FPGA Central

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

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 lot

From 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

"lucy" <[email protected]> wrote in message news:<coe1m5$r4q$[email protected]>...
> 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

I 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

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" <[email protected]> wrote in message news:<coe1m5$r4q$[email protected]>...
> 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