Question about multiple linear regression model in adaptive filer

Hi,
On "Adaptive filter theory" by Simon Haykin, it gave the multiple
linear regression model as:

d(n) = A^H Um(n)+v(n)

A and U are vectors.

I don't understand the reason for this model why it put noise v(n)
just before the desired signal d(n). For normal FIR filtering, the
noise is just before the filter input. This multiple linear regression
model is not the same for the  filter practice. Furthmore, after the
introduction of this model, it applied it to the Wiener filtering,
which is not consider the noise component before the introduction of
multiple linear regression model.

I think the abstract model may be different from the practice, but it
should not be diverse far away fundamentally. In the digital
communication system simulation, noise is always added at the filter
input. Can you explain it to me? Thanks in advance

On 28 Jun, 17:44, fl <rxjw...@gmail.com> wrote:
> Hi,
> On "Adaptive filter theory" by Simon Haykin, it gave the multiple
> linear regression model as:
>
> d(n) = A^H Um(n)+v(n)
>
> A and U are vectors.
>
> I don't understand the reason for this model why it put noise v(n)
> just before the desired signal d(n). For normal FIR filtering, the
> noise is just before the filter input. This multiple linear regression
> model is not the same for the &#4294967295;filter practice.

That's because you are dealing with and *adaptive* filter.
One needs a random component internal to the filter in
order to get it to adapt to changes in the input.

Rune

On 28 Jun, 18:16, Rune Allnor <all...@tele.ntnu.no> wrote:
> On 28 Jun, 17:44, fl <rxjw...@gmail.com> wrote:
>
> > Hi,
> > On "Adaptive filter theory" by Simon Haykin, it gave the multiple
> > linear regression model as:
>
> > d(n) = A^H Um(n)+v(n)
>
> > A and U are vectors.
>
> > I don't understand the reason for this model why it put noise v(n)
> > just before the desired signal d(n). For normal FIR filtering, the
> > noise is just before the filter input. This multiple linear regression
> > model is not the same for the &#4294967295;filter practice.
>
> That's because you are dealing with and *adaptive* filter.
> One needs a random component internal to the filter in
> order to get it to adapt to changes in the input.

I was a bit absent-minded yesterday. The above is true for
the Kalman filter. In your case, the noise term v(n) might
also be an adaption error.

Rune