Multichannel (MISO) Wiener filter design

Started by April 9, 2008
Problem: Design one wiener filter that best matches a time snapshot of
data taken from multiple channels of equal interest, that is, the
domain of the signal is 2D, specifically <channel, time> with # of
time samples >> # channels. Think of a window in a grey scale 2D
image.

The Easter bunny tells me one approach is:

1.	Average the autocorrelation matrices for each channel
2.	Average the crosscorrelation vectors for each channel
3.	Solve for one Wiener filter

Anyone ever encounter this sort of thing?

Thanks in advance for your thoughts!

stuart403@gmail.com wrote:
> Problem: Design one wiener filter that best matches a time snapshot of > data taken from multiple channels of equal interest, that is, the > domain of the signal is 2D, specifically <channel, time> with # of > time samples >> # channels. Think of a window in a grey scale 2D > image.
What are you trying to accomplish? Be specific.
> The Easter bunny tells me one approach is: > > 1. Average the autocorrelation matrices for each channel > 2. Average the crosscorrelation vectors for each channel > 3. Solve for one Wiener filter
In what sense this filter is supposed to be optimal?
> Anyone ever encounter this sort of thing?
There is a generalization of the Wiener filter for the multiple dimensions. This problem is known to be prone to the ill behaviour. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
> What are you trying to accomplish? Be specific.
I would like to find a filter h(n) that best matches L channel signals xl(n) to one desired signal d(n) in the L2 sense. The channels are highly correlated (almost identical) but small phase shifts and random noise can occur in any one of the channel signals. Redundancy to eliminate noise basically.
> In what sense this filter is supposed to be optimal?
L2.
> There is a generalization of the Wiener filter for the multiple dimensions.
This problem is known to be prone to the ill behaviour. If you know of good papers/books containing this please let me know of them. With any luck the many-to-one design will not introduce spikes. Thanks Vladimir
On Apr 10, 9:26 am, stuart...@gmail.com wrote:
> Problem: Design one wiener filter that best matches a time snapshot of > data taken from multiple channels of equal interest, that is, the > domain of the signal is 2D, specifically <channel, time> with # of > time samples >> # channels. Think of a window in a grey scale 2D > image. > > The Easter bunny tells me one approach is: > > 1. Average the autocorrelation matrices for each channel > 2. Average the crosscorrelation vectors for each channel > 3. Solve for one Wiener filter > > Anyone ever encounter this sort of thing? > > Thanks in advance for your thoughts!
S. Doclo and M. Moonen, "GSVD-based optimal filtering for single and multimicrophone speech enhancement," Signal Processing, IEEE Transactions on [see also Acoustics, Speech, and Signal Processing, IEEE Transactions on], vol. 50, pp. 2230-2244, 2002. K.
On Apr 10, 9:26 am, stuart...@gmail.com wrote:
> Problem: Design one wiener filter that best matches a time snapshot of > data taken from multiple channels of equal interest, that is, the > domain of the signal is 2D, specifically <channel, time> with # of > time samples >> # channels. Think of a window in a grey scale 2D > image. > > The Easter bunny tells me one approach is: > > 1. Average the autocorrelation matrices for each channel > 2. Average the crosscorrelation vectors for each channel > 3. Solve for one Wiener filter > > Anyone ever encounter this sort of thing? > > Thanks in advance for your thoughts!
S. Doclo and M. Moonen, "GSVD-based optimal filtering for single and multimicrophone speech enhancement," Signal Processing, IEEE Transactions on [see also Acoustics, Speech, and Signal Processing, IEEE Transactions on], vol. 50, pp. 2230-2244, 2002. K.
> What are you trying to accomplish? Be specific.
I would like to find a filter h(n) that best matches L channel signals xl(n) to one desired signal d(n) in the L2 sense. The channels are highly correlated (almost identical) but small phase shifts and random noise can occur in any one of the channel signals. Redundancy to eliminate noise basically.
> In what sense this filter is supposed to be optimal?
L2.
> There is a generalization of the Wiener filter for the multiple dimensions.
This problem is known to be prone to the ill behaviour. If you know of good papers/books containing this please let me know of them. With any luck the many-to-one design will not introduce spikes. Thanks Vladimir

stuart403@gmail.com wrote:
> Problem: Design one wiener filter that best matches a time snapshot of > data taken from multiple channels of equal interest, that is, the > domain of the signal is 2D, specifically <channel, time> with # of > time samples >> # channels. Think of a window in a grey scale 2D > image.
What are you trying to accomplish? Be specific.
> The Easter bunny tells me one approach is: > > 1. Average the autocorrelation matrices for each channel > 2. Average the crosscorrelation vectors for each channel > 3. Solve for one Wiener filter
In what sense this filter is supposed to be optimal?
> Anyone ever encounter this sort of thing?
There is a generalization of the Wiener filter for the multiple dimensions. This problem is known to be prone to the ill behaviour. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Problem: Design one wiener filter that best matches a time snapshot of
data taken from multiple channels of equal interest, that is, the
domain of the signal is 2D, specifically <channel, time> with # of
time samples >> # channels. Think of a window in a grey scale 2D
image.

The Easter bunny tells me one approach is:

1.	Average the autocorrelation matrices for each channel
2.	Average the crosscorrelation vectors for each channel
3.	Solve for one Wiener filter

Anyone ever encounter this sort of thing?

Thanks in advance for your thoughts!