Compute fourier coefficients with Python?









up vote
1
down vote

favorite
1












I'm trying to compute the following Fourier coefficients
$frac1s_f int_0^s_f V_pot(s)cos (fracnpis_fs ) mathrmds,$



where $V_pot$ is a previous def function of this form. enter image description here I really don't know what numerical method I can use, however I began with Simpson’s rule of scipy library.



import numpy as np
from scipy.integrate import simps

Nf= 200
IVp = np.zeros(2*Nf)
snn = np.zeros(NP)
def f(k):
for i in range(0,NP):
sn=(i-1)*H
snn[i]=sn
return (1/SF)*np.cos(np.pi*k*sn/SF)*Vpot(sn)

for k in range(0,2*Nf):
Func= f(k)
y1=np.array(Func,dtype=float)
I= simps(y1,snn)


I had this error:



IndexError: tuple index out of range









share|improve this question























  • Well, scipy.integrate has a bunch of options to choose from.
    – mikuszefski
    Nov 12 at 6:45










  • Concerning your error, always provide the full trace back.
    – mikuszefski
    Nov 12 at 6:46










  • And please change your code, such that it is actually running.
    – mikuszefski
    Nov 12 at 6:49










  • Discretize the integral, see the discretized integral as part of a discretized cosine transform or a discretized Fourier transform, apply the fft and ifft methods.
    – LutzL
    Nov 12 at 8:54














up vote
1
down vote

favorite
1












I'm trying to compute the following Fourier coefficients
$frac1s_f int_0^s_f V_pot(s)cos (fracnpis_fs ) mathrmds,$



where $V_pot$ is a previous def function of this form. enter image description here I really don't know what numerical method I can use, however I began with Simpson’s rule of scipy library.



import numpy as np
from scipy.integrate import simps

Nf= 200
IVp = np.zeros(2*Nf)
snn = np.zeros(NP)
def f(k):
for i in range(0,NP):
sn=(i-1)*H
snn[i]=sn
return (1/SF)*np.cos(np.pi*k*sn/SF)*Vpot(sn)

for k in range(0,2*Nf):
Func= f(k)
y1=np.array(Func,dtype=float)
I= simps(y1,snn)


I had this error:



IndexError: tuple index out of range









share|improve this question























  • Well, scipy.integrate has a bunch of options to choose from.
    – mikuszefski
    Nov 12 at 6:45










  • Concerning your error, always provide the full trace back.
    – mikuszefski
    Nov 12 at 6:46










  • And please change your code, such that it is actually running.
    – mikuszefski
    Nov 12 at 6:49










  • Discretize the integral, see the discretized integral as part of a discretized cosine transform or a discretized Fourier transform, apply the fft and ifft methods.
    – LutzL
    Nov 12 at 8:54












up vote
1
down vote

favorite
1









up vote
1
down vote

favorite
1






1





I'm trying to compute the following Fourier coefficients
$frac1s_f int_0^s_f V_pot(s)cos (fracnpis_fs ) mathrmds,$



where $V_pot$ is a previous def function of this form. enter image description here I really don't know what numerical method I can use, however I began with Simpson’s rule of scipy library.



import numpy as np
from scipy.integrate import simps

Nf= 200
IVp = np.zeros(2*Nf)
snn = np.zeros(NP)
def f(k):
for i in range(0,NP):
sn=(i-1)*H
snn[i]=sn
return (1/SF)*np.cos(np.pi*k*sn/SF)*Vpot(sn)

for k in range(0,2*Nf):
Func= f(k)
y1=np.array(Func,dtype=float)
I= simps(y1,snn)


I had this error:



IndexError: tuple index out of range









share|improve this question















I'm trying to compute the following Fourier coefficients
$frac1s_f int_0^s_f V_pot(s)cos (fracnpis_fs ) mathrmds,$



where $V_pot$ is a previous def function of this form. enter image description here I really don't know what numerical method I can use, however I began with Simpson’s rule of scipy library.



import numpy as np
from scipy.integrate import simps

Nf= 200
IVp = np.zeros(2*Nf)
snn = np.zeros(NP)
def f(k):
for i in range(0,NP):
sn=(i-1)*H
snn[i]=sn
return (1/SF)*np.cos(np.pi*k*sn/SF)*Vpot(sn)

for k in range(0,2*Nf):
Func= f(k)
y1=np.array(Func,dtype=float)
I= simps(y1,snn)


