Infinite-Precision Dgital Filters

Folks,

Did I miss something in the last few years? Do they really
have "infinite-precision" digital filters? This paper's
abstract seems to say so. Please set me straight.

--Randy


From
http://ieeexplore.ieee.org/xpls/abs_all.jsp?tp=&arnumber=1205815&isnumber=27140

  An optimal entropy coding scheme for efficient implementation of
pulse shaping FIR filters in digital receivers

  Vinod, A.P.   Premkumar, A.B.   Lai, E.M.-K.
  Sch. of Comput. Eng., Nanyang Technol. Univ., Singapore;

  This paper appears in: Circuits and Systems, 2003. ISCAS '03.
Proceedings of the 2003 International Symposium on
  Publication Date: 25-28 May 2003
  Volume: 4,  On page(s): IV-229- IV-232 vol.4
  ISSN:
  ISBN: 0-7803-7761-3
  INSPEC Accession Number: 7762555
  Digital Object Identifier: 10.1109/ISCAS.2003.1205815
  Posted online: 2003-06-25 15:31:41.0
  Abstract

  The most computationally intensive part of wide-band receivers is the
  IF processing block. Digital filtering is the main task in IF
  processing. Infinite precision filters require complicated digital
  circuits due to coefficient multiplication. This paper presents an
  efficient method to implement pulse shaping filters for a dual-mode
  GSM/W-CDMA receiver. We use an arithmetic scheme, known as pseudo
  floating-point (PFP) representation to encode the filter
  coefficients. By employing a span reduction technique, we show that
  the filters can be coded using an optimal entropy scheme employing
PFP
  which requires only considerably fewer bits than conventional 24-bit
  and 16-bit fixed-point filters. Simulation results show that the
  magnitude responses of the filters coded in PFP meet the attenuation
  requirements of GSM/W-CDMA specifications.

Randy Yates wrote:
> Folks,
>
> Did I miss something in the last few years? Do they really
> have "infinite-precision" digital filters? This paper's
> abstract seems to say so. Please set me straight.

My very simple view is that a finite representation of a number
(i.e. a finite number of bits or digits), necessarily implies that
there is a finite number of states of that representation, and
hence a finite number of... ehm... numbers.

In this finite set of numbers, there must necessarily be at least
one that is in some sense "the smallest", and hence we have
finite precision.

The consequence of all this, is that an infinte number of
digits/bits is needed to obtain infinite precision.

That's how I would argue against such a claim. But then, I'm
but an engineer.

Rune

Rune Allnor wrote:

> 
> Randy Yates wrote:
>> Folks,
>>
>> Did I miss something in the last few years? Do they really
>> have "infinite-precision" digital filters? This paper's
>> abstract seems to say so. Please set me straight.
> 
> My very simple view is that a finite representation of a number
> (i.e. a finite number of bits or digits), necessarily implies that
> there is a finite number of states of that representation, and
> hence a finite number of... ehm... numbers.
> 
> In this finite set of numbers, there must necessarily be at least
> one that is in some sense "the smallest", and hence we have
> finite precision.
> 
> The consequence of all this, is that an infinte number of
> digits/bits is needed to obtain infinite precision.
> 
> That's how I would argue against such a claim. But then, I'm
> but an engineer.
> 
> Rune

Isn't any BIBO stable filter "infinite-precision", if they are implemented
with integer coefficients and integer samples? "Infinite-precision" in the
sense that the filter does not increase the quantization noise. Obviously
such filter can be implemented with finite-number of bits. The loss in the
precision happens before the filtering (i.e., in the sampling stage).

-- 
Jani Huhtanen
Tampere University of Technology, Pori

Randy Yates wrote:

> Folks,
>
> Did I miss something in the last few years? Do they really
> have "infinite-precision" digital filters? This paper's
> abstract seems to say so. Please set me straight.
>
> --Randy
>
>
...
>  Infinite precision filters require complicated digital
> circuits due to coefficient multiplication.

My guess is that they are alluring to the wide accumulator needed for
FIRs (hinted at by the use of "pseudo-floating-point", whatever that
is).

Regards,
Andor

Randy Yates wrote:

> Folks,
> 
> Did I miss something in the last few years? Do they really
> have "infinite-precision" digital filters? This paper's
> abstract seems to say so. Please set me straight.
> 
> --Randy
> 
> 
> From
>
http://ieeexplore.ieee.org/xpls/abs_all.jsp?tp=&arnumber=1205815&isnumber=27140
> 

Heh, funny. They seem to refer to coefficients represented with floating
point numbers as "infinite-precision". From the paper:
"The infinite-precision filter, h(n), is generated by the
raised cosine FIR filter design program provided by the
MATLAB ?firrcos? function.". 

As far as I know, Matlab isn't really that good ;)

@Andor:
Pseudo floating-point is their representation for quantized numbers. They
encode a value in two parts: shift (exponent) and span (mantissa). Basicly
the shift tells how many bits the span has to be shifted to obtain the
actual value.

