Weighted least square fr signal reconstruction
in [Matlab]
|
Prev: looking for help (I think its a basic MATLAB question)
Next: converting audio wav file into binary using matlab
From: Greg Heath on 6 Jul 2010 23:54 On Jun 1, 1:10 am, "kk KKsingh" <akikumar1...(a)gmail.com> wrote: > Hello Greg ! > > I have read few papers ! In which they construct the missing amplitudes by WEIGHTED LEAST SQUARES ! if you google "Reconstruction using least sqaure regularization", you will find plenty of papers ! > > Even on this website these people have solver written in Chttp://www-user..tu-chemnitz.de/~potts/nfft/guide3/doc/group__solver.html > > 1. They calculate DFT > 2. They apply weights > 3. They do reconstruction in frequency domain > > Is some thing like this is available in Matlab too ! I mean when we say least square regularization we mean reconstruction of amplitudes not a approximation which dftgh do I'm not sure to which version of dftgh you refer. For some time there is an option to use either the Fourier formula or a least squares formula. If you use the Fourier formula for the transform, the inverse transform is obtained using least squares and vice versa. It is not clear just what you mean by reconstruction and not an approximation. The best you can do is an interpolating approximation. Hope this helps. Greg
From: kk KKsingh on 7 Jul 2010 00:12 Greg Heath <heath(a)alumni.brown.edu> wrote in message <abd83995-d1f2-4b8a-bf55-ce9cb7ea7553(a)5g2000yqz.googlegroups.com>... > On Jun 1, 1:10 am, "kk KKsingh" <akikumar1...(a)gmail.com> wrote: > > Hello Greg ! > > > > I have read few papers ! In which they construct the missing amplitudes by WEIGHTED LEAST SQUARES ! if you google "Reconstruction using least sqaure regularization", you will find plenty of papers ! > > > > Even on this website these people have solver written in Chttp://www-user.tu-chemnitz.de/~potts/nfft/guide3/doc/group__solver.html > > > > 1. They calculate DFT > > 2. They apply weights > > 3. They do reconstruction in frequency domain > > > > Is some thing like this is available in Matlab too ! I mean when we say least square regularization we mean reconstruction of amplitudes not a approximation which dftgh do > > I'm not sure to which version of dftgh you refer. > For some time there is an option to use either > the Fourier formula or a least squares formula. > > If you use the Fourier formula for the transform, > the inverse transform is obtained using least squares > and vice versa. > > It is not clear just what you mean by reconstruction > and not an approximation. The best you can do is an > interpolating approximation. > > Hope this helps. > > Greg Hi Greg! This is how things work, as far as i know start wiith uniform original signal 1. Take a decimated sample 2. Apply dftgh you will get a approximate spectra 3. Now Make the system Over determine 4. Apply least square on the spectra 5. Zero pad the spectrum so that you have same number of samples as original signal 6. Ifft it 7. Here is your uniform signal Thanks Kumar
From: Greg Heath on 7 Jul 2010 21:50 On Jul 7, 12:12 am, "kk KKsingh" <akikumar1...(a)gmail.com> wrote: > Greg Heath <he...(a)alumni.brown.edu> wrote in message <abd83995-d1f2-4b8a-bf55-ce9cb7ea7...(a)5g2000yqz.googlegroups.com>... > > On Jun 1, 1:10 am, "kk KKsingh" <akikumar1...(a)gmail.com> wrote: > > > Hello Greg ! > > > > I have read few papers ! In which they construct the missing amplitudes by WEIGHTED LEAST SQUARES ! if you google "Reconstruction using least sqaure regularization", you will find plenty of papers ! > > > > Even on this website these people have solver written in Chttp://www-user.tu-chemnitz.de/~potts/nfft/guide3/doc/group__solver.html > > > > 1. They calculate DFT > > > 2. They apply weights > > > 3. They do reconstruction in frequency domain > > > > Is some thing like this is available in Matlab too ! I mean when we say least square regularization we mean reconstruction of amplitudes not a approximation which dftgh do > > > I'm not sure to which version of dftgh you refer. > > For some time there is an option to use either > > the Fourier formula or a least squares formula. > > > If you use the Fourier formula for the transform, > > the inverse transform is obtained using least squares > > and vice versa. > > > It is not clear just what you mean by reconstruction > > and not an approximation. The best you can do is an > > interpolating approximation. > > > Hope this helps. > > > Greg > > Hi Greg! > > This is how things work, as far as i know > start wiith uniform original signal You mean uniformly spaced? How many points: N0 = ? > 1. Take a decimated sample Randomly remove ~10% of the points? Nr = ceil(N0/10) > 2. Apply dftgh you will get a approximate spectra Which option: Fourier Spectra or LS Spectra? Uniformly spaced? How many points; M = ? > 3. Now Make the system Over determine What does that mean: M > N = N0-Nr? > 4. Apply least square on the spectra Meaning you obtained the spectrum using the Fourier formula. > 5. Zero pad the spectrum so that you > have same number of samples as original signal Doen't make sense. M > N0-Nr to begin with but you can make M as large as you want. There is no need to zero pad. > 6. Ifft it > > 7. Here is your uniform signal I don't think so. How about code for an example? Greg.
