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Computing the phase spectrum of a signal

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1

Using the output from either JTransform, or JWave, how should the phase spectrum be computed?

Do I simply write a similar method, but instead I compute the phase using:
Math.atan2(im / re) * Math.PI * 180?

I've used the following to calculate the magnitude spectrum:

@Override
public void computeSpectrum()

 // The spectrum into which we store the data
 super.spectrum = new double[signal.getSampledAmplitudes().length >> 1];

 // Compute the magnitude spectrum of the signal
 double re = 0, im = 0;
 for (int bin = 0; bin < spectrum.length - 1; ++bin) 
 re = super.frequencyDomain[2 * bin];
 im = super.frequencyDomain[2 * bin + 1];
 super.spectrum[bin] = Math.sqrt(re * re + im * im);
 

java fft dft

share|improve this question

edited Mar 26 at 0:59

SleuthEye

11.2k22 gold badges2222 silver badges4949 bronze badges

asked Mar 25 at 20:29

DanDan

2355 bronze badges

add a comment | 

1

Using the output from either JTransform, or JWave, how should the phase spectrum be computed?

Do I simply write a similar method, but instead I compute the phase using:
Math.atan2(im / re) * Math.PI * 180?

I've used the following to calculate the magnitude spectrum:

@Override
public void computeSpectrum()

 // The spectrum into which we store the data
 super.spectrum = new double[signal.getSampledAmplitudes().length >> 1];

 // Compute the magnitude spectrum of the signal
 double re = 0, im = 0;
 for (int bin = 0; bin < spectrum.length - 1; ++bin) 
 re = super.frequencyDomain[2 * bin];
 im = super.frequencyDomain[2 * bin + 1];
 super.spectrum[bin] = Math.sqrt(re * re + im * im);
 

java fft dft

share|improve this question

edited Mar 26 at 0:59

SleuthEye

11.2k22 gold badges2222 silver badges4949 bronze badges

asked Mar 25 at 20:29

DanDan

2355 bronze badges

add a comment | 

Using the output from either JTransform, or JWave, how should the phase spectrum be computed?

Do I simply write a similar method, but instead I compute the phase using:
Math.atan2(im / re) * Math.PI * 180?

I've used the following to calculate the magnitude spectrum:

@Override
public void computeSpectrum()

 // The spectrum into which we store the data
 super.spectrum = new double[signal.getSampledAmplitudes().length >> 1];

 // Compute the magnitude spectrum of the signal
 double re = 0, im = 0;
 for (int bin = 0; bin < spectrum.length - 1; ++bin) 
 re = super.frequencyDomain[2 * bin];
 im = super.frequencyDomain[2 * bin + 1];
 super.spectrum[bin] = Math.sqrt(re * re + im * im);
 

java fft dft

share|improve this question

edited Mar 26 at 0:59

SleuthEye

11.2k22 gold badges2222 silver badges4949 bronze badges

asked Mar 25 at 20:29

DanDan

2355 bronze badges

@Override
public void computeSpectrum()

 // The spectrum into which we store the data
 super.spectrum = new double[signal.getSampledAmplitudes().length >> 1];

 // Compute the magnitude spectrum of the signal
 double re = 0, im = 0;
 for (int bin = 0; bin < spectrum.length - 1; ++bin) 
 re = super.frequencyDomain[2 * bin];
 im = super.frequencyDomain[2 * bin + 1];
 super.spectrum[bin] = Math.sqrt(re * re + im * im);
 

share|improve this question

edited Mar 26 at 0:59

SleuthEye

11.2k22 gold badges2222 silver badges4949 bronze badges

asked Mar 25 at 20:29

DanDan

2355 bronze badges

share|improve this question

edited Mar 26 at 0:59

SleuthEye

11.2k22 gold badges2222 silver badges4949 bronze badges

asked Mar 25 at 20:29

DanDan

2355 bronze badges

edited Mar 26 at 0:59

SleuthEye

11.2k22 gold badges2222 silver badges4949 bronze badges

edited Mar 26 at 0:59

SleuthEye

11.2k22 gold badges2222 silver badges4949 bronze badges

asked Mar 25 at 20:29

DanDan

2355 bronze badges

asked Mar 25 at 20:29

DanDan

2355 bronze badges

1 Answer
1

active

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0

Indeed you can compute the phase spectrum in radians with a similar loop as you've used for the magnitude spectrum :

double re = 0, im = 0;
for (int bin = 0; bin < spectrum.length - 1; ++bin) 
 re = super.frequencyDomain[2 * bin];
 im = super.frequencyDomain[2 * bin + 1];
 super.spectrum[bin] = Math.atan2(im, re);

If you prefer a result in degrees simply convert the phases with toDegrees()

...
 super.spectrum[bin] = Math.toDegrees(Math.atan2(im, re));

share|improve this answer

answered Mar 26 at 0:57

SleuthEyeSleuthEye

11.2k22 gold badges2222 silver badges4949 bronze badges

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Will this yield a both positive and negative phase spectrum? Or do I have to 'unwrap' the phase?
  
  – Dan
  Mar 26 at 9:07
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  As per atan2 documentation: "This method computes the phase theta by computing an arc tangent of y/x in the range of -pi to pi."
  
  – SleuthEye
  Mar 26 at 12:24
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  To get rid of noise in the phase spectrum, would I compute the amplitude (sqrt(re * re * im * im)) beforehand, and discard it it's below a certain threshold, or would I do this directly to the phase value (Math.atan2(im, re))?
  