-- 
Jani Huhtanen
Tampere University of Technology, Pori

Jani Huhtanen wrote:

...
> http://ieeexplore.ieee.org/xpls/abs_all.jsp?tp=&arnumber=1205815&isnumber=27140
> >
>
> Heh, funny. They seem to refer to coefficients represented with floating
> point numbers as "infinite-precision". From the paper:
> "The infinite-precision filter, h(n), is generated by the
> raised cosine FIR filter design program provided by the
> MATLAB ?firrcos? function.".
>
> As far as I know, Matlab isn't really that good ;)
>
> @Andor:
> Pseudo floating-point is their representation for quantized numbers. They
> encode a value in two parts: shift (exponent) and span (mantissa).

Now all the need is a sign bit, and they can drop the pseudo prefix.
Guess I gave them too much credit in my first post. Sad.

Hi Jani,

Thank you for making explicit this notion that was
also floating around in my head.

However..., the paper seems to imply that you can start
with an *arbitrary* infinite-precision filter and then
implement it with digital circuits.

Are my language interpretation skills sliding, or
is there statement, at a minimum, unclear?

--Randy


Jani Huhtanen wrote:
> Rune Allnor wrote:
>
> >
> > Randy Yates wrote:
> >> Folks,
> >>
> >> Did I miss something in the last few years? Do they really
> >> have "infinite-precision" digital filters? This paper's
> >> abstract seems to say so. Please set me straight.
> >
> > My very simple view is that a finite representation of a number
> > (i.e. a finite number of bits or digits), necessarily implies that
> > there is a finite number of states of that representation, and
> > hence a finite number of... ehm... numbers.
> >
> > In this finite set of numbers, there must necessarily be at least
> > one that is in some sense "the smallest", and hence we have
> > finite precision.
> >
> > The consequence of all this, is that an infinte number of
> > digits/bits is needed to obtain infinite precision.
> >
> > That's how I would argue against such a claim. But then, I'm
> > but an engineer.
> >
> > Rune
>
> Isn't any BIBO stable filter "infinite-precision", if they are implemented
> with integer coefficients and integer samples? "Infinite-precision" in the
> sense that the filter does not increase the quantization noise. Obviously
> such filter can be implemented with finite-number of bits. The loss in the
> precision happens before the filtering (i.e., in the sampling stage).
> 
> -- 
> Jani Huhtanen
> Tampere University of Technology, Pori

Randy Yates wrote:

> Hi Jani,
> 
> Thank you for making explicit this notion that was
> also floating around in my head.
> 
> However..., the paper seems to imply that you can start
> with an *arbitrary* infinite-precision filter and then
> implement it with digital circuits.

Yes it seems so. They also claim that Matlabs firrcos function can be used
to create such infinite-precision coefficients :). So one just has to
substitute 'infinite-precision' with 'floating-point' and all makes sense
again.

> --Randy

-- 
Jani Huhtanen
Tampere University of Technology, Pori

Andor wrote:
> Jani Huhtanen wrote:
>
> ...
> > http://ieeexplore.ieee.org/xpls/abs_all.jsp?tp=&arnumber=1205815&isnumber=27140
> > >
> >
> > Heh, funny. They seem to refer to coefficients represented with floating
> > point numbers as "infinite-precision". From the paper:
> > "The infinite-precision filter, h(n), is generated by the
> > raised cosine FIR filter design program provided by the
> > MATLAB ?firrcos? function.".
> >
> > As far as I know, Matlab isn't really that good ;)
> >
> > @Andor:
> > Pseudo floating-point is their representation for quantized numbers. They
> > encode a value in two parts: shift (exponent) and span (mantissa).
>
> Now all the need is a sign bit, and they can drop the pseudo prefix.
> Guess I gave them too much credit in my first post. Sad.


My first questoin is:

are they refering to infinite precision of the DATA or infinite
precision of the COEFFICIENTS of the filter?

I thought that the correct application of dither gives you infinite
precision of the DATA, at least thats what we have been telling the
audio guys....:-)

It appears the paper is refering to infinte precision of the
coefficients?  Correct?

Mark

Mark wrote:

> 
> Andor wrote:
>> Jani Huhtanen wrote:
>>
>> ...
>> >
http://ieeexplore.ieee.org/xpls/abs_all.jsp?tp=&arnumber=1205815&isnumber=27140
>> > >
>> >
>> > Heh, funny. They seem to refer to coefficients represented with
>> > floating point numbers as "infinite-precision". From the paper:
>> > "The infinite-precision filter, h(n), is generated by the
>> > raised cosine FIR filter design program provided by the
>> > MATLAB ?firrcos? function.".
>> >
>> > As far as I know, Matlab isn't really that good ;)
>> >
>> > @Andor:
>> > Pseudo floating-point is their representation for quantized numbers.
>> > They encode a value in two parts: shift (exponent) and span (mantissa).
>>
>> Now all the need is a sign bit, and they can drop the pseudo prefix.
>> Guess I gave them too much credit in my first post. Sad.
> 
> 
> My first questoin is:
> 
> are they refering to infinite precision of the DATA or infinite
> precision of the COEFFICIENTS of the filter?
> 
> I thought that the correct application of dither gives you infinite
> precision of the DATA, at least thats what we have been telling the
> audio guys....:-)

Could you elaborate this a bit? As I see it, quantized data cannot ever be
infinite precision (in practice), however, transforms on quantized data may
in some cases be infinite-precision. 

> 
> It appears the paper is refering to infinte precision of the
> coefficients?  Correct?
> 
> Mark

Correct. 

-- 
Jani Huhtanen
Tampere University of Technology, Pori