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From: Antony on 26 Jul 2010 00:18
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
From: TideMan on 26 Jul 2010 00:34
On Jul 26, 4:18 pm, "Antony " <mutang.b...(a)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?
From: Greg Heath on 26 Jul 2010 06:18
On Jul 26, 12:18 am, "Antony " <mutang.b...(a)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

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