From: kk KKsingh on 7 Jul 2010 22:19 Greg Heath <heath(a)alumni.brown.edu> wrote in message <83be9349-ae7a-4c2b-807d-8b2bceb420fb(a)j8g2000yqd.googlegroups.com>... > On Jul 7, 12:12 am, "kk KKsingh" <akikumar1...(a)gmail.com> wrote: > > Greg Heath <he...(a)alumni.brown.edu> wrote in message <abd83995-d1f2-4b8a-bf55-ce9cb7ea7...(a)5g2000yqz.googlegroups.com>... > > > On Jun 1, 1:10 am, "kk KKsingh" <akikumar1...(a)gmail.com> wrote: > > > > Hello Greg ! > > > > > > I have read few papers ! In which they construct the missing amplitudes by WEIGHTED LEAST SQUARES ! if you google "Reconstruction using least sqaure regularization", you will find plenty of papers ! > > > > > > Even on this website these people have solver written in Chttp://www-user.tu-chemnitz.de/~potts/nfft/guide3/doc/group__solver.html > > > > > > 1. They calculate DFT > > > > 2. They apply weights > > > > 3. They do reconstruction in frequency domain > > > > > > Is some thing like this is available in Matlab too ! I mean when we say least square regularization we mean reconstruction of amplitudes not a approximation which dftgh do > > > > > I'm not sure to which version of dftgh you refer. > > > For some time there is an option to use either > > > the Fourier formula or a least squares formula. > > > > > If you use the Fourier formula for the transform, > > > the inverse transform is obtained using least squares > > > and vice versa. > > > > > It is not clear just what you mean by reconstruction > > > and not an approximation. The best you can do is an > > > interpolating approximation. > > > > > Hope this helps. > > > > > Greg > > > > Hi Greg! > > > > This is how things work, as far as i know > > start wiith uniform original signal > > You mean uniformly spaced? > How many points: N0 = ? > > > 1. Take a decimated sample > > Randomly remove ~10% of the points? > Nr = ceil(N0/10) > > > 2. Apply dftgh you will get a approximate spectra > > Which option: Fourier Spectra or LS Spectra? > > Uniformly spaced? > How many points; M = ? > > > 3. Now Make the system Over determine > > What does that mean: M > N = N0-Nr? > > > 4. Apply least square on the spectra > > Meaning you obtained the spectrum using > the Fourier formula. > > > 5. Zero pad the spectrum so that you > > have same number of samples as original signal > > Doen't make sense. M > N0-Nr to begin with > but you can make M as large as you want. > There is no need to zero pad. > > > 6. Ifft it > > > > 7. Here is your uniform signal > > I don't think so. > > How about code for an example? > > Greg. I just uploaded a small tutorial in file exchange ! Will let you know the moment it will appear :) Thanks
From: kk KKsingh on 8 Jul 2010 02:32
Greg Heath <heath(a)alumni.brown.edu> wrote in message <83be9349-ae7a-4c2b-807d-8b2bceb420fb(a)j8g2000yqd.googlegroups.com>... > On Jul 7, 12:12 am, "kk KKsingh" <akikumar1...(a)gmail.com> wrote: > > Greg Heath <he...(a)alumni.brown.edu> wrote in message <abd83995-d1f2-4b8a-bf55-ce9cb7ea7...(a)5g2000yqz.googlegroups.com>... > > > On Jun 1, 1:10 am, "kk KKsingh" <akikumar1...(a)gmail.com> wrote: > > > > Hello Greg ! > > > > > > I have read few papers ! In which they construct the missing amplitudes by WEIGHTED LEAST SQUARES ! if you google "Reconstruction using least sqaure regularization", you will find plenty of papers ! > > > > > > Even on this website these people have solver written in Chttp://www-user.tu-chemnitz.de/~potts/nfft/guide3/doc/group__solver.html > > > > > > 1. They calculate DFT > > > > 2. They apply weights > > > > 3. They do reconstruction in frequency domain > > > > > > Is some thing like this is available in Matlab too ! I mean when we say least square regularization we mean reconstruction of amplitudes not a approximation which dftgh do > > > > > I'm not sure to which version of dftgh you refer. > > > For some time there is an option to use either > > > the Fourier formula or a least squares formula. > > > > > If you use the Fourier formula for the transform, > > > the inverse transform is obtained using least squares > > > and vice versa. > > > > > It is not clear just what you mean by reconstruction > > > and not an approximation. The best you can do is an > > > interpolating approximation. > > > > > Hope this helps. > > > > > Greg > > > > Hi Greg! > > > > This is how things work, as far as i know > > start wiith uniform original signal > > You mean uniformly spaced? > How many points: N0 = ? > > > 1. Take a decimated sample > > Randomly remove ~10% of the points? > Nr = ceil(N0/10) > > > 2. Apply dftgh you will get a approximate spectra > > Which option: Fourier Spectra or LS Spectra? > > Uniformly spaced? > How many points; M = ? > > > 3. Now Make the system Over determine > > What does that mean: M > N = N0-Nr? > > > 4. Apply least square on the spectra > > Meaning you obtained the spectrum using > the Fourier formula. > > > 5. Zero pad the spectrum so that you > > have same number of samples as original signal > > Doen't make sense. M > N0-Nr to begin with > but you can make M as large as you want. > There is no need to zero pad. > > > 6. Ifft it > > > > 7. Here is your uniform signal > > I don't think so. > > How about code for an example? > > Greg. For a time being Greg Dont you think http://docs.google.com/fileview?id=0B9lyGDKrglBfYjIzMWVlY2YtMGJhOS00N2QwLWE0Y2MtMGQwOWIyMmY5ODMy&hl=en&authkey=CKe5h7YM This is same thing, Thats what i was talking from the long back :) Kumar |