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DFT\MDFT Filter Bank + Proccessing

Started by JacobG September 20, 2011
Greetings,

I am dealing with the task of channelizing an input signal to M different
channels (for instance 32 channels), so the different channels may be
processed and synthesized back together.
The prototype filter should bring a 40db stop band attenuation.

I starting by simulating a uniform dft filter bank, where the input signal
is commutated into the prototype filter polyphase filters, and the outputs
of the M polyphase filters are inputs to an FFT. For synthesis, the
opposite structure is used.

The problem with DFT filter banks is that they don't cancel aliasing from
the different channels, so the prototype filter should be planned for the
problem using non linear optimization. 
The optimizations i found on the internet, plan a 4*M length prototype
which is too long for my needs.

Another type of filter bank is the Modified DFT filter bank, which has a
efficient implementation, and prototype filters can be planned for perfect
reconstruction.
The problem is that when i simulate the output of the FFT of the analysis
filter bank, the outputs don't respond solely for different channels,
and if I process the outputs (for instance i delete a specific channel),
i get a noisy output signal.

My question is if there is a way to use MDFT in such a way that i can
process the channels individually (perhaps i have mistakes in my
simulation?) ?
Do you know of any good prototype filters for the case of 16 or 32 or 64
channels for the Uniform MDFT case.
Any advice will help.

Jacob


On 9/20/2011 9:09 AM, JacobG wrote:
> Greetings, > > I am dealing with the task of channelizing an input signal to M different > channels (for instance 32 channels), so the different channels may be > processed and synthesized back together. > The prototype filter should bring a 40db stop band attenuation. > > I starting by simulating a uniform dft filter bank, where the input signal > is commutated into the prototype filter polyphase filters, and the outputs > of the M polyphase filters are inputs to an FFT. For synthesis, the > opposite structure is used. > > The problem with DFT filter banks is that they don't cancel aliasing from > the different channels, so the prototype filter should be planned for the > problem using non linear optimization. > The optimizations i found on the internet, plan a 4*M length prototype > which is too long for my needs. > > Another type of filter bank is the Modified DFT filter bank, which has a > efficient implementation, and prototype filters can be planned for perfect > reconstruction. > The problem is that when i simulate the output of the FFT of the analysis > filter bank, the outputs don't respond solely for different channels, > and if I process the outputs (for instance i delete a specific channel), > i get a noisy output signal. > > My question is if there is a way to use MDFT in such a way that i can > process the channels individually (perhaps i have mistakes in my > simulation?) ? > Do you know of any good prototype filters for the case of 16 or 32 or 64 > channels for the Uniform MDFT case. > Any advice will help.
Why FFT? It seems that you want to send 1 high-speed data stream over several lower-speed channels. Why not simply MUX, then DEMUX at the other end? Jerry -- Engineering is the art of making what you want from things you can get.
I think the problem is that there is no perfect filter. I can't split a
signal perfectly into channels. There will always be some aliasing.

The aliasing then cancels, when recombining. 
For example, consider a raised-cosine filter on a symbol stream. I can't
implement a perfect lowpass at the cutoff frequency, so technical
applications leave some ~20 % excess bandwidth. 
When downsampling back to the original rate, the excess bandwidth folds
back into the fundamental bandwidth and the "alias" restores the original
signal. 

I suspect what you're trying is to filter with an ideal bandpass (that is,
equivalent to the raised cosine filter with zero rolloff). This won't work
with a finite length filter.
>I think the problem is that there is no perfect filter. I can't split a >signal perfectly into channels. There will always be some aliasing. > >The aliasing then cancels, when recombining. >For example, consider a raised-cosine filter on a symbol stream. I can't >implement a perfect lowpass at the cutoff frequency, so technical >applications leave some ~20 % excess bandwidth. >When downsampling back to the original rate, the excess bandwidth folds >back into the fundamental bandwidth and the "alias" restores the original >signal. > >I suspect what you're trying is to filter with an ideal bandpass (that
is,
>equivalent to the raised cosine filter with zero rolloff). This won't
work
>with a finite length filter. >
Hi, Did you refer to the "scrambled" outputs of the MDFT channels? In the Uniform DFT filter banks there is aliasing, but it can be minimized by planning the prototype LPF filter coefficients, so the aliasing from different channels will cancel each other- using for example this- http://www.ece.mcgill.ca/~bchamp/papers/Jounal/SigPro2009a.pdf . Using the Modified DFT technique, if I use a "good" filter, should the outputs of the FFT correspond to individual channels (even though there will always be some aliasing from different channel sidelobs and neighbouring channels transition-bands)? Jacob
>Why FFT? It seems that you want to send 1 high-speed data stream over >several lower-speed channels. Why not simply MUX, then DEMUX at the >other end? > >Jerry >-- >Engineering is the art of making what you want from things you can get. >
Hi, I want to split 1 high-speed data stream containing multiple frequencies , into lower speed channels that will seperate those frequencies. The FFT is used for modulating a prototype LPF, so it will realize frequency shifts of it for bandpass filtering. It's explained great here- http://www.signumconcepts.com/download/paper035.pdf thanks for the reply, Jacob
>Hi, >I want to split 1 high-speed data stream containing multiple frequencies
,
>into lower speed channels that will seperate those frequencies. > >The FFT is used for modulating a prototype LPF, so it will realize >frequency shifts of it for bandpass filtering. It's explained great here- >http://www.signumconcepts.com/download/paper035.pdf
Try oversamled filter bank. For example simulink models http://electronix.ru/forum/index.php?s=&showtopic=23652&view=findpost&p=929325 http://electronix.ru/forum/index.php?showtopic=23652&st=15&p=513268&#entry513268
>Try oversamled filter bank. >For example simulink models >http://electronix.ru/forum/index.php?s=&showtopic=23652&view=findpost&p=929325 > >http://electronix.ru/forum/index.php?showtopic=23652&st=15&p=513268&#entry513268 >
Many thanks Alexander, I will try it.