How can we determine phase information using Window Fourier Transform?

[hamidlukhnowi]

Hello Everyone,

Actually my question is related to Window Fourier transform (WFT). I have studied that with the help of WFT we can easily determine the phase of the image. Like by multiplying the window to only a specific part of the input and considering the outside part of the window equals to 0, we can find the phase information of the input and can reconstruct it. But still i don't clearly understand how this can be possible. like if i have an image of 256*256 and i will multiply it with 41*41 size window then how i can retrieve the information of the phase.

Thanks in advance
Regards

 

[rbj]

i know about windows and the Fourier Transform, but have never heard the term "Window Fourier Transform". the acronym WFT usually means the Winograd Fourier Transform.

applying a window that is shorter than the length your data does mean a loss of information. multiplying a number by zero means you lost forever the value of that number.

 

[hamidlukhnowi]

First Of all sir thanks for your reply.
By window Fourier transform,i meant Short term/time Fourier transform. And Window Fourier transform is mentioned by Kemao Qian in many of his publications.
Yeah my case is that i am applying a window whose size is smaller than the input data. Now i want to retrieve the phase information of the input image after the multiplication of the window tot eh input image.
I am using Gaussian Window function for this purpose.
Please guide me how i can do this.
Thanks

 

[PhilDSP]

Hi Hamidlukhnowi,

I have to echo rbj's observation that the term "Window Fourier Transform" is not a standard one and also that using ambiguous and redundant names such as that is essentially a source of confusion.

The Short Term Fourier Transform is basically the same thing as the Discrete Fourier Transform but where one has chosen an arbitrarily short data window. The STFT is applied continuously over the length of your data. The idea is to capture the dynamics of changes in frequency and phase in a closer way than a more typical DFT can.

In order for either a DFT or STFT to work properly the windowed data segments need to overlap and applying the correct overlap functions is critical.

 

[hamidlukhnowi]

Thanks PhilDSP for the reply.
Yeah sure next time i will take care about the name.
Actually i want to apply the window not to the whole input image, rather just on some part and then from that i want to retrieve the information of phase.
Let suppose my input is 128*128 and my window size is 41*41, now i want to apply this window only one time, my questions are how i will be sure that the are where i am applying widow will constitute major frequency elements or not? and also how to retrieve the phase information?

Waiting for a favorable response.
Thanks

 

[PhilDSP]

how i will be sure that the are where i am applying widow will constitute major frequency elements or not? and also how to retrieve the phase information?

You can't be sure. One thing is that as you shorten the length of the data window the resolution of the FT deteriorates. Another is that the lowest frequency you can resolve (that is not filtered into the DC bucket) increases. So you need some knowledge before hand about the constitution of the frequency components. (Run a single data window FFT on your entire data).

Information about determining the phase can be found here:

https://www.physicsforums.com/showthread.php?t=588679

 

[rbj]

why are you using the Gaussian window?

there are uses for it, but i am curious what your use is.

a decade ago, i did a paper for IEEE where i was trying to extract the frequency sweep rate of time-varying sinusoids and i used a gaussian for that.

http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=969581

i can send you a copy if you don't want to send IEEE money for it.

otherwise, i never used a gaussian window for anything.

BTW, the USENET newsgroup comp.dsp is the best place to bring questions like this. you can use DSPrelated.com or Google Groups.

 

[hamidlukhnowi]

@PhilDSP, thanks for the informative reply. As u mentioned "One thing is that as you shorten the length of the data window the resolution of the FT deteriorates". I am not shortening the length of the data window, i am just multiplying an outside window with my input data. the size of the data will be the same only the region of interest will be then computed to retrieve the phase. After studying some research work i found this algorithm works for recovering the phase "Gerchberg-Saxton (GS) algorithm". but it depends on the iteration which we have to done for retrieving the phase. Do you any other algorithm which doesn't depends on the iteration rather gives the result earlier?

 

[hamidlukhnowi]

@rbj...There is not any specific reason for using Gaussian window but in my case i found it easy to make and also my teacher wants to use this, but i am flexible to use any other if good reasons are there for using them.
Thanks for the offer of IEEE but i can access IEEE from my university domain.:)
but still i am confused how to do this..i am not getting any clear idea...actually my image input image is some how encrypted and i have to reconstruct the image with using STFT by retrieving the phase.