Oscillators

This example shows how to generate different signals using the Oscillator module. This module integrates basic structures that implements a simple interface compatible with the std::generate standard function.

eDSP implements 4 different oscillators:

Square Signal
Triangular Signal
Sawtooth Signal
Sinusoidal Signal

All of them are available by default in the oscillators folder.

Square Signal

The square wave can be constructed from straight line segments. The square waves contain a wide range of harmonics. It can be defined as simply the sign function of a sinusoid:

$$ x(t) = {sgn}\left(\sin {\frac {t}{T}}\right)={sgn}\left(\sin ft\right)$$

which will be 1 when the sinusoid is positive, −1 when the sinusoid is negative, and 0 at the discontinuities. Here, T is the period of the square wave, or equivalently, f is its frequency, where f = 1/T.

The class square_oscillator implements a basic square signal oscillator. In this example we generate a square signal with a period of 10KHz sampled at 42.1KHz:



In [1]:

    
import pedsp.oscillator as oscillator
import pedsp.algorithm as algorithm
import matplotlib.pyplot as plt
import numpy as np

amplitude = 1.;
sample_rate = 8000;
frequency = 5;
duration_secs = 2;
samples = int(duration_secs * sample_rate); 
duty = 0.5;

square = oscillator.Square(amp=amplitude, sr=sample_rate, f=frequency, duty=duty)
data = square.generate(N=samples)

Then we can display the final result:



In [2]:

    
t = algorithm.linspace(0, duration_secs, samples)
plt.plot(t, data)
plt.show()

Sawtooth Signal

A sawtooth waveform increases linearly from -1 to 1 in $ [0, 2 \pi wi] $ interval, and decreases linearly from 1 to -1 in the interval $ \left[ 2 \pi w, 2 \pi \right] $, where $ w $ is the width of the periodic signal. If $ w $ is 0.5, the function generates a standard triangular wave. The triangle wave shares many geometric similarities with the sawtooth wave, except it has two sloping line segments.

A more general form, and with period T, is:

$$ {\displaystyle 2\left({\frac {t}{T}}-\left\lfloor {\frac {1}{2}}+{\frac {t}{T}}\right\rfloor \right)} $$

The class sawtooth_oscillator implements a basic square signal oscillator. In this example we generate a square signal with a period of 10KHz sampled at 42.1KHz:



In [3]:

    
width = 0.7
sawtooth = oscillator.Sawtooth(amp=amplitude, sr=sample_rate, f=frequency, width=width)
data = sawtooth.generate(N=samples)

Then, to display:



In [4]:

    
plt.plot(t, data)
plt.show()

Interactive mode



In [5]:

    
from __future__ import print_function
from ipywidgets import interact, interactive, fixed, interact_manual
import ipywidgets as widgets

@interact(dtype=widgets.Dropdown(
                options=['square', 'sinusoidal', 'sawtooth'],
                value='square',
                description='Type:',
                disabled=False), 
          frequency=widgets.IntSlider(min=1,max=20,step=1,value=10), 
          duration=widgets.IntSlider(min=1,max=5,step=1,value=1),
          alpha=widgets.FloatSlider(min=0.0,max=1.0, value=0.3))
def display_oscillator(dtype, frequency, duration, alpha):
    sr = 42000
    g = None
    if dtype == "square":
        g = oscillator.Square(amp=1, sr=sr, f=frequency, duty=alpha)
    elif dtype == "sinusoidal":
        g = oscillator.Sinusoidal(amp=1, sr=sr, f=frequency, p=0)
    else:
        g = oscillator.Sawtooth(amp=1, sr=sr, f=frequency, width=alpha)
   
    samples = int(duration * sr)
    data = g.generate(N=samples)
    t = algorithm.linspace(0, duration, samples)
    plt.plot(t, data)
    plt.show()



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