I had this error:



IndexError: tuple index out of range






python fft numerical-methods numerical-integration dft






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited Nov 13 at 18:33

























asked Nov 12 at 5:15









PCat27

185




185











  • Well, scipy.integrate has a bunch of options to choose from.
    – mikuszefski
    Nov 12 at 6:45










  • Concerning your error, always provide the full trace back.
    – mikuszefski
    Nov 12 at 6:46










  • And please change your code, such that it is actually running.
    – mikuszefski
    Nov 12 at 6:49










  • Discretize the integral, see the discretized integral as part of a discretized cosine transform or a discretized Fourier transform, apply the fft and ifft methods.
    – LutzL
    Nov 12 at 8:54
















  • Well, scipy.integrate has a bunch of options to choose from.
    – mikuszefski
    Nov 12 at 6:45










  • Concerning your error, always provide the full trace back.
    – mikuszefski
    Nov 12 at 6:46










  • And please change your code, such that it is actually running.
    – mikuszefski
    Nov 12 at 6:49










  • Discretize the integral, see the discretized integral as part of a discretized cosine transform or a discretized Fourier transform, apply the fft and ifft methods.
    – LutzL
    Nov 12 at 8:54















Well, scipy.integrate has a bunch of options to choose from.
– mikuszefski
Nov 12 at 6:45




Well, scipy.integrate has a bunch of options to choose from.
– mikuszefski
Nov 12 at 6:45












Concerning your error, always provide the full trace back.
– mikuszefski
Nov 12 at 6:46




Concerning your error, always provide the full trace back.
– mikuszefski
Nov 12 at 6:46












And please change your code, such that it is actually running.
– mikuszefski
Nov 12 at 6:49




And please change your code, such that it is actually running.
– mikuszefski
Nov 12 at 6:49












Discretize the integral, see the discretized integral as part of a discretized cosine transform or a discretized Fourier transform, apply the fft and ifft methods.
– LutzL
Nov 12 at 8:54




Discretize the integral, see the discretized integral as part of a discretized cosine transform or a discretized Fourier transform, apply the fft and ifft methods.
– LutzL
Nov 12 at 8:54












1 Answer
1






active

oldest

votes

















up vote
2
down vote



accepted










Your task can be done via



Nf = 200
s = np.linspace(0, Sf, Nf+1);
V_s = Vpot(s)
I = [ simps(s, np.cos(np.pi*k*s/Sf)*V_s ) / Sf for k in range(0,2*Nf) ]


But really, investigate how to do this via the FFT or related methods.






share|improve this answer




















  • ok, thanks, I was able to calculate the integral, however, I will see FFT related methods because the integration has a considerable error.
    – PCat27
    Nov 12 at 15:59











  • First make sure that the formulas were correctly translated into code, including all constants and parameters. The Simpson method has order 4, that should give good results in the lower frequencies. For the higher frequencies you get into the territory of the sampling theorem.
    – LutzL
    Nov 12 at 16:07










  • I compared with simps and scipy.integrate.quad and I obtained two different integrations. You can see the complete code in (github.com/dayacaca/Python-prog/blob/integrals/RollepUP_spiral/… )
    – PCat27
    Nov 12 at 17:49











  • I'm not really sure what I'm looking at. The distance computation computes points on the spiral from some related area inputs? Alternating in some way? Can you give a more geometric-physical description of what the model computes?
    – LutzL
    Nov 12 at 21:15










  • Ok, found your post math.stackexchange.com/questions/2914813/… that explains the construction of the spiral. I think there may be an error in adding pi to the angle in the lower half.
    – LutzL
    Nov 12 at 21:39










Your Answer






StackExchange.ifUsing("editor", function ()
StackExchange.using("externalEditor", function ()
StackExchange.using("snippets", function ()
StackExchange.snippets.init();
);
);
, "code-snippets");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "1"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);













draft saved

draft discarded


















StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstackoverflow.com%2fquestions%2f53256277%2fcompute-fourier-coefficients-with-python%23new-answer', 'question_page');

);

