what did they mean by this definition of the filter?

[Sergey Efremov <svefremov@xxxxxxxxx>]

» [b,a]=besself(1,0.1)

b =

         0    0.1000


a =

    1.0000    0.1000

» help filter

 FILTER One-dimensional digital filter.
    Y = FILTER(B,A,X) filters the data in vector X
with the
    filter described by vectors A and B to create the
filtered
    data Y.  The filter is a "Direct Form II
Transposed"
    implementation of the standard difference
equation:
 
    a(1)*y(n) = b(1)*x(n) + b(2)*x(n-1) + ... +
b(nb+1)*x(n-nb)
                          - a(2)*y(n-1) - ... -
a(na+1)*y(n-na)
 
    If a(1) is not equal to 1, FILTER normalizes the
filter
    coefficients by a(1). 
 
    When X is a matrix, FILTER operates on the columns
of X.  When X
    is an N-D array, FILTER operates along the first
non-singleton
    dimension.
 
    [Y,Zf] = FILTER(B,A,X,Zi) gives access to initial
and final
    conditions, Zi and Zf, of the delays.  Zi is a
vector of length
    MAX(LENGTH(A),LENGTH(B))-1 or an array of such
vectors, one for
    each column of X.
 
    FILTER(B,A,X,[],DIM) or FILTER(B,A,X,Zi,DIM)
operates along the
    dimension DIM.
 
    See also FILTER2, FILTFILT (in the Signal
Processing Toolbox).
=========================================================================

does anyone understand what is wrong with this
description of the filter?

If I substitute coefficients for Bessel filter of 1-st
order with cut-off Wn=0.1 of Nyquist frequency
I get

y=0.1*x[1]-0.1*y[1];

This obviously would not converge to the y...

Sergey Efremov

--- omega-digest-request@xxxxxxxxxx wrote:


> ATTACHMENT part 1 message/rfc822 
> 
> omega-digest Digest				Volume 2004 : Issue 180
> 
> Today's Topics:
>   Re: More Fun With Filters             [ Sergey
> Efremov <svefremov@xxxxxxxxx ]
> 

> ATTACHMENT part 2 message/rfc822 
> Date: Wed, 7 Jul 2004 18:22:44 -0700
> From: Sergey Efremov <svefremov@xxxxxxxxx>
> To: omega-list@xxxxxxxxxx
> Subject: Re: More Fun With Filters
> 
> 3-D ORDER Bessel filter coefficients. 
> 
> A3 andf A4 can not be fit by power or polynomials as
> functions of the cut-off frequency.
> 
> Sergey
> 

> ATTACHMENT part 2.2 image/gif name=JUNK.gif