Trapezoidal wave in Python

Question

How do I generate a trapezoidal wave in Python?

I looked into the modules such as SciPy and NumPy, but in vain. Is there a module such as the scipy.signal.gaussian which returns an array of values representing the Gaussian function wave?

I generated this using the trapezoidal kernel of Astropy, Trapezoid1DKernel(30,slope=1.0) . I want to implement this in Python without using Astropy.

Answer 1

While the width and the slope are sufficient to define a triangular signal, you would need a third parameter for a trapezoidal signal: the amplitude.

Using those three parameters, you can easily adjust the scipy.signal.sawtooth function to give you a trapeziodal shape by truncating and offsetting the triangular shaped function.

from scipy import signal
import matplotlib.pyplot as plt
import numpy as np


def trapzoid_signal(t, width=2., slope=1., amp=1., offs=0):
    a = slope*width*signal.sawtooth(2*np.pi*t/width, width=0.5)/4.
    a[a>amp/2.] = amp/2.
    a[a<-amp/2.] = -amp/2.
    return a + amp/2. + offs

t = np.linspace(0, 6, 501)
plt.plot(t,trapzoid_signal(t, width=2, slope=2, amp=1.), label="width=2, slope=2, amp=1")
plt.plot(t,trapzoid_signal(t, width=4, slope=1, amp=0.6), label="width=4, slope=1, amp=0.6")

plt.legend( loc=(0.25,1.015))
plt.show()

Note that you may also like to define a phase, depeding on the use case.

In order to define a single pulse, you might want to modify the function a bit and supply an array which ranges over [0,width].

from scipy import signal
import matplotlib.pyplot as plt
import numpy as np

def trapzoid_signal(t, width=2., slope=1., amp=1., offs=0):
    a = slope*width*signal.sawtooth(2*np.pi*t/width, width=0.5)/4.
    a += slope*width/4.
    a[a>amp] = amp
    return a + offs

for w,s,a in zip([2,5], [2,1], [1,0.6]):
    t = np.linspace(0, w, 501)
    l = "width={}, slope={}, amp={}".format(w,s,a)
    plt.plot(t,trapzoid_signal(t, width=w, slope=s, amp=a), label=l)

plt.legend( loc="upper right")
plt.show()

Answer 2

From the SciPy website it looks like this isn't included (they currently have sawtooth and square, but not trapezoid). As a generalised version of the C example the following will do what you want,

import numpy as np
import matplotlib.pyplot as plt

def trapezoidalWave(xin, width=1., slope=1.):
    x = xin%(4*width)
    if (x <= width):
        # Ascending line
        return x*slope;
    elif (x <= 2.*width):
        # Top horizontal line
        return width*slope
    elif (x <= 3.*width):
        # Descending line
        return 3.*width*slope - x*slope
    elif (x <= 4*width):
        # Bottom horizontal line
        return 0.


x = np.linspace(0.,20,1000)
for i in x:
    plt.plot(i, trapezoidalWave(i), 'k.')
    plt.plot(i, trapezoidalWave(i, 1.5, 2.), 'r.')
plt.show()

which looks like,

This can be done more elegantly with Heaviside functions which allow you to use NumPy arrays,

import numpy as np
import matplotlib.pyplot as plt

def H(x):
    return 0.5 * (np.sign(x) + 1)

def trapWave(xin, width=1., slope=1.):
    x = xin%(4*width)
    y = ((H(x)-H(x-width))*x*slope +
         (H(x-width)-H(x-2.*width))*width*slope +
         (H(x-2.*width)-H(x-3.*width))*(3.*width*slope - x*slope))
    return y

x = np.linspace(0.,20,1000)
plt.plot(x, trapWave(x))
plt.plot(x, trapWave(x, 1.5, 2.))
plt.show()

For this example, the Heaviside version is about 20 times faster!