  – Dan
  Apr 2 at 9:23
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  If you are trying to isolate sections with a strong coherent signal having a relatively slow varying phase from otherwise weaker noise with randomly fluctuating phase, then the former would be the way to go (ie thresholding based on computed amplitude)
  
  – SleuthEye
  Apr 3 at 3:26
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Its to get rid of float / double rounding issues.
  
  – Dan
  Apr 3 at 5:18
  

  
  
  
  

 | 
show 1 more comment

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0

Indeed you can compute the phase spectrum in radians with a similar loop as you've used for the magnitude spectrum :

double re = 0, im = 0;
for (int bin = 0; bin < spectrum.length - 1; ++bin) 
 re = super.frequencyDomain[2 * bin];
 im = super.frequencyDomain[2 * bin + 1];
 super.spectrum[bin] = Math.atan2(im, re);

If you prefer a result in degrees simply convert the phases with toDegrees()

...
 super.spectrum[bin] = Math.toDegrees(Math.atan2(im, re));

share|improve this answer

answered Mar 26 at 0:57

SleuthEyeSleuthEye

11.2k22 gold badges2222 silver badges4949 bronze badges

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Will this yield a both positive and negative phase spectrum? Or do I have to 'unwrap' the phase?
  
  – Dan
  Mar 26 at 9:07
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  As per atan2 documentation: "This method computes the phase theta by computing an arc tangent of y/x in the range of -pi to pi."
  
  – SleuthEye
  Mar 26 at 12:24
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  To get rid of noise in the phase spectrum, would I compute the amplitude (sqrt(re * re * im * im)) beforehand, and discard it it's below a certain threshold, or would I do this directly to the phase value (Math.atan2(im, re))?
  
  – Dan
  Apr 2 at 9:23
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  If you are trying to isolate sections with a strong coherent signal having a relatively slow varying phase from otherwise weaker noise with randomly fluctuating phase, then the former would be the way to go (ie thresholding based on computed amplitude)
  
  – SleuthEye
  Apr 3 at 3:26
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Its to get rid of float / double rounding issues.
  
  – Dan
  Apr 3 at 5:18
  

  
  
  
  

 | 
show 1 more comment

0

Indeed you can compute the phase spectrum in radians with a similar loop as you've used for the magnitude spectrum :

double re = 0, im = 0;
for (int bin = 0; bin < spectrum.length - 1; ++bin) 
 re = super.frequencyDomain[2 * bin];
 im = super.frequencyDomain[2 * bin + 1];
 super.spectrum[bin] = Math.atan2(im, re);

If you prefer a result in degrees simply convert the phases with toDegrees()

...
 super.spectrum[bin] = Math.toDegrees(Math.atan2(im, re));

share|improve this answer

answered Mar 26 at 0:57

SleuthEyeSleuthEye

11.2k22 gold badges2222 silver badges4949 bronze badges

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Will this yield a both positive and negative phase spectrum? Or do I have to 'unwrap' the phase?
  
  – Dan
  Mar 26 at 9:07
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  As per atan2 documentation: "This method computes the phase theta by computing an arc tangent of y/x in the range of -pi to pi."
  
  – SleuthEye
  Mar 26 at 12:24
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  To get rid of noise in the phase spectrum, would I compute the amplitude (sqrt(re * re * im * im)) beforehand, and discard it it's below a certain threshold, or would I do this directly to the phase value (Math.atan2(im, re))?
  
  – Dan
  Apr 2 at 9:23
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  If you are trying to isolate sections with a strong coherent signal having a relatively slow varying phase from otherwise weaker noise with randomly fluctuating phase, then the former would be the way to go (ie thresholding based on computed amplitude)
  
  – SleuthEye
  Apr 3 at 3:26
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Its to get rid of float / double rounding issues.
  
  – Dan
  Apr 3 at 5:18
  

  
  
  
  

 | 
show 1 more comment

Indeed you can compute the phase spectrum in radians with a similar loop as you've used for the magnitude spectrum :

double re = 0, im = 0;
for (int bin = 0; bin < spectrum.length - 1; ++bin) 
 re = super.frequencyDomain[2 * bin];
 im = super.frequencyDomain[2 * bin + 1];
 super.spectrum[bin] = Math.atan2(im, re);

If you prefer a result in degrees simply convert the phases with toDegrees()

...
 super.spectrum[bin] = Math.toDegrees(Math.atan2(im, re));

share|improve this answer

answered Mar 26 at 0:57

SleuthEyeSleuthEye

11.2k22 gold badges2222 silver badges4949 bronze badges

double re = 0, im = 0;
for (int bin = 0; bin < spectrum.length - 1; ++bin) 
 re = super.frequencyDomain[2 * bin];
 im = super.frequencyDomain[2 * bin + 1];
 super.spectrum[bin] = Math.atan2(im, re);

...
 super.spectrum[bin] = Math.toDegrees(Math.atan2(im, re));

share|improve this answer

answered Mar 26 at 0:57

SleuthEyeSleuthEye

11.2k22 gold badges2222 silver badges4949 bronze badges

answered Mar 26 at 0:57

SleuthEyeSleuthEye

11.2k22 gold badges2222 silver badges4949 bronze badges

answered Mar 26 at 0:57

SleuthEyeSleuthEye

11.2k22 gold badges2222 silver badges4949 bronze badges