Post as a guest















Required, but never shown

























1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
2
down vote



accepted










Your task can be done via



Nf = 200
s = np.linspace(0, Sf, Nf+1);
V_s = Vpot(s)
I = [ simps(s, np.cos(np.pi*k*s/Sf)*V_s ) / Sf for k in range(0,2*Nf) ]


But really, investigate how to do this via the FFT or related methods.






share|improve this answer




















  • ok, thanks, I was able to calculate the integral, however, I will see FFT related methods because the integration has a considerable error.
    – PCat27
    Nov 12 at 15:59











  • First make sure that the formulas were correctly translated into code, including all constants and parameters. The Simpson method has order 4, that should give good results in the lower frequencies. For the higher frequencies you get into the territory of the sampling theorem.
    – LutzL
    Nov 12 at 16:07










  • I compared with simps and scipy.integrate.quad and I obtained two different integrations. You can see the complete code in (github.com/dayacaca/Python-prog/blob/integrals/RollepUP_spiral/… )
    – PCat27
    Nov 12 at 17:49











  • I'm not really sure what I'm looking at. The distance computation computes points on the spiral from some related area inputs? Alternating in some way? Can you give a more geometric-physical description of what the model computes?
    – LutzL
    Nov 12 at 21:15










  • Ok, found your post math.stackexchange.com/questions/2914813/… that explains the construction of the spiral. I think there may be an error in adding pi to the angle in the lower half.
    – LutzL
    Nov 12 at 21:39














up vote
2
down vote



accepted










Your task can be done via



Nf = 200
s = np.linspace(0, Sf, Nf+1);
V_s = Vpot(s)
I = [ simps(s, np.cos(np.pi*k*s/Sf)*V_s ) / Sf for k in range(0,2*Nf) ]


But really, investigate how to do this via the FFT or related methods.






share|improve this answer




















  • ok, thanks, I was able to calculate the integral, however, I will see FFT related methods because the integration has a considerable error.
    – PCat27
    Nov 12 at 15:59











  • First make sure that the formulas were correctly translated into code, including all constants and parameters. The Simpson method has order 4, that should give good results in the lower frequencies. For the higher frequencies you get into the territory of the sampling theorem.
    – LutzL
    Nov 12 at 16:07










  • I compared with simps and scipy.integrate.quad and I obtained two different integrations. You can see the complete code in (github.com/dayacaca/Python-prog/blob/integrals/RollepUP_spiral/… )
    – PCat27
    Nov 12 at 17:49











  • I'm not really sure what I'm looking at. The distance computation computes points on the spiral from some related area inputs? Alternating in some way? Can you give a more geometric-physical description of what the model computes?
    – LutzL
    Nov 12 at 21:15










  • Ok, found your post math.stackexchange.com/questions/2914813/… that explains the construction of the spiral. I think there may be an error in adding pi to the angle in the lower half.
    – LutzL
    Nov 12 at 21:39












up vote
2
down vote



accepted







up vote
2
down vote



accepted






Your task can be done via



Nf = 200
s = np.linspace(0, Sf, Nf+1);
V_s = Vpot(s)
I = [ simps(s, np.cos(np.pi*k*s/Sf)*V_s ) / Sf for k in range(0,2*Nf) ]


But really, investigate how to do this via the FFT or related methods.






share|improve this answer












Your task can be done via



Nf = 200
s = np.linspace(0, Sf, Nf+1);
V_s = Vpot(s)
I = [ simps(s, np.cos(np.pi*k*s/Sf)*V_s ) / Sf for k in range(0,2*Nf) ]


But really, investigate how to do this via the FFT or related methods.







share|improve this answer












share|improve this answer



share|improve this answer










answered Nov 12 at 9:04









LutzL

13.4k21326




13.4k21326











  • ok, thanks, I was able to calculate the integral, however, I will see FFT related methods because the integration has a considerable error.
    – PCat27
    Nov 12 at 15:59











  • First make sure that the formulas were correctly translated into code, including all constants and parameters. The Simpson method has order 4, that should give good results in the lower frequencies. For the higher frequencies you get into the territory of the sampling theorem.
    – LutzL
    Nov 12 at 16:07










  • I compared with simps and scipy.integrate.quad and I obtained two different integrations. You can see the complete code in (github.com/dayacaca/Python-prog/blob/integrals/RollepUP_spiral/… )
    – PCat27
    Nov 12 at 17:49











