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In numpy - how do I compute phase and amplitude of a sinusoid by correlating it with a sine and cosine?

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0

I have an incoming sinusoid with a known frequency. I understand that one can compute it's phase and amplitude by computing it's correlation with a sine and a cosine. How would I do this using numpy?

Or maybe there is a better way to do this. Looking at this here, but I don't know how to do the computation in numpy.

I'm a numpy rookie. I would appreciate some pointers.

python numpy signal-processing

share|improve this question

edited Mar 23 at 5:10

Ziffusion

asked Mar 23 at 4:57

ZiffusionZiffusion

6,75211844

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  In which form do you have the sinusoid? In the form of points ,I guess ?
  
  – Tojrah
  Mar 23 at 5:09
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Yes. I have sample values at regular intervals for an entire cycle.
  
  – Ziffusion
  Mar 23 at 5:11
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Do you have some special points(peak point or zero amplitude points because then it would be easier
  
  – Tojrah
  Mar 23 at 5:18
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Well, I could scan the samples for zero crossings, or max values, but they are not guaranteed to be present. Take a look at the link I added to the question. I would like to implement the computation described in the article in numpy. Need some help with that.
  
  – Ziffusion
  Mar 23 at 5:21
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Are you looking for something like stackoverflow.com/questions/55317667/…?
  
  – Reedinationer
  Mar 23 at 19:49
  

  
  
  
  

add a comment | 

0

I have an incoming sinusoid with a known frequency. I understand that one can compute it's phase and amplitude by computing it's correlation with a sine and a cosine. How would I do this using numpy?

Or maybe there is a better way to do this. Looking at this here, but I don't know how to do the computation in numpy.

I'm a numpy rookie. I would appreciate some pointers.

python numpy signal-processing

share|improve this question

edited Mar 23 at 5:10

Ziffusion

asked Mar 23 at 4:57

ZiffusionZiffusion

6,75211844

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  In which form do you have the sinusoid? In the form of points ,I guess ?
  
  – Tojrah
  Mar 23 at 5:09
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Yes. I have sample values at regular intervals for an entire cycle.
  
  – Ziffusion
  Mar 23 at 5:11
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Do you have some special points(peak point or zero amplitude points because then it would be easier
  
  – Tojrah
  Mar 23 at 5:18
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Well, I could scan the samples for zero crossings, or max values, but they are not guaranteed to be present. Take a look at the link I added to the question. I would like to implement the computation described in the article in numpy. Need some help with that.
  
  – Ziffusion
  Mar 23 at 5:21
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Are you looking for something like stackoverflow.com/questions/55317667/…?
  
  – Reedinationer
  Mar 23 at 19:49
  

  
  
  
  

add a comment | 

I have an incoming sinusoid with a known frequency. I understand that one can compute it's phase and amplitude by computing it's correlation with a sine and a cosine. How would I do this using numpy?

Or maybe there is a better way to do this. Looking at this here, but I don't know how to do the computation in numpy.

I'm a numpy rookie. I would appreciate some pointers.

python numpy signal-processing

share|improve this question

edited Mar 23 at 5:10

Ziffusion

asked Mar 23 at 4:57

ZiffusionZiffusion

6,75211844

share|improve this question

edited Mar 23 at 5:10

Ziffusion

asked Mar 23 at 4:57

ZiffusionZiffusion

6,75211844

share|improve this question

edited Mar 23 at 5:10

Ziffusion

asked Mar 23 at 4:57

ZiffusionZiffusion

6,75211844

asked Mar 23 at 4:57

ZiffusionZiffusion

6,75211844

asked Mar 23 at 4:57

ZiffusionZiffusion

6,75211844

1 Answer
1

active

oldest

votes

1

One convenient method would be to take advantage of Euler's formula e^(i phi) = cos phi + i sin phi:

def get_cos_params(samples):
 N = len(samples)
 x = np.linspace(-np.pi, np.pi, N, endpoint=False)
 template = np.exp(1j * x)
 corr = 2 / N * template@samples
 R = np.abs(corr)
 phi = np.log(corr).imag
 return R, phi

Example:

N = np.random.randint(10, 1000)
phi = np.random.uniform(-np.pi, np.pi)
R = np.random.uniform(0.1, 10)
x = np.linspace(-np.pi, np.pi, N, endpoint=False)
signal = R * np.cos(x-phi)
R_recon, phi_recon = get_cos_params(signal)
print(np.isclose(R, R_recon), np.isclose(phi, phi_recon))
# True True

share|improve this answer

answered Mar 23 at 5:49

Paul PanzerPaul Panzer

32k21845

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Do you mind explaining what's going on here? I would really appreciate it if you could clarify what you are doing conceptually, and maybe annotate some lines in the answer with comments saying what is happening. Also - I get a syntax error on "template@samples".
  
