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FFT axis scaling- linear to angular spacing
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Katy Pointer
Nov 25, 2011, 11:33:08 AM11/25/11
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Dear All,
I am having trouble with axis scaling for FFTs.
I know that for an FFT from time to frequency if t=time interval, Fs=1/t =sampling interval and N=number of samples then the frequency spacing is f=Fs/N =1/N*t or w=2*pi/N*t (for angular frequency).
I have data which I have measured (an antenna radiation pattern) in sphereical coordinates i.e. azimuth and elevation and have IFFT-ed the data back to linear space (to image the aperture) i.e. x and y coordinates. My question is what should the linear spacing of my IFFT-ed data be? Should I include the factor or 2*pi, should I use angular spacing in degrees of radians?
I haven't been able to work this out and have been stuck of a while, so help would be greatly appriciated.
Thanks,
Katy
I am having trouble with axis scaling for FFTs.
I know that for an FFT from time to frequency if t=time interval, Fs=1/t =sampling interval and N=number of samples then the frequency spacing is f=Fs/N =1/N*t or w=2*pi/N*t (for angular frequency).
I have data which I have measured (an antenna radiation pattern) in sphereical coordinates i.e. azimuth and elevation and have IFFT-ed the data back to linear space (to image the aperture) i.e. x and y coordinates. My question is what should the linear spacing of my IFFT-ed data be? Should I include the factor or 2*pi, should I use angular spacing in degrees of radians?
I haven't been able to work this out and have been stuck of a while, so help would be greatly appriciated.
Thanks,
Katy
Rune Allnor
Nov 25, 2011, 11:37:30 AM11/25/11
to
If so, you need to work throuh the theory.
The wavenumber k is related to the angle
of arrival theta along the lines of
k ~ sin(theta),
the details depending on the geometry
of the antenna.
Rune
Matt J
Nov 25, 2011, 11:52:08 AM11/25/11
to
"Katy Pointer" wrote in message <jaog04$2pv$1...@newscl01ah.mathworks.com>...
Some minor corrections here. First, Fs would be your sampling frequency, not your sampling interval. Second, if f=Fs/N then f=1/N/t and w=2*pi/N/t
>My question is what should the linear spacing of my IFFT-ed data be? Should I include the factor or 2*pi, should I use angular spacing in degrees of radians?
==============
Do not use the factor of 2*pi. MATLAB's fft/ifft assume frequency to be expressed in Hz, as you can verify by reading DOC FFT.
So, your time spacing will be t=1/N/f
> I have data which I have measured (an antenna radiation pattern) in sphereical coordinates i.e. azimuth and elevation and have IFFT-ed the data back to linear space (to image the aperture) i.e. x and y coordinates.
===============
I have no idea how an IFFT could turn spherical samples into cartesian ones, but then again I have no background in antenna design.
> Dear All,
>
> I am having trouble with axis scaling for FFTs.
>
> I know that for an FFT from time to frequency if t=time interval, Fs=1/t =sampling interval and N=number of samples then the frequency spacing is f=Fs/N =1/N*t or w=2*pi/N*t (for angular frequency).
===============
>
> I am having trouble with axis scaling for FFTs.
>
> I know that for an FFT from time to frequency if t=time interval, Fs=1/t =sampling interval and N=number of samples then the frequency spacing is f=Fs/N =1/N*t or w=2*pi/N*t (for angular frequency).
Some minor corrections here. First, Fs would be your sampling frequency, not your sampling interval. Second, if f=Fs/N then f=1/N/t and w=2*pi/N/t
>My question is what should the linear spacing of my IFFT-ed data be? Should I include the factor or 2*pi, should I use angular spacing in degrees of radians?
Do not use the factor of 2*pi. MATLAB's fft/ifft assume frequency to be expressed in Hz, as you can verify by reading DOC FFT.
So, your time spacing will be t=1/N/f
> I have data which I have measured (an antenna radiation pattern) in sphereical coordinates i.e. azimuth and elevation and have IFFT-ed the data back to linear space (to image the aperture) i.e. x and y coordinates.
I have no idea how an IFFT could turn spherical samples into cartesian ones, but then again I have no background in antenna design.
Katy Pointer
Nov 25, 2011, 11:52:08 AM11/25/11
to
Rune Allnor <all...@tele.ntnu.no> wrote in message <0566351c-fc41-4f53...@w7g2000yqc.googlegroups.com>...
Not sure if this is 'beamforming'. I'm basically measuring the raditation pattern of an antenna in the far-field and then IFFT-ing the data to get an image of the aperture. It is related to diffraction theory, but I have worked through that theory and have got nowhere :(.
Rune Allnor
Nov 25, 2011, 12:01:29 PM11/25/11
to
On 25 Nov, 17:52, "Katy Pointer" <kellis_...@hotmail.co.uk> wrote:
> Rune Allnor <all...@tele.ntnu.no> wrote in message <0566351c-fc41-4f53-be93-2f1b77b10...@w7g2000yqc.googlegroups.com>...
