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Thread Subject:
Question of Fourier Transoform of a transposed matrix? Thanks a lot.

Subject: Question of Fourier Transoform of a transposed matrix? Thanks a lot.

From: Antony

Date: 26 Jul, 2010 04:18:04

Message: 1 of 4

Dear all, I wonder when the following Fourier Transform of a transposed matrix is valid:
  (F(a))* = F(a')
where F is the Fourier transformation, a is a matrix, * means the complex conjugate and ' means the transpose.

  I search online for the property of Fourier transformation, but get no answer. The article says that 'a' is diagonalized when convolving, but I don't understand these words very much. Could you please help me clarify the principle of this equation? When does this equation is valid? Or where to find the explanations on this stuff? Thanks very much.

Antony

Subject: Question of Fourier Transoform of a transposed matrix? Thanks a

From: TideMan

Date: 26 Jul, 2010 04:34:05

Message: 2 of 4

On Jul 26, 4:18 pm, "Antony " <mutang.b...@gmail.com> wrote:
> Dear all, I wonder when the following Fourier Transform of a transposed matrix is valid:
>   (F(a))* = F(a')
> where F is the Fourier transformation, a is a matrix, * means the complex conjugate and ' means the transpose.
>
>   I search online for the property of Fourier transformation, but get no answer. The article says that 'a' is diagonalized when convolving, but I don't understand these words very much. Could you please help me clarify the principle of this equation? When does this equation is valid? Or where to find the explanations on this stuff? Thanks very much.
>
> Antony

And the Matlab question is?

Subject: Question of Fourier Transoform of a transposed matrix? Thanks a

From: Greg Heath

Date: 26 Jul, 2010 10:18:16

Message: 3 of 4

On Jul 26, 12:18 am, "Antony " <mutang.b...@gmail.com> wrote:
> Dear all, I wonder when the following Fourier Transform of a transposed matrix is valid:
>   (F(a))* = F(a')
> where F is the Fourier transformation, a is a matrix, * means the complex conjugate and ' means the transpose.

In MATLAB

1. fft(a) transforms the columns of a
2. * means scalar or matrix multiplication
3. conj(a) is the complex conjugate
4. transpose(a) or a.' is the transpose
3. a' is the complex conjugate transpose

Experiment with

a = rand(2,3)+i*rand(2,3)

See wikipedia for Fourier transform properties

Hope this helps.

Greg

Subject: Question of Fourier Transoform of a transposed matrix? Thanks a

From: Antony

Date: 27 Jul, 2010 03:51:04

Message: 4 of 4

Greg Heath <heath@alumni.brown.edu> wrote in message <6d745488-d2d1-49c8-b869-f6048ed86580@s9g2000yqd.googlegroups.com>...
> On Jul 26, 12:18 am, "Antony " <mutang.b...@gmail.com> wrote:
> > Dear all, I wonder when the following Fourier Transform of a transposed matrix is valid:
> >   (F(a))* = F(a')
> > where F is the Fourier transformation, a is a matrix, * means the complex conjugate and ' means the transpose.
>
> In MATLAB
>
> 1. fft(a) transforms the columns of a
> 2. * means scalar or matrix multiplication
> 3. conj(a) is the complex conjugate
> 4. transpose(a) or a.' is the transpose
> 3. a' is the complex conjugate transpose
>
> Experiment with
>
> a = rand(2,3)+i*rand(2,3)
>
> See wikipedia for Fourier transform properties
>
> Hope this helps.
>
> Greg

Thank you, guys in this board. The problem has been partially solved now through verification in MATLAB. So thanks a lot to MATLAB, *-*.

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