  – Ziffusion
  Mar 23 at 12:46
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  @Ziffusion You must be on an old python version. Either upgrade or replace all x@y with np.dot(x, y). Re what is happening, conceptually. Going by your question I naturally assumed that you have already grasped the concept and only needed an example implementation in order to get up to speed with numpy. I've mentioned Euler's formula. Once you are aware of that the code should be pretty close to self-explanatory:
  
  – Paul Panzer
  Mar 23 at 15:02
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  Step 1 Use Euler's formula to create a combined cosine and sine template with the correct sampling rate. Step 2 Multiply with the signal and compute the "integral". Step 3 translate the integral value to polar coordinates and use the fact that these actually are the amplitude and phase. Please try to identify these steps in the code yourself. If you get stuck in the process I'll be happy to help you out but you are supposed to make some effort yourself first.
  
  – Paul Panzer
  Mar 23 at 15:02
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Thanks. I am an engineer and should know this better. But been futzing with software for 30 years now, and all of this stuff has kind of faded away. Am diving back into it now. Thanks for the pointers. I think the link that I have in the question actually has some great context.
  
  – Ziffusion
  Mar 23 at 15:47
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  If you have some time (and the inclination), can you chat with me so I can ask you a few questions? You seem to know what you are talking about, and it'll just get me there faster. Stackoverflow has chat I believe.
  
  – Ziffusion
  Mar 23 at 16:02
  

  
  
  
  

 | 
show 2 more comments

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1

One convenient method would be to take advantage of Euler's formula e^(i phi) = cos phi + i sin phi:

def get_cos_params(samples):
 N = len(samples)
 x = np.linspace(-np.pi, np.pi, N, endpoint=False)
 template = np.exp(1j * x)
 corr = 2 / N * template@samples
 R = np.abs(corr)
 phi = np.log(corr).imag
 return R, phi

Example:

N = np.random.randint(10, 1000)
phi = np.random.uniform(-np.pi, np.pi)
R = np.random.uniform(0.1, 10)
x = np.linspace(-np.pi, np.pi, N, endpoint=False)
signal = R * np.cos(x-phi)
R_recon, phi_recon = get_cos_params(signal)
print(np.isclose(R, R_recon), np.isclose(phi, phi_recon))
# True True

share|improve this answer

answered Mar 23 at 5:49

Paul PanzerPaul Panzer

32k21845

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Do you mind explaining what's going on here? I would really appreciate it if you could clarify what you are doing conceptually, and maybe annotate some lines in the answer with comments saying what is happening. Also - I get a syntax error on "template@samples".
  
  – Ziffusion
  Mar 23 at 12:46
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  @Ziffusion You must be on an old python version. Either upgrade or replace all x@y with np.dot(x, y). Re what is happening, conceptually. Going by your question I naturally assumed that you have already grasped the concept and only needed an example implementation in order to get up to speed with numpy. I've mentioned Euler's formula. Once you are aware of that the code should be pretty close to self-explanatory:
  
  – Paul Panzer
  Mar 23 at 15:02
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  Step 1 Use Euler's formula to create a combined cosine and sine template with the correct sampling rate. Step 2 Multiply with the signal and compute the "integral". Step 3 translate the integral value to polar coordinates and use the fact that these actually are the amplitude and phase. Please try to identify these steps in the code yourself. If you get stuck in the process I'll be happy to help you out but you are supposed to make some effort yourself first.
  
  – Paul Panzer
  Mar 23 at 15:02
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Thanks. I am an engineer and should know this better. But been futzing with software for 30 years now, and all of this stuff has kind of faded away. Am diving back into it now. Thanks for the pointers. I think the link that I have in the question actually has some great context.
  
  – Ziffusion
  Mar 23 at 15:47
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  If you have some time (and the inclination), can you chat with me so I can ask you a few questions? You seem to know what you are talking about, and it'll just get me there faster. Stackoverflow has chat I believe.
  
