How to sample a transfer function (angular spectrum) in the frequency domain?
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I am having this problem in Fourier optics, where I am using the Angular spectrum method (a lti filter) to calculate the electric field at the required plane given the distance p and the electric field of another parallel plane.
Essentially I have to implement the following equation for light propagation given in the continuous time domain as a convolution.
i_required(x,y) = i_given(x,y)*hp(x,y)
Now, my doubt is when computing this using discrete Fourier transforms.
Note the Angular spectrum function is defined only in frequency domain Hp(fx,fy). For ease of explanation sampling of i_given(x, y) is done at 1 unit in each dimension.
The steps I am doing:
- Take DFT2 (Discrete fourier transform along rows and columns) of
given samples ofi_given(x, y)and let it beI(u, v)foru,v = 1:N
- Sample the frequency domain of the transfer function
Hp(fx, fy)
atfx = u/N,fy = v/N - Multiply
H(u,v)I(u,v))and take the IDFT2
What is the consequence of sampling in frequency domain (Step 2)?
Will this cause aliasing in time-domain? Ways to mitigate effects if any?
fft sampling dft time-frequency
asked Nov 26 '18 at 19:20
024oloy96024oloy96
11
add a comment |
I am having this problem in Fourier optics, where I am using the Angular spectrum method (a lti filter) to calculate the electric field at the required plane given the distance p and the electric field of another parallel plane.
Essentially I have to implement the following equation for light propagation given in the continuous time domain as a convolution.
i_required(x,y) = i_given(x,y)*hp(x,y)
Now, my doubt is when computing this using discrete Fourier transforms.
Note the Angular spectrum function is defined only in frequency domain Hp(fx,fy). For ease of explanation sampling of i_given(x, y) is done at 1 unit in each dimension.
The steps I am doing:
- Take DFT2 (Discrete fourier transform along rows and columns) of
given samples ofi_given(x, y)and let it beI(u, v)foru,v = 1:N
- Sample the frequency domain of the transfer function
Hp(fx, fy)
atfx = u/N,fy = v/N - Multiply
H(u,v)I(u,v))and take the IDFT2
What is the consequence of sampling in frequency domain (Step 2)?
Will this cause aliasing in time-domain? Ways to mitigate effects if any?
fft sampling dft time-frequency
asked Nov 26 '18 at 19:20
024oloy96024oloy96
11
add a comment |
I am having this problem in Fourier optics, where I am using the Angular spectrum method (a lti filter) to calculate the electric field at the required plane given the distance p and the electric field of another parallel plane.
Essentially I have to implement the following equation for light propagation given in the continuous time domain as a convolution.
i_required(x,y) = i_given(x,y)*hp(x,y)
Now, my doubt is when computing this using discrete Fourier transforms.
Note the Angular spectrum function is defined only in frequency domain Hp(fx,fy). For ease of explanation sampling of i_given(x, y) is done at 1 unit in each dimension.
The steps I am doing:
- Take DFT2 (Discrete fourier transform along rows and columns) of
given samples ofi_given(x, y)and let it beI(u, v)foru,v = 1:N
- Sample the frequency domain of the transfer function
Hp(fx, fy)
atfx = u/N,fy = v/N - Multiply
H(u,v)I(u,v))and take the IDFT2
What is the consequence of sampling in frequency domain (Step 2)?
Will this cause aliasing in time-domain? Ways to mitigate effects if any?
fft sampling dft time-frequency
asked Nov 26 '18 at 19:20
024oloy96024oloy96
11
I am having this problem in Fourier optics, where I am using the Angular spectrum method (a lti filter) to calculate the electric field at the required plane given the distance p and the electric field of another parallel plane.
Essentially I have to implement the following equation for light propagation given in the continuous time domain as a convolution.
i_required(x,y) = i_given(x,y)*hp(x,y)
Now, my doubt is when computing this using discrete Fourier transforms.
Note the Angular spectrum function is defined only in frequency domain Hp(fx,fy). For ease of explanation sampling of i_given(x, y) is done at 1 unit in each dimension.
The steps I am doing:
- Take DFT2 (Discrete fourier transform along rows and columns) of
given samples ofi_given(x, y)and let it beI(u, v)foru,v = 1:N
- Sample the frequency domain of the transfer function
Hp(fx, fy)
atfx = u/N,fy = v/N - Multiply
H(u,v)I(u,v))and take the IDFT2
What is the consequence of sampling in frequency domain (Step 2)?
Will this cause aliasing in time-domain? Ways to mitigate effects if any?
fft sampling dft time-frequency
fft sampling dft time-frequency
asked Nov 26 '18 at 19:20
024oloy96024oloy96
11
asked Nov 26 '18 at 19:20
024oloy96024oloy96
11
edited Nov 26 '18 at 19:52
024oloy96
asked Nov 26 '18 at 19:20
024oloy96024oloy96
11
asked Nov 26 '18 at 19:20
024oloy96024oloy96
11
asked Nov 26 '18 at 19:20
024oloy96024oloy96
11
11
add a comment |
add a comment |
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