Compute fourier coefficients with Python?
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. 
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
asked Nov 12 '18 at 5:15
PCat27PCat27
185
add a comment |
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. 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
asked Nov 12 '18 at 5:15
PCat27PCat27
185
Well, scipy.integrate has a bunch of options to choose from.
– mikuszefski
Nov 12 '18 at 6:45
Concerning your error, always provide the full trace back.
– mikuszefski
Nov 12 '18 at 6:46
And please change your code, such that it is actually running.
– mikuszefski
Nov 12 '18 at 6:49
Discretize the integral, see the discretized integral as part of a discretized cosine transform or a discretized Fourier transform, apply thefftandifftmethods.
– LutzL
Nov 12 '18 at 8:54
add a comment |
1
1
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. 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
asked Nov 12 '18 at 5:15
PCat27PCat27
185
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. 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
python fft numerical-methods numerical-integration dft
asked Nov 12 '18 at 5:15
PCat27PCat27
185
asked Nov 12 '18 at 5:15
PCat27PCat27
185
edited Nov 13 '18 at 18:33
PCat27
asked Nov 12 '18 at 5:15
PCat27PCat27
185
asked Nov 12 '18 at 5:15
PCat27PCat27
185
asked Nov 12 '18 at 5:15
PCat27PCat27
185
185
Well, scipy.integrate has a bunch of options to choose from.
– mikuszefski
Nov 12 '18 at 6:45
Concerning your error, always provide the full trace back.
– mikuszefski
Nov 12 '18 at 6:46
And please change your code, such that it is actually running.
– mikuszefski
Nov 12 '18 at 6:49
Discretize the integral, see the discretized integral as part of a discretized cosine transform or a discretized Fourier transform, apply thefftandifftmethods.
– LutzL
Nov 12 '18 at 8:54
add a comment |
Well, scipy.integrate has a bunch of options to choose from.
– mikuszefski
Nov 12 '18 at 6:45
Concerning your error, always provide the full trace back.
– mikuszefski
Nov 12 '18 at 6:46
And please change your code, such that it is actually running.
– mikuszefski
Nov 12 '18 at 6:49
Discretize the integral, see the discretized integral as part of a discretized cosine transform or a discretized Fourier transform, apply thefftandifftmethods.
– LutzL
Nov 12 '18 at 8:54
Well, scipy.integrate has a bunch of options to choose from.
– mikuszefski
Nov 12 '18 at 6:45
Well, scipy.integrate has a bunch of options to choose from.
– mikuszefski
Nov 12 '18 at 6:45
Concerning your error, always provide the full trace back.
– mikuszefski
Nov 12 '18 at 6:46
Concerning your error, always provide the full trace back.
– mikuszefski
Nov 12 '18 at 6:46
And please change your code, such that it is actually running.
– mikuszefski
Nov 12 '18 at 6:49
And please change your code, such that it is actually running.
– mikuszefski
Nov 12 '18 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 '18 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 '18 at 8:54
add a comment |
1 Answer
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active
oldest
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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.
answered Nov 12 '18 at 9:04
LutzLLutzL
14.1k21426
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 '18 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 '18 at 16:07
I compared withsimpsandscipy.integrate.quadand I obtained two different integrations. You can see the complete code in (github.com/dayacaca/Python-prog/blob/integrals/RollepUP_spiral/… )
– PCat27
Nov 12 '18 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 '18 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 '18 at 21:39
|
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
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oldest
votes
2
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.
answered Nov 12 '18 at 9:04
LutzLLutzL
14.1k21426
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 '18 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 '18 at 16:07
I compared withsimpsandscipy.integrate.quadand I obtained two different integrations. You can see the complete code in (github.com/dayacaca/Python-prog/blob/integrals/RollepUP_spiral/… )
– PCat27
Nov 12 '18 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 '18 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 '18 at 21:39
|
show 1 more comment
2
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.
answered Nov 12 '18 at 9:04
LutzLLutzL
14.1k21426
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 '18 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 '18 at 16:07
I compared withsimpsandscipy.integrate.quadand I obtained two different integrations. You can see the complete code in (github.com/dayacaca/Python-prog/blob/integrals/RollepUP_spiral/… )
– PCat27
Nov 12 '18 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 '18 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 '18 at 21:39
|
show 1 more comment
2
2
2
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.
answered Nov 12 '18 at 9:04
LutzLLutzL
14.1k21426
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.
answered Nov 12 '18 at 9:04
LutzLLutzL
14.1k21426
answered Nov 12 '18 at 9:04
LutzLLutzL
14.1k21426
answered Nov 12 '18 at 9:04
LutzLLutzL
14.1k21426
answered Nov 12 '18 at 9:04
LutzLLutzL
14.1k21426
14.1k21426
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 '18 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 '18 at 16:07
I compared withsimpsandscipy.integrate.quadand I obtained two different integrations. You can see the complete code in (github.com/dayacaca/Python-prog/blob/integrals/RollepUP_spiral/… )
– PCat27
Nov 12 '18 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 '18 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 '18 at 21:39
|
show 1 more comment
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 '18 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 '18 at 16:07
I compared withsimpsandscipy.integrate.quadand I obtained two different integrations. You can see the complete code in (github.com/dayacaca/Python-prog/blob/integrals/RollepUP_spiral/… )
– PCat27
Nov 12 '18 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 '18 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 '18 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 '18 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 '18 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 '18 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 '18 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 '18 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 '18 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 '18 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 '18 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 '18 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 '18 at 21:39
|
show 1 more comment
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Well, scipy.integrate has a bunch of options to choose from.
– mikuszefski
Nov 12 '18 at 6:45
Concerning your error, always provide the full trace back.
– mikuszefski
Nov 12 '18 at 6:46
And please change your code, such that it is actually running.
– mikuszefski
Nov 12 '18 at 6:49
Discretize the integral, see the discretized integral as part of a discretized cosine transform or a discretized Fourier transform, apply the
fftandifftmethods.– LutzL
Nov 12 '18 at 8:54