  • I'm not really sure what I'm looking at. The distance computation computes points on the spiral from some related area inputs? Alternating in some way? Can you give a more geometric-physical description of what the model computes?
    – LutzL
    Nov 12 at 21:15










  • Ok, found your post math.stackexchange.com/questions/2914813/… that explains the construction of the spiral. I think there may be an error in adding pi to the angle in the lower half.
    – LutzL
    Nov 12 at 21:39
















  • ok, thanks, I was able to calculate the integral, however, I will see FFT related methods because the integration has a considerable error.
    – PCat27
    Nov 12 at 15:59











  • First make sure that the formulas were correctly translated into code, including all constants and parameters. The Simpson method has order 4, that should give good results in the lower frequencies. For the higher frequencies you get into the territory of the sampling theorem.
    – LutzL
    Nov 12 at 16:07










  • I compared with simps and scipy.integrate.quad and I obtained two different integrations. You can see the complete code in (github.com/dayacaca/Python-prog/blob/integrals/RollepUP_spiral/… )
    – PCat27
    Nov 12 at 17:49











  • I'm not really sure what I'm looking at. The distance computation computes points on the spiral from some related area inputs? Alternating in some way? Can you give a more geometric-physical description of what the model computes?
    – LutzL
    Nov 12 at 21:15










  • Ok, found your post math.stackexchange.com/questions/2914813/… that explains the construction of the spiral. I think there may be an error in adding pi to the angle in the lower half.
    – LutzL
    Nov 12 at 21:39















ok, thanks, I was able to calculate the integral, however, I will see FFT related methods because the integration has a considerable error.
– PCat27
Nov 12 at 15:59





ok, thanks, I was able to calculate the integral, however, I will see FFT related methods because the integration has a considerable error.
– PCat27
Nov 12 at 15:59













First make sure that the formulas were correctly translated into code, including all constants and parameters. The Simpson method has order 4, that should give good results in the lower frequencies. For the higher frequencies you get into the territory of the sampling theorem.
– LutzL
Nov 12 at 16:07




First make sure that the formulas were correctly translated into code, including all constants and parameters. The Simpson method has order 4, that should give good results in the lower frequencies. For the higher frequencies you get into the territory of the sampling theorem.
– LutzL
Nov 12 at 16:07












I compared with simps and scipy.integrate.quad and I obtained two different integrations. You can see the complete code in (github.com/dayacaca/Python-prog/blob/integrals/RollepUP_spiral/… )
– PCat27
Nov 12 at 17:49





I compared with simps and scipy.integrate.quad and I obtained two different integrations. You can see the complete code in (github.com/dayacaca/Python-prog/blob/integrals/RollepUP_spiral/… )
– PCat27
Nov 12 at 17:49













I'm not really sure what I'm looking at. The distance computation computes points on the spiral from some related area inputs? Alternating in some way? Can you give a more geometric-physical description of what the model computes?
– LutzL
Nov 12 at 21:15




I'm not really sure what I'm looking at. The distance computation computes points on the spiral from some related area inputs? Alternating in some way? Can you give a more geometric-physical description of what the model computes?
– LutzL
Nov 12 at 21:15












Ok, found your post math.stackexchange.com/questions/2914813/… that explains the construction of the spiral. I think there may be an error in adding pi to the angle in the lower half.
– LutzL
Nov 12 at 21:39




Ok, found your post math.stackexchange.com/questions/2914813/… that explains the construction of the spiral. I think there may be an error in adding pi to the angle in the lower half.
– LutzL
Nov 12 at 21:39

















draft saved

draft discarded
















































Thanks for contributing an answer to Stack Overflow!


  • Please be sure to answer the question. Provide details and share your research!

But avoid


  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.

To learn more, see our tips on writing great answers.





Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


Please pay close attention to the following guidance:


  • Please be sure to answer the question. Provide details and share your research!

But avoid


  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.

To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstackoverflow.com%2fquestions%2f53256277%2fcompute-fourier-coefficients-with-python%23new-answer', 'question_page');

);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







Popular posts from this blog

Top Tejano songwriter Luis Silva dead of heart attack at 64

政党

天津地下鉄3号線