My goal is to generate an accurate sine wave. My problem is that when I use BigDecimal and StrictMath to generate the values, some of the zero crossings are wrong and the symmetry is broken.
Here is an array generated with a frequency of 1, a phase of 0, an amplitude of 1, a time of 1 second and a sample rate of 10 (I'll post the code later in this post):
>[0] 0.0
>[1] 0.5877852522924731
[2] 0.9510565162951535
[3] 0.9510565162951536
[4] 0.5877852522924732
[5] 1.2246467991473532E-16
[6] -0.587785252292473
[7] -0.9510565162951535
>[8] -0.9510565162951536
>[9] -0.5877852522924734
Shouldn't [5] be 0 for accuracy? Shouldn't (4 = 1) as well as (2 = 3),(9 = 6) and (7 = 8)?
A 2nd case, where the phase is equal to StrictMath.PI/2.0 appears to produce accuracy at [5]:
>[0] 1.0
>[1] 0.8090169943749475
[2] 0.3090169943749475
[3] -0.3090169943749473
>[4] -0.8090169943749473
>[5] -1.0
[6] -0.8090169943749476
>[7] -0.3090169943749476
>[8] 0.3090169943749472
[9] 0.8090169943749472
In this case, where the starting point is less accurate , [5] is more accurate, but once again, shouldn't (-4 = 1) as well as (-2 = 3),(-9 = 6) and (-7 = 8)?
So my question is why is this the case? Why are the zero crossings wrong, but the 1 and -1 crossings right? Why is the sine symmetry broken?
Here is my code for generating the values:
package Wave;
import java.math.BigDecimal;
/**
* @author Alexander Johnston
* Copyright 2019
* A class for sine waves
*/
public class SineWave extends Wave {
/** Creates a sine wave
* @param a as the amplitude of the sin wave from -amplitude to amplitude
* @param f as the frequency of the sine wave in Hz
* @param p as the phase of the sine wave
*/
public SineWave(BigDecimal a, BigDecimal f, BigDecimal p) {
this.a = a;
this.f = f;
this.p = p;
}
/* (non-Javadoc)
* @see waves.Wave#getSample(BigDecimal, float)
*/
public double[] getSample(BigDecimal t, float sr) {
int nsd;
BigDecimal nsdp = (new BigDecimal(Float.toString(sr)).multiply(t));
if(nsdp.compareTo(new BigDecimal(Integer.MAX_VALUE)) == -1) {
nsd = nsdp.intValue();
} else {
System.out.print("wave time is too long to fit in an array");
return null;
}
double[] w = new double[nsd];
for(int i = 0; i < w.length; i++) {
w[i] = a.multiply(new BigDecimal(StrictMath.sin(((new BigDecimal(2.0).multiply(new BigDecimal(StrictMath.PI)).multiply(f).multiply(new BigDecimal(i)).divide((new BigDecimal(Float.toString(sr))))).add(p)).doubleValue()))).doubleValue();
}
p = p.add(new BigDecimal(2.0).multiply(new BigDecimal(StrictMath.PI).multiply(f).multiply(t)));
return w;
}
}
The wave class:
package Wave;
import java.math.BigDecimal;
/**
* @author Alexander Johnston
* Copyright 2019
* A class for waves to extend
*/
public abstract class Wave {
// Amplitude of the wave
protected BigDecimal a;
// Frequency of the wave in Hz
protected BigDecimal f;
// Phase of the wave, between 0 and (2*Math.PI)
protected BigDecimal p;
/** Generates a wave with with the correct amplitude
* @param t as the length of the wave in seconds
* @return An array with the wave generated with specified amplitude as amplitude over time
*/
abstract public double[] getSample(BigDecimal t, float sr);
}
and the main method:
import java.math.BigDecimal;
import Wave.SineWave;
public class main {
public static void main(String[] args) {
BigDecimal a = new BigDecimal(1.0);
BigDecimal f = new BigDecimal(1.0);
BigDecimal p = new BigDecimal(0.0);
SineWave sw = new SineWave(a, f, p);
p = new BigDecimal(StrictMath.PI).divide(new BigDecimal(2.0));
SineWave swps = new SineWave(a, f, p);
BigDecimal t = new BigDecimal(1.0);
float sr = 10;
// The first array in this post
double [] swdns = sw.getSample(t, sr);
// The second array in this post
double [] swpsdns = swps.getSample(t, sr);
}
Thank you for taking the time to look over my post. Your help is greatly appreciated.
