Hi everyone, I know this is a pretty classic problem, however I couldn't find any useful links or introductions into solving this problem. I basically have two simple signals which have low correlation mostly, however given certain conditions will maintain high levels of correlation. Is there an optimal way to detect those periods of high correlation? I can use a sliding window approach, but that seems somewhat naive. I am looking at using DFT, but I'm unclear exactly on what the alg for that would look like or how much in the way of processing that will save me. Any pointers, links, suggestions would be very much appreciated. Cheers, Kate.

# Finding windows of high correlation?

Started by ●February 21, 2007

Reply by ●February 21, 20072007-02-21

On Feb 21, 5:01 am, ksheph...@gmail.com wrote:> Hi everyone, > > I know this is a pretty classic problem, however I couldn't find any > useful links or introductions into solving this problem. > > I basically have two simple signals which have low correlation mostly, > however given certain conditions will maintain high levels of > correlation. Is there an optimal way to detect those periods of high > correlation? I can use a sliding window approach, but that seems > somewhat naive. I am looking at using DFT, but I'm unclear exactly > on what the alg for that would look like or how much in the way of > processing that will save me. > > Any pointers, links, suggestions would be very much appreciated. > > Cheers, > > Kate.As you thought, you could convolve the signals together to determine where their maximum cross-correlation is at a maximum. This is the exact operation performed by matched filters in communications systems. As always, you can use an FFT-based fast convolution approach to speed the process up. Try this link: http://www.dspguide.com/ch18/1.htm Jason

Reply by ●February 21, 20072007-02-21

On Feb 21, 4:01 am, ksheph...@gmail.com wrote:> Hi everyone, > > I know this is a pretty classic problem, however I couldn't find any > useful links or introductions into solving this problem. > > I basically have two simple signals which have low correlation mostly, > however given certain conditions will maintain high levels of > correlation.I think it will help significantly if you re-state the above more precisely. What do you mean that your signals are "simple"? And what are these "certain conditions" that will maintain high levels of correlation? Is it because the signal levels change? Are you correlating an incoming stream with a template signal? Julius

Reply by ●February 22, 20072007-02-22

On Feb 21, 7:15 am, "julius" <juli...@gmail.com> wrote:> On Feb 21, 4:01 am, ksheph...@gmail.com wrote: > > > Hi everyone, > > > I know this is a pretty classic problem, however I couldn't find any > > useful links or introductions into solving this problem. > > > I basically have two simple signals which have low correlation mostly, > > however given certain conditions will maintain high levels of > > correlation. > > I think it will help significantly if you re-state > the above more precisely. > > What do you mean that your signals are "simple"? > > And what are these "certain conditions" that will > maintain high levels of correlation? Is it because > the signal levels change? > > Are you correlating an incoming stream with a > template signal? > > JuliusCertainly, they are two seperate audio signals. I'm not sure what the conditions are just yet, however I am hoping to determine them by locating periods of high correlation between the two signals. Thanks for you the link to DSP guide, it was pure gold. Cheers, Kate.

Reply by ●February 22, 20072007-02-22

kshephard@gmail.com wrote: ...> Certainly, they are two seperate audio signals. I'm not sure what > the conditions are just yet, however I am hoping to determine them by > locating periods of high correlation between the two signals.... Correlation involves extended time.* How far separated might your "periods of high correlation" be? Jerry ______________________________________ The great pianist Vladimir Horowitz held the non-mystical view that the sound of a piano is determined by the velocity and timing of the hammers and dampers on the strings, nothing more. He said, "There is such a thing as pianistic touch, but it can't be demonstrated with one note." -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Reply by ●February 22, 20072007-02-22

On 21 Feb, 11:01, ksheph...@gmail.com wrote:> Hi everyone, > > I know this is a pretty classic problem, however I couldn't find any > useful links or introductions into solving this problem. > > I basically have two simple signals which have low correlation mostly, > however given certain conditions will maintain high levels of > correlation. Is there an optimal way to detect those periods of high > correlation? I can use a sliding window approach, but that seems > somewhat naive. I am looking at using DFT, but I'm unclear exactly > on what the alg for that would look like or how much in the way of > processing that will save me. > > Any pointers, links, suggestions would be very much appreciated.It is a bit unclear exactly what you want to measure. Do you expect the high correlaon to occur with reative time shifts between the data, or does it suffice to monitor the zero-lag correlation coefficient? If you can get away with monitoring the zero-lag coefficient, you can do it very efficiently as follows: --- Initialization 1) Decide on a window length N 2) Compute the zero-lag correlation coefficient for the N first samples in the two data streams 3) Store the current coefficient as r0(0) --- Loop for n = 1 to ... do 4) Subtract the contribution from the two earliest data points x(n-1)*conj(y(n-1)), from r0(n-1) 5) Add the contribution from the next data points, x(n+N)*conj(y(n +N)), to the correlation and store the result as r0(n) end and that's about it. Rune