# 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?

```
```
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.

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.

```
```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.

```
```
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.

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?