> It is related to diffraction theory, but I have worked through that theory and have got nowhere :(.
Then you need to work through it again, either in
greater detail or from a different... eh... angle.
Rune
> Rune Allnor <all...@tele.ntnu.no> wrote in message <0566351c-fc41-4f53-be93-2f1b77b10...@w7g2000yqc.googlegroups.com>...
> > On 25 Nov, 17:33, "Katy Pointer" <kellis_...@hotmail.co.uk> wrote:
> > > Dear All,
>
> > > I am having trouble with axis scaling for FFTs.
>
> > > I know that for an FFT from time to frequency if t=time interval, Fs=1/t =sampling interval and N=number of samples then the frequency spacing is f=Fs/N =1/N*t or w=2*pi/N*t (for angular frequency).
>
> > > I have data which I have measured (an antenna radiation pattern) in sphereical coordinates i.e. azimuth and elevation and have IFFT-ed the data back to linear space (to image the aperture) i.e. x and y coordinates. My question is what should the linear spacing of my IFFT-ed data be? Should I include the factor or 2*pi, should I use angular spacing in degrees of radians?
> > > I haven't been able to work this out and have been stuck of a while, so help would be greatly appriciated.
>
> > Is this beamforming?
>
> > If so, you need to work throuh the theory.
> > The wavenumber k is related to the angle
> > of arrival theta along the lines of
>
> > k ~ sin(theta),
>
> > the details depending on the geometry
> > of the antenna.
>
> > Rune
>
> Not sure if this is 'beamforming'. I'm basically measuring the raditation pattern of an antenna in the far-field and then IFFT-ing the data to get an image of the aperture.
That's beamforming.
> > > Dear All,
>
> > > I am having trouble with axis scaling for FFTs.
>
> > > I know that for an FFT from time to frequency if t=time interval, Fs=1/t =sampling interval and N=number of samples then the frequency spacing is f=Fs/N =1/N*t or w=2*pi/N*t (for angular frequency).
>
> > > I have data which I have measured (an antenna radiation pattern) in sphereical coordinates i.e. azimuth and elevation and have IFFT-ed the data back to linear space (to image the aperture) i.e. x and y coordinates. My question is what should the linear spacing of my IFFT-ed data be? Should I include the factor or 2*pi, should I use angular spacing in degrees of radians?
> > > I haven't been able to work this out and have been stuck of a while, so help would be greatly appriciated.
>
> > Is this beamforming?
>
> > If so, you need to work throuh the theory.
> > The wavenumber k is related to the angle
> > of arrival theta along the lines of
>
> > k ~ sin(theta),
>
> > the details depending on the geometry
> > of the antenna.
>
> > Rune
>
> Not sure if this is 'beamforming'. I'm basically measuring the raditation pattern of an antenna in the far-field and then IFFT-ing the data to get an image of the aperture.
> It is related to diffraction theory, but I have worked through that theory and have got nowhere :(.
greater detail or from a different... eh... angle.
Rune
Katy Pointer
Nov 25, 2011, 1:37:08 PM11/25/11
to
Rune Allnor <all...@tele.ntnu.no> wrote in message <6e99d038-2ac6-4561...@h42g2000yqd.googlegroups.com>...
In which case, as you said, I'm obviously approacing it from the wrong "angle". Do you have a suggestion of any books or papers I could read that might be able to help me?
Katy
Katy
Rune Allnor
Nov 25, 2011, 2:15:35 PM11/25/11
to
On 25 Nov, 19:37, "Katy Pointer" <kellis_...@hotmail.co.uk> wrote:
> Rune Allnor <all...@tele.ntnu.no> wrote in message <6e99d038-2ac6-4561-a771-3f7c1f387...@h42g2000yqd.googlegroups.com>...
You have described your problem somewhat too
coarsly with respect to exactly what you are
up to, to give very specific advice.
Google for terms like "beamforming", "radon transform",
"Fourier-Bessel transform", "direction of arrival", and
see what fits your task best.
Rune
> Rune Allnor <all...@tele.ntnu.no> wrote in message <6e99d038-2ac6-4561-a771-3f7c1f387...@h42g2000yqd.googlegroups.com>...
coarsly with respect to exactly what you are
up to, to give very specific advice.
Google for terms like "beamforming", "radon transform",
"Fourier-Bessel transform", "direction of arrival", and
see what fits your task best.
Rune
Honglei Chen
Nov 25, 2011, 11:28:56 PM11/25/11
to
"Katy Pointer" <kelli...@hotmail.co.uk> wrote in message
news:jaog04$2pv$1...@newscl01ah.mathworks.com...
Are you trying to derive the signal that excite each element in a uniform
linear array from the measured pattern? If so, the frequency increment in
FFT corresponds to d*sin(theta)/lambda where d is the element spacing, theta
is the angle from the normal and lambda is the wavelength. However, for a
linear array, you really just need azimuth angle to obtain this information
so I'm not sure why you also need elevation information.
HTH
Honglei
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