Signal Reconstruction
in [Matlab]
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From: kk KKsingh on 4 Mar 2010 16:13 Even i can get the Fourier domain spectrum by Taylor approximation.....after that i need to work on it...........question is how "kk KKsingh" <akikumar1983(a)gmail.com> wrote in message <hmo4d1$7pi$1(a)fred.mathworks.com>... > Sir, > > My question is a general one not with the author of the file. > > KK > > > Rune Allnor <allnor(a)tele.ntnu.no> wrote in message <4058b34d-2feb-46b6-b992-0ce110a65b8f(a)y17g2000yqd.googlegroups.com>... > > On 4 Mar, 11:24, "kk KKsingh" <akikumar1...(a)gmail.com> wrote: > > > But the files likehttp://www.mathworks.com/matlabcentral/fileexchange/25135-nufft-nfft-... > > > > > > calculates the approximate fourier spectrum now key to come back in the time domain is to do least sqaure reconstruction of this spectrum and get the corrected spectra and finally...fft and we r back in time domain on regular grid > > > > > > For example purpose i can take dft for irregular samples which will give us approximate spectrum.........the files above can just replace the dft but that is not a issue ! issue is how to get the regular grid time domain signal back from dft spectrum > > > > If you have questions about files you found on the file > > exchange, ask the authors of those fles. > > > > Rune
From: Greg Heath on 5 Mar 2010 05:09 On Mar 4, 3:43 am, "kk KKsingh" <akikumar1...(a)gmail.com> wrote: > Is there any code available which i can study ! where signal is reconstructed in frequency domain using Least sqaure...Like one of file submisson was Fast gridding method.....they calculate the frequency domain spectrum or i should say that they calculated A^(H)WY (which is dft with weights) now i want to apply least square on this ..fr reconstruction so that i can apply ifft and get back my signal.. If ( x , t and f are column vectors) (1) W = exp( -2*pi*j * f * t' ) (2) X = W * ( x .* dts ) where dts is a weighted modification of diff(t), then x should be reconstructed using (3) x = ( W \ X ) ./ dts instead of the more familiar (4) x = W' * ( X .* dfs ) On the other hand, if you assume that (4) is valid, the spectrum should be obtained from (5) X = ( W \ x ) ./ dfs instead of (2). To minimize confusion, define XFT and XLS using (2) and (5), respectively. Hope this helps. Greg
From: Greg Heath on 5 Mar 2010 05:41 On Mar 5, 5:09 am, Greg Heath <he...(a)alumni.brown.edu> wrote: > On Mar 4, 3:43 am, "kk KKsingh" <akikumar1...(a)gmail.com> wrote: > > > Is there any code available which i can study ! where signal is reconstructed in frequency domain using Least sqaure...Like one of file submisson was Fast gridding method.....they calculate the frequency domain spectrum or i should say that they calculated A^(H)WY (which is dft with weights) now i want to apply least square on this ..fr reconstruction so that i can apply ifft and get back my signal.. > > If ( x , t and f are column vectors) > > (1) W = exp( -2*pi*j * f * t' ) > > (2) X = W * ( x .* dts ) > > where dts is a weighted modification of diff(t), > then x should be reconstructed using > > (3) x = ( W \ X ) ./ dts > > instead of the more familiar > > (4) x = W' * ( X .* dfs ) > > On the other hand, if you assume > that (4) is valid, the spectrum should > be obtained from > > (5) X = ( W \ x ) ./ dfs > > instead of (2). > > To minimize confusion, define XFT and > XLS using (2) and (5), respectively. Now if X is defined on a uniform grid using (5), you should be able to interpolate x on a uniform grid, t2, using W2 = exp( -2*pi*j * f * t2' ) x2 = W2' * ( XLS .* dfs ) When length(t2) = N = length(f) x2 = C(Fs,N) * ifft( XLS ) where C is a constant that depends on Fs and N (I'm too sleepy to figure it out now ... Good Night!) Hope this helps. Greg
From: kk KKsingh on 13 Mar 2010 01:29 Hey greg! Its not a signal reconstruction, its the same grid on which we are getting a signal Greg Heath <heath(a)alumni.brown.edu> wrote in message <d257682b-ea25-4528-a907-71f9672ce4c3(a)z35g2000yqd.googlegroups.com>... > On Mar 5, 5:09 am, Greg Heath <he...(a)alumni.brown.edu> wrote: > > On Mar 4, 3:43 am, "kk KKsingh" <akikumar1...(a)gmail.com> wrote: > > > > > Is there any code available which i can study ! where signal is reconstructed in frequency domain using Least sqaure...Like one of file submisson was Fast gridding method.....they calculate the frequency domain spectrum or i should say that they calculated A^(H)WY (which is dft with weights) now i want to apply least square on this ..fr reconstruction so that i can apply ifft and get back my signal.. > > > > If ( x , t and f are column vectors) > > > > (1) W = exp( -2*pi*j * f * t' ) > > > > (2) X = W * ( x .* dts ) > > > > where dts is a weighted modification of diff(t), > > then x should be reconstructed using > > > > (3) x = ( W \ X ) ./ dts > > > > instead of the more familiar > > > > (4) x = W' * ( X .* dfs ) > > > > On the other hand, if you assume > > that (4) is valid, the spectrum should > > be obtained from > > > > (5) X = ( W \ x ) ./ dfs > > > > instead of (2). > > > > To minimize confusion, define XFT and > > XLS using (2) and (5), respectively. > > Now if X is defined on a uniform grid using > (5), you should be able to interpolate x on a > uniform grid, t2, using > > W2 = exp( -2*pi*j * f * t2' ) > > x2 = W2' * ( XLS .* dfs ) > > When > > length(t2) = N = length(f) > > x2 = C(Fs,N) * ifft( XLS ) > > where C is a constant that depends on Fs and N > > (I'm too sleepy to figure it out now ... Good Night!) > > Hope this helps. > > Greg
From: Greg Heath on 13 Mar 2010 01:44 On Mar 13, 1:29 am, "kk KKsingh" <akikumar1...(a)gmail.com> wrote: > Heygreg! Its not a signal reconstruction, its the same grid on which we are getting a signal ] Reconstruction means to construct again. Therefore, I have no idea what you mean. Please explain. and PLEASE DO NOT TOP.POST. It is very annoying to have to scroll down to make sense of what is said above. Greg
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