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# multiple coherence function

## multiple coherence function

(OP)
The multiple coherence function can be defined by:

These values are FRF auto/cross powers in my context. Multiple coherence means there are multiple inputs. For 2 inputs the dimensions of Pxy is 2x1, Pxx is 2x2, Pyy is 1x1. I'm expecting the plot to be mostly 1 with dips at the FRF anti-resonances.

Should this also be between 0 and 1? Are the values (Px, Pxx, Pyy) the averaged values?

Thanks,

### RE: multiple coherence function

Usually it's called partial coherence if you are looking for references.

I'm very rusty on this, but yes, the total of the partial coherences should be 1 at each frequency in the absence of noise and non linearities. Px etc are your ensemble averages.

Cheers

Greg Locock

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### RE: multiple coherence function

(OP)
Right, you can calculate the coherence between any input and any output and if there is more than one input then that would partial. For the multiple coherence, it is the coherence between one output and all of it's inputs.

Also, does the coherence necessarily need to be real? I'm not sure what a complex coherence would mean...

### RE: multiple coherence function

In a single coherence the coherence at a frequency works out to the (squared?) ratio of the sum of the individual magnitudes in the ensemble to magnitude of the vector sum of those contributions. As such it is always real.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

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