Hi all, I heard tht white noise can be used to do system identification: finding the impulse response of an LTI system: generate a white noise x(t), and then input it to a system h(t), measure the output y(t), then find the R_yx(t), this is in fact the system impulse response h(t)... I understand this by showing it mathematically, yet I want to know what do people do in reality? How do they find autocorrelation between x(t) and y(t)? Do they do some estimation? Do they just take measured samples and find Power spectral density first then reversely find autocorrelation? Thanks a lot
In reality, how do people measure autocorrelation function?
Started by ●November 28, 2004
Reply by ●November 29, 20042004-11-29
lucy wrote:> Hi all, > > I heard tht white noise can be used to do system identification: finding the > impulse response of an LTI system: generate a white noise x(t), and then > input it to a system h(t), measure the output y(t), then find the R_yx(t), > this is in fact the system impulse response h(t)... > > I understand this by showing it mathematically, yet I want to know what do > people do in reality? How do they find autocorrelation between x(t) and > y(t)? Do they do some estimation? Do they just take measured samples and > find Power spectral density first then reversely find autocorrelation? > > Thanks a lotFrom within my digital audio workstation I time reverse the x(t) sequence and convolve it with the y(t) because those two functions are readily at hand. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein
Reply by ●November 29, 20042004-11-29
"lucy" <losemind@yahoo.com> wrote in message news:<coe1m5$r4q$1@news.Stanford.EDU>...> Hi all, > > I heard tht white noise can be used to do system identification: finding the > impulse response of an LTI system: generate a white noise x(t), and then > input it to a system h(t), measure the output y(t), then find the R_yx(t), > this is in fact the system impulse response h(t)... > > I understand this by showing it mathematically, yet I want to know what do > people do in reality? How do they find autocorrelation between x(t) and > y(t)? Do they do some estimation? Do they just take measured samples and > find Power spectral density first then reversely find autocorrelation? > > Thanks a lotI think detailed answers to such questions depend to a large extent on the constraints and particular considerations for each application. For some general aspects of practical data processing, check out the books by Bendat and Piersol; in particular Bendat & Piersol: Random Data, 3rd. ed., Wiley, 2000. Rune
Reply by ●November 29, 20042004-11-29
In reality, if the input to the system is also available, one could easily identify a system by using an adaptive filter in the identification mode and one could decorrelate the output samples without even knowing the filter under consideration by using an adaptive filter in the deconvolution mode. But if only the output samples are available, you need to go for spectral estimation techniques. amar "lucy" <losemind@yahoo.com> wrote in message news:<coe1m5$r4q$1@news.Stanford.EDU>...> Hi all, > > I heard tht white noise can be used to do system identification: finding the > impulse response of an LTI system: generate a white noise x(t), and then > input it to a system h(t), measure the output y(t), then find the R_yx(t), > this is in fact the system impulse response h(t)... > > I understand this by showing it mathematically, yet I want to know what do > people do in reality? How do they find autocorrelation between x(t) and > y(t)? Do they do some estimation? Do they just take measured samples and > find Power spectral density first then reversely find autocorrelation? > > Thanks a lot