ain't ya just proud of me? it's at http://dsp.stackexchange.com/questions/18316/cascaded-cross-correlation doesn't look like anyone is taking it up. would anyone here at comp.dsp be willing to look at it? it's about cross-correlation and using it to sorta measure the delay between one signal and another. i would like to know if that delay measure adds when the sorta delay elements (there's potentially filtering besides the delay) are cascaded. if someone can take a whack at it, i would appreciate it. i'll be whacking at it myself. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
so i have asked my very first question on the dsp stack exchange site...
Started by ●September 23, 2014
Reply by ●September 23, 20142014-09-23
On 9/23/2014 5:52 PM, robert bristow-johnson wrote:> > ain't ya just proud of me? > > it's at > > http://dsp.stackexchange.com/questions/18316/cascaded-cross-correlation > > > doesn't look like anyone is taking it up. would anyone here at comp.dsp > be willing to look at it? it's about cross-correlation and using it to > sorta measure the delay between one signal and another. i would like to > know if that delay measure adds when the sorta delay elements (there's > potentially filtering besides the delay) are cascaded. > > if someone can take a whack at it, i would appreciate it. i'll be > whacking at it myself. >Hi, Robert. I felt too lazy to try to prove your theorem, so instead I've found a simple counterexample. Consider the following rectangle-shaped functions: a = {0, 0, 1}; b = {0, 1, 0.75}; c = {0, 0.75, 1}; Which are defined in the following way. E.g., b = 0 for 0<t<Pi*2/3, b = 1 for Pi*2/3<t<Pi*4/3 and b = 0.75 for Pi*4/3<t<Pi*2. You see the idea. It's easy to work with such rectangle functions because the autocorrelation of an even rectangle function reaches its maximum at zero, so we can consider only shifts which are multiple integers of the rectangle width. So, what happens with our cross-correlation maximums? It's easy to see that they are reached at Tbc = 0 and Tac = 0, while Tab = -2/3*Pi. So Tac certainly doesn't equal Tab + Tbc. Evgeny.
Reply by ●September 23, 20142014-09-23
Reply by ●September 23, 20142014-09-23
Reply by ●September 24, 20142014-09-24
On 9/23/2014 9:52 AM, robert bristow-johnson wrote:> > ain't ya just proud of me? > > it's at > > http://dsp.stackexchange.com/questions/18316/cascaded-cross-correlation > > > doesn't look like anyone is taking it up. would anyone here at comp.dsp > be willing to look at it? it's about cross-correlation and using it to > sorta measure the delay between one signal and another. i would like to > know if that delay measure adds when the sorta delay elements (there's > potentially filtering besides the delay) are cascaded. > > if someone can take a whack at it, i would appreciate it. i'll be > whacking at it myself.Uh, are you asking people here to go there to answer your question? Why not ask it here? -- Rick
Reply by ●September 24, 20142014-09-24
Oops, I mixed up the value of the peak correlation with the position of the peak. I'll think about it some more. Here's a counter- example. Let the transfer function between X and Y be 1 + a1* Z^-k where a1 = 1.1. Let the transfer function between Y and Z be 1 - a2*Z^-k where a2 = 0.5. The peak correlation between X and Y will occur at a lag of K samples (because a1> 1). The peak correlation between Y and Z will occur at a lag of zero samples (because a2 < 1). The peak correlation between X and Z will occur at a lag of zero samples. That's because some cancellation of the delayed impulse at sample k took place, reducing its value to the point where it no longer dominates. Bob
Reply by ●September 24, 20142014-09-24
On 9/24/2014 3:06 PM, radams2000@gmail.com wrote:> Oops, I mixed up the value of the peak correlation with the position of the peak. I'll think about it some more. > > Here's a counter- example. > > Let the transfer function between X and Y be 1 + a1* Z^-k where a1 = 1.1. > > Let the transfer function between Y and Z be 1 - a2*Z^-k where a2 = 0.5. > > The peak correlation between X and Y will occur at a lag of K samples (because a1> 1). The peak correlation between Y and Z will occur at a lag of zero samples (because a2 < 1). The peak correlation between X and Z will occur at a lag of zero samples. That's because some cancellation of the delayed impulse at sample k took place, reducing its value to the point where it no longer dominates. > > Bob >It's a nice example. Should I trust my gut feeling that (strictly speaking) the above reasoning holds correct only in cases involving zero ISI? Evgeny.
Reply by ●September 24, 20142014-09-24
Have a free upvote on the grounds I dont like stackexchange and I have a peripheral interest in autocorrelation
Reply by ●September 24, 20142014-09-24
On 9/24/14 3:44 AM, rickman wrote:> On 9/23/2014 9:52 AM, robert bristow-johnson wrote: >> >> ain't ya just proud of me? >> >> it's at >> >> http://dsp.stackexchange.com/questions/18316/cascaded-cross-correlation >> >> >> doesn't look like anyone is taking it up. would anyone here at comp.dsp >> be willing to look at it? it's about cross-correlation and using it to >> sorta measure the delay between one signal and another. i would like to >> know if that delay measure adds when the sorta delay elements (there's >> potentially filtering besides the delay) are cascaded. >> >> if someone can take a whack at it, i would appreciate it. i'll be >> whacking at it myself. > > Uh, are you asking people here to go there to answer your question? Why > not ask it here? >i was thinking about that. i'll admit that i've grown tired of doing ASCII math. in a sense, i *am* asking here. it's why i posted this. just asking that you go to the link to see the expression of the question. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●September 24, 20142014-09-24
On 9/24/14 7:06 AM, radams2000@gmail.com wrote:> Oops, I mixed up the value of the peak correlation with the position of the peak. I'll think about it some more. > > Here's a counter- example. > > Let the transfer function between X and Y be 1 + a1* Z^-k where a1 = 1.1. > > Let the transfer function between Y and Z be 1 - a2*Z^-k where a2 = 0.5. > > The peak correlation between X and Y will occur at a lag of K samples (because a1> 1). The peak correlation between Y and Z will occur at a lag of zero samples (because a2< 1). The peak correlation between X and Z will occur at a lag of zero samples. That's because some cancellation of the delayed impulse at sample k took place, reducing its value to the point where it no longer dominates. >i have to confess, Bob, that i am not persuaded. i set up the question a bit more with the start of an answer (in two modes, one using the language of Hilbert Spaces and the other not). please take another look at the page, if you want. L8r, -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
