Cross-Correlation and Phase Difference

[dynaman]

Hi guys

I'm trying to implement a phase shift meter in VB.NET between 2 audio signals. I'm using Math.NET cross-correlation functions however they can't calculate the phase shift or lag between the 2 signals as far as I can tell. Can anyone recommend a .NET DSP library that can calculate phase shift using FFT cross-correlation methods?

thanks

DM

 

[GregLocock]

Are you just looking for the phase part of the transfer function? if so then just use arg(Syy/Syx) where S is the cross or auto spectrum.

Of course matters could be vastly clarified if you included a link to math.net.

Cheers

Greg Locock


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[dynaman]

https://numerics.mathdotnet.com/api/MathNet.Numerics.Statistics/Correlation.htm

 

[GregLocock]

You are using the stats package, you'll probably have more luck here

https://numerics.mathdotnet.com/api/MathNet.Numerics.IntegralTransforms/Fourier.htm

It's a pretty horrific website, I can't be bothered to dig through it.

Cheers

Greg Locock


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[dynaman]

Yeah, it's a bit frustrating. I couldn't find anything specific to cross-correlation in that library. From what I understand, this process can be used;

[ul]
[li]take the FFT of both signals[/li]
[li]multiply one with conjugate of the other (element-wise multiplication)[/li]
[li]do the inverse FFT[/li]
[li]get max value as a correlation coefficient and its index as the delay(signal lag)[/li]
[/ul]

I just wish there was a library that had a "find phase difference" function.

thanks

DM

 

[GregLocock]

I don't understand your process.

The formula is, where F is the complex fourier transform,is phase((Fx.*Fy)./(Fy.*Fy)) where dot indicates element by element. Perhaps easier for you is that the phase of the transfer function is phase(Fx.*Fy).-phase(Fy.*Fy), which simplifies back to phase(Fx).-phase(Fy). Note that the delay is a function of frequency and is meaningless where there is little signal. The coherence is a useful measure of phase stability.

Cheers

Greg Locock


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[dynaman]

Hi Greg

Can I please clarify by what you mean when the delay is meaningless where there is little signal? Is there are a better process for measuring phase difference when the signals are small and somewhat noisy?

regards

DM

 

[GregLocock]

Adding noise to one or both channels adds a random phase to the signal. So the phase delay gets very messy.

https://en.wikipedia.org/wiki/Coherence_(signal_processing)

Cheers

Greg Locock


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[dynaman]

Yeah. Is there a way to get accurate phase difference measurements then?

 

[GregLocock]

Lots of averages. Typically I'd use 32 for real life data, but 512 would not be unusual.

Cheers

Greg Locock


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[dynaman]

Hi Greg

I currently use

http://www.mitov.com/products/signallab#components

to perform many DSP functions. There are components in this library that allow FFT operations however, I'm still not clear how to extract the phase difference between 2 audio signals as discussed above?

cheers

DM

 

[GregLocock]

SLCarttopolar(SLDividecomplex(SLFourier(signal1),SLFourier(signal2))) should give you the complex spectrum of the transfer function in (mag,phase) format, or you could try one of the other formulations i gave above. there are others, with various deep and meaningful differences, but that's where I'd start.



Cheers

Greg Locock


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[dynaman]

Thanks, Greg,

I appreciate the guidance. Will let you know how it goes.

cheers

DM

 

[dynaman]

Hi Greg

Just implemented the complex spectrum of the transfer function and plotted phase vs frequency. It seems to work OK if the two signals are sine waves. However one is a sine wave and the other is a square wave (i.e. pulse of 5% duty cycle). It seems to give noisy readings that seem to jump around for this configuration even after averaging results.

Sorry, a bit confused about implementing the method.

regards

DM

 

[GregLocock]

There's no information at any frequency other than the frequency of the sine wave so you are essentially dividing by zero.

Cheers

Greg Locock


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[dynaman]

So I tried simulating my results using Multi-Instrument Pro (

https://www.virtins.com/multi-instrument.shtml)

I can generate essentially the same results for the Phase Spectrum. However, Multi-Instrument has a great Cross-Correlation function which calculates the delay between Signal 1 & Signal 2 even with noise present. I'm not sure how they created that function?

 

[dynaman]

Well I was able to replicate Multi-Instrument Pro's function by applying the method as originally stated;

[ul]
[li]take the FFT of both signals[/li]
[li]multiply one with conjugate of the other (element-wise multiplication)[/li]
[li]do the inverse FFT[/li]
[/ul]

Plotting the Inverse FFT result vs time Delay produces the same result. I think I'm on the home stretch now.