  – Ziffusion
  Mar 23 at 16:02
  

  
  
  
  

 | 
show 2 more comments

1

One convenient method would be to take advantage of Euler's formula e^(i phi) = cos phi + i sin phi:

def get_cos_params(samples):
 N = len(samples)
 x = np.linspace(-np.pi, np.pi, N, endpoint=False)
 template = np.exp(1j * x)
 corr = 2 / N * template@samples
 R = np.abs(corr)
 phi = np.log(corr).imag
 return R, phi

Example:

N = np.random.randint(10, 1000)
phi = np.random.uniform(-np.pi, np.pi)
R = np.random.uniform(0.1, 10)
x = np.linspace(-np.pi, np.pi, N, endpoint=False)
signal = R * np.cos(x-phi)
R_recon, phi_recon = get_cos_params(signal)
print(np.isclose(R, R_recon), np.isclose(phi, phi_recon))
# True True

share|improve this answer

answered Mar 23 at 5:49

Paul PanzerPaul Panzer

32k21845

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Do you mind explaining what's going on here? I would really appreciate it if you could clarify what you are doing conceptually, and maybe annotate some lines in the answer with comments saying what is happening. Also - I get a syntax error on "template@samples".
  
  – Ziffusion
  Mar 23 at 12:46
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  @Ziffusion You must be on an old python version. Either upgrade or replace all x@y with np.dot(x, y). Re what is happening, conceptually. Going by your question I naturally assumed that you have already grasped the concept and only needed an example implementation in order to get up to speed with numpy. I've mentioned Euler's formula. Once you are aware of that the code should be pretty close to self-explanatory:
  
  – Paul Panzer
  Mar 23 at 15:02
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  Step 1 Use Euler's formula to create a combined cosine and sine template with the correct sampling rate. Step 2 Multiply with the signal and compute the "integral". Step 3 translate the integral value to polar coordinates and use the fact that these actually are the amplitude and phase. Please try to identify these steps in the code yourself. If you get stuck in the process I'll be happy to help you out but you are supposed to make some effort yourself first.
  
  – Paul Panzer
  Mar 23 at 15:02
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Thanks. I am an engineer and should know this better. But been futzing with software for 30 years now, and all of this stuff has kind of faded away. Am diving back into it now. Thanks for the pointers. I think the link that I have in the question actually has some great context.
  
  – Ziffusion
  Mar 23 at 15:47
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  If you have some time (and the inclination), can you chat with me so I can ask you a few questions? You seem to know what you are talking about, and it'll just get me there faster. Stackoverflow has chat I believe.
  
  – Ziffusion
  Mar 23 at 16:02
  

  
  
  
  

 | 
show 2 more comments

One convenient method would be to take advantage of Euler's formula e^(i phi) = cos phi + i sin phi:

def get_cos_params(samples):
 N = len(samples)
 x = np.linspace(-np.pi, np.pi, N, endpoint=False)
 template = np.exp(1j * x)
 corr = 2 / N * template@samples
 R = np.abs(corr)
 phi = np.log(corr).imag
 return R, phi

Example:

N = np.random.randint(10, 1000)
phi = np.random.uniform(-np.pi, np.pi)
R = np.random.uniform(0.1, 10)
x = np.linspace(-np.pi, np.pi, N, endpoint=False)
signal = R * np.cos(x-phi)
R_recon, phi_recon = get_cos_params(signal)
print(np.isclose(R, R_recon), np.isclose(phi, phi_recon))
# True True

share|improve this answer

answered Mar 23 at 5:49

Paul PanzerPaul Panzer

32k21845

def get_cos_params(samples):
 N = len(samples)
 x = np.linspace(-np.pi, np.pi, N, endpoint=False)
 template = np.exp(1j * x)
 corr = 2 / N * template@samples
 R = np.abs(corr)
 phi = np.log(corr).imag
 return R, phi

N = np.random.randint(10, 1000)
phi = np.random.uniform(-np.pi, np.pi)
R = np.random.uniform(0.1, 10)
x = np.linspace(-np.pi, np.pi, N, endpoint=False)
signal = R * np.cos(x-phi)
R_recon, phi_recon = get_cos_params(signal)
print(np.isclose(R, R_recon), np.isclose(phi, phi_recon))
# True True

share|improve this answer

answered Mar 23 at 5:49

Paul PanzerPaul Panzer

32k21845

answered Mar 23 at 5:49

Paul PanzerPaul Panzer

32k21845

answered Mar 23 at 5:49

Paul PanzerPaul Panzer

32k21845