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From: dbd on 30 May 2010 14:09
On May 30, 2:57 am, "Shen Zhi" <markk...(a)hotmail.com> wrote:
> A factor that the high-order FIR filter coefficients dynamic range is quite
> large.
> For example, its center coefficient may be 0.5~1, but the most outside (or
> the smallest) coefficient may be 0.00...001. That means in fix-point system,
> the wordlength to be used must be long, or the small coefficient will be
> quantized to zero.
> So I'm thinking whether the discussion in 'coefficient dynamic range' also
> has contribution to improve the FIR filter design.
> ...

The sensitivity of the output of a direct form-I FIR filter to
quantization errors in the coefficients is the same for all
coefficients. This sensitivity is not a function of the coefficient
nominal value. The same word length is appropriate for all
coefficients.

Dale B. Dalrymple
From: Jerry Avins on 30 May 2010 16:48
On 5/30/2010 2:09 PM, dbd wrote:
> On May 30, 2:57 am, "Shen Zhi"<markk...(a)hotmail.com> wrote:
>> A factor that the high-order FIR filter coefficients dynamic range is quite
>> large.
>> For example, its center coefficient may be 0.5~1, but the most outside (or
>> the smallest) coefficient may be 0.00...001. That means in fix-point system,
>> the wordlength to be used must be long, or the small coefficient will be
>> quantized to zero.
>> So I'm thinking whether the discussion in 'coefficient dynamic range' also
>> has contribution to improve the FIR filter design.
>> ...
>
> The sensitivity of the output of a direct form-I FIR filter to
> quantization errors in the coefficients is the same for all
> coefficients. This sensitivity is not a function of the coefficient
> nominal value. The same word length is appropriate for all
> coefficients.

A remarkable result, all the more for its being obvious once stated.

Jerry
--
Engineering is the art of making what you want from things you can get.
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From: Zhi.Shen on 30 May 2010 22:49
Hi, Steve
I just read some materials about Lattice architecture.
What its benefit is,compared to direct form?
I found it doubles the Multipliers and the Adders, but what we get?

"Steve Pope" <spope33(a)speedymail.org> д����Ϣ����:htu0q1$98o$2(a)blue.rahul.net...
> Shen Zhi <markkknd(a)hotmail.com> wrote:
>
>> A factor that the high-order FIR filter coefficients dynamic
>> range is quite large. For example, its center coefficient may
>> be 0.5~1, but the most outside (or the smallest) coefficient may
>> be 0.00...001. That means in fix-point system, the wordlength to
>> be used must be long, or the small coefficient will be quantized
>> to zero.
>
> This is true but long word-widths are no longer the headache
> they once were. It is reasonable these days to have ~40 bits
> of accuracy in an accumulator. At the end of the computation,
> it can be rounded/saturated down to a smaller width.
>
>> So I'm thinking whether the discussion in 'coefficient dynamic
>> range' also has contribution to improve the FIR filter design.
>
> To reduce the neccessary coefficient precision, consider using a
> lattice architecture, not a cascaded architecture (because a few of
> the cascades tend to still require a lot coefficient precision).
>
>
> Steve


From: Steve Pope on 31 May 2010 00:16
Zhi.Shen <zhi.m.shen(a)gmail.com> wrote:

>I just read some materials about Lattice architecture.
>What its benefit is,compared to direct form?
>I found it doubles the Multipliers and the Adders, but what we get?

It doubles the number of multiply/adds but often the coefficients
can be lower precision.

Also, unrelated to your question, it can lead to a more stable
IIR filter.

It may not be appropriate for all filters, but if you're
having problems with coefficient precision it may be worth
checking into.

Steve
From: Zhi.Shen on 31 May 2010 02:41
Hi, Steve

In some DSP books, it always be described to be used in Nonlinear phase FIR
filter,
why few of them are about linear phase FIR filter?

"Steve Pope" <spope33(a)speedymail.org> д����Ϣ����:htvd61$o5v$1(a)blue.rahul.net...
> Zhi.Shen <zhi.m.shen(a)gmail.com> wrote:
>
>>I just read some materials about Lattice architecture.
>>What its benefit is,compared to direct form?
>>I found it doubles the Multipliers and the Adders, but what we get?
>
> It doubles the number of multiply/adds but often the coefficients
> can be lower precision.
>
> Also, unrelated to your question, it can lead to a more stable
> IIR filter.
>
> It may not be appropriate for all filters, but if you're
> having problems with coefficient precision it may be worth
> checking into.
>
> Steve


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