/how-to-plot-sine-wave-in-python-with-sudden-amplitude-change

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