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Thread Subject:
Least Squares

Subject: Least Squares

From: kk KKsingh

Date: 4 Mar, 2010 06:36:05

Message: 1 of 4

Suppose i have signal and i am missing some samples, then i can apply dft on it and get the spectrum but now i want to reconstuct it back can some one show me the least square technique for doing this

Subject: Least Squares

From: Bruno Luong

Date: 4 Mar, 2010 07:21:02

Message: 2 of 4

"kk KKsingh" <akikumar1983@gmail.com> wrote in message <hmnkcl$kju$1@fred.mathworks.com>...
> Suppose i have signal and i am missing some samples, then i can apply dft on it and get the spectrum but now i want to reconstuct it back can some one show me the least square technique for doing this

You do you apply dft on missing data? If you call FFT on the array of valid data then your result is invalid.

Bruno

Subject: Least Squares

From: Bruno Luong

Date: 4 Mar, 2010 07:23:05

Message: 3 of 4

"kk KKsingh" <akikumar1983@gmail.com> wrote in message <hmnkcl$kju$1@fred.mathworks.com>...
> Suppose i have signal and i am missing some samples, then i can apply dft on it and get the spectrum but now i want to reconstuct it back can some one show me the least square technique for doing this

And BTW, least-squares in time and Fourier's domain are identical according to Parseval's theorem.

Bruno

Subject: Least Squares

From: kk KKsingh

Date: 4 Mar, 2010 10:11:21

Message: 4 of 4

I am applying the NDFT actually..Non uniform Discrete Fourier transform which will give me approximate spectrum........so i need to reconstruct the data in Fourier domain..I am trying to reproduce a paper result. Also my weights are distance between the samples........NDFT will look some thing like


X(f) = sum(k=1,N){ deltat *x(k) * exp(-2*pi/max(t)-min(t)*j*t(k)*m }

deltat=t(n+1)-t(n-1)/2
t(0)=(t(N)-Period))
t(1)=(t(1)+Period))

So now i ahve approximate spectrum i want to construct the data in Fourier domain now by least square then apply IFFT and get a regular signal.....again deltat is more like weight which i can even apply after calculating the DFT term ( with sample actual location)
kk



"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <hmnn4p$ah6$1@fred.mathworks.com>...
> "kk KKsingh" <akikumar1983@gmail.com> wrote in message <hmnkcl$kju$1@fred.mathworks.com>...
> > Suppose i have signal and i am missing some samples, then i can apply dft on it and get the spectrum but now i want to reconstuct it back can some one show me the least square technique for doing this
>
> And BTW, least-squares in time and Fourier's domain are identical according to Parseval's theorem.
>
> Bruno

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