From: Rune Allnor on
On 23 Feb, 17:59, "kk KKsingh" <akikumar1...(a)gmail.com> wrote:
> Can you give me your comments on the below :)

OK, you are close enough; I won't mess around anymore.
The key is the term Wnk. In the regularly sampled case,
the implicit assumption is that both n and k are integers.
For the irregular case, relax that assumption such that
n and/or k might be any real number.

Next, express the irregular Fourier transform in terms of
a matrix W, where W(i,j) = Wnk = exp(sqrt(-1)*2*pi*f(i)*k(j))
or something like that.

So the crux is to come up with the W matrix that expresses
the transform, which might be irregular in both time and
frequency. The key is Manolakis & Proakis (4th ed., 2007)
equations 7.1.21/7.1.22 where n and k are *not* integers.
In that case you will be able to express the irregularly
sampled FT as a matrix-vector product similar to equation
7.1.26, where you need to modify the matrix W as given
for the regular case in eq 7.1.25.

Rune
From: kk KKsingh on

Thank you sir

Rune Allnor <allnor(a)tele.ntnu.no> wrote in message <2818cbed-68d0-40a3-971d-75b23d2e483e(a)y26g2000vbb.googlegroups.com>...
> On 23 Feb, 17:59, "kk KKsingh" <akikumar1...(a)gmail.com> wrote:
> > Can you give me your comments on the below :)
>
> OK, you are close enough; I won't mess around anymore.
> The key is the term Wnk. In the regularly sampled case,
> the implicit assumption is that both n and k are integers.
> For the irregular case, relax that assumption such that
> n and/or k might be any real number.
>
> Next, express the irregular Fourier transform in terms of
> a matrix W, where W(i,j) = Wnk = exp(sqrt(-1)*2*pi*f(i)*k(j))
> or something like that.
>
> So the crux is to come up with the W matrix that expresses
> the transform, which might be irregular in both time and
> frequency. The key is Manolakis & Proakis (4th ed., 2007)
> equations 7.1.21/7.1.22 where n and k are *not* integers.
> In that case you will be able to express the irregularly
> sampled FT as a matrix-vector product similar to equation
> 7.1.26, where you need to modify the matrix W as given
> for the regular case in eq 7.1.25.
>
> Rune
From: kk KKsingh on
Rune Allnor <allnor(a)tele.ntnu.no> wrote in message <2818cbed-68d0-40a3-971d-75b23d2e483e(a)y26g2000vbb.googlegroups.com>...
> On 23 Feb, 17:59, "kk KKsingh" <akikumar1...(a)gmail.com> wrote:
> > Can you give me your comments on the below :)
>
> OK, you are close enough; I won't mess around anymore.
> The key is the term Wnk. In the regularly sampled case,
> the implicit assumption is that both n and k are integers.
> For the irregular case, relax that assumption such that
> n and/or k might be any real number.
>
> Next, express the irregular Fourier transform in terms of
> a matrix W, where W(i,j) = Wnk = exp(sqrt(-1)*2*pi*f(i)*k(j))
> or something like that.
>
> So the crux is to come up with the W matrix that expresses
> the transform, which might be irregular in both time and
> frequency. The key is Manolakis & Proakis (4th ed., 2007)
> equations 7.1.21/7.1.22 where n and k are *not* integers.
> In that case you will be able to express the irregularly
> sampled FT as a matrix-vector product similar to equation
> 7.1.26, where you need to modify the matrix W as given
> for the regular case in eq 7.1.25.
>
> Rune

you mean some thing like this
if N=500
M=1001 (frequency domain points)

f=(-M/2):(M/2-1); freq axis
for i=1:length(N);
for j=1:length(M);
Wnk = exp(sqrt(-1)*2*pi*t2(i)*f(j))
end
end


so Fourier matrix will be irregular matrix , am i right sir