FPGA Central

Hi,

I am trying to implement a low pass IIR filter with data range of +1 & -1
The filter coefficients I get from Matlab are greater than 1. So, I need t
scale down all coefficients, that makes a(1) coefficient not equal to 1 an
makes the time difference equation to be:

y(m)= 1/a(1) * [b(1)*x(m) + b(2)*x(m-1) + ... + b(nb)*x(nb-1)
-a(2)*y(m-1)-....-a(na)*y(na-1) ]

This multiplication of 1/a(1) is a number greater than 1, that I can no
allow in the system. How can I get around this problem? I need to keep al
data within +1 & -1 format and I am using Q15 binary format fo
implementation of the filter.
It might sound a stupid question but any help is appreciated.

Thanks

Moodz

Moodz wrote:
> Hi,
>
> I am trying to implement a low pass IIR filter with data range of +1 & -1.
> The filter coefficients I get from Matlab are greater than 1. So, I need to
> scale down all coefficients, that makes a(1) coefficient not equal to 1 and
> makes the time difference equation to be:
>
> y(m)= 1/a(1) * [b(1)*x(m) + b(2)*x(m-1) + ... + b(nb)*x(nb-1)
> -a(2)*y(m-1)-....-a(na)*y(na-1) ]
>
> This multiplication of 1/a(1) is a number greater than 1, that I can not
> allow in the system. How can I get around this problem? I need to keep all
> data within +1 & -1 format and I am using Q15 binary format for
> implementation of the filter.
> It might sound a stupid question but any help is appreciated.

Can you get half the correct result? If so, double when you're finished.
(Use r + r instead of 2*r to avoid multiplying.)

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

On Jul 7, 4:02 pm, "Moodz" <nov_rain1...@yahoo.com> wrote:
> Hi,
>
> I am trying to implement a low pass IIR filter with data range of +1 & -1.
> The filter coefficients I get from Matlab are greater than 1. So, I need to
> scale down all coefficients, that makes a(1) coefficient not equal to 1 and
> makes the time difference equation to be:
>
> y(m)= 1/a(1) * [b(1)*x(m) + b(2)*x(m-1) + ... + b(nb)*x(nb-1)
> -a(2)*y(m-1)-....-a(na)*y(na-1) ]
>
> This multiplication of 1/a(1) is a number greater than 1, that I can not
> allow in the system. How can I get around this problem? I need to keep all
> data within +1 & -1 format and I am using Q15 binary format for
> implementation of the filter.
> It might sound a stupid question but any help is appreciated.
>
> Thanks
>
> Moodz

Is there a reason you do not precalculate the coefficients and then
put them in your system? This way everything is going to be smaller
than one and you don't need to multiply in realtime.

Hope this helps,
Ali

"Moodz" <[email protected]> writes:

> Hi,
>
> I am trying to implement a low pass IIR filter with data range of +1 & -1.
> The filter coefficients I get from Matlab are greater than 1. So, I need to
> scale down all coefficients, that makes a(1) coefficient not equal to 1 and
> makes the time difference equation to be:
>
> y(m)= 1/a(1) * [b(1)*x(m) + b(2)*x(m-1) + ... + b(nb)*x(nb-1)
> -a(2)*y(m-1)-....-a(na)*y(na-1) ]
>
> This multiplication of 1/a(1) is a number greater than 1, that I can not
> allow in the system. How can I get around this problem? I need to keep all
> data within +1 & -1 format and I am using Q15 binary format for
> implementation of the filter.
> It might sound a stupid question but any help is appreciated.
>
> Thanks
>
> Moodz

First of all, if your filter gain is higher than 1, you're not going
to get an output signal with the same range as the input signal. It
can't be done.

If your filter gain is 1 or less, then you can allow coefficients
greater than 1 in your filter - you just have to scale them and the
intermediate results properly.
--
% Randy Yates % "Rollin' and riding and slippin' and
%% Fuquay-Varina, NC % sliding, it's magic."
%%% 919-577-9882 %
%%%% <[email protected]> % 'Living' Thing', *A New World Record*, ELO
http://home.earthlink.net/~yatescr

On Jul 7, 4:02 pm, "Moodz" <nov_rain1...@yahoo.com> wrote:
> Hi,
>
> I am trying to implement a low pass IIR filter with data range of +1 & -1.
> The filter coefficients I get from Matlab are greater than 1. So, I need to
> scale down all coefficients, that makes a(1) coefficient not equal to 1 and
> makes the time difference equation to be:
>
> y(m)= 1/a(1) * [b(1)*x(m) + b(2)*x(m-1) + ... + b(nb)*x(nb-1)
> -a(2)*y(m-1)-....-a(na)*y(na-1) ]
>
> This multiplication of 1/a(1) is a number greater than 1, that I can not
> allow in the system. How can I get around this problem? I need to keep all
> data within +1 & -1 format and I am using Q15 binary format for
> implementation of the filter.
> It might sound a stupid question but any help is appreciated.
>
> Thanks
>
> Moodz

If you have a coefficient c > 1, split it into two pieces c1 + c2 == c
and do two MACs.

John

On Sat, 07 Jul 2007 15:02:48 -0500, Moodz wrote:

> Hi,
>
> I am trying to implement a low pass IIR filter with data range of +1 & -1.
>
> The filter coefficients I get from Matlab are greater than 1. So, I need to
>
> scale down all coefficients, that makes a(1) coefficient not equal to 1 and
>
> makes the time difference equation to be:
>
> y(m)= 1/a(1) * [b(1)*x(m) + b(2)*x(m-1) + ... + b(nb)*x(nb-1)
> -a(2)*y(m-1)-....-a(na)*y(na-1) ]
>
> This multiplication of 1/a(1) is a number greater than 1, that I can not
>
> allow in the system. How can I get around this problem? I need to keep all
>
> data within +1 & -1 format and I am using Q15 binary format for
>
> implementation of the filter.
> It might sound a stupid question but any help is appreciated.
>
First, be sure to split your filter into a cascaded set of 1st-order and
resonant 2nd-order filters -- the effects of rounding and coefficient
errors is pretty bad as you go beyond a 2nd-order filter.

If you do this, you'll find that none of your denominator coefficients
approaches 2. At this point you can take Jerry's suggestion of
calculating x(n)/2 and doubling it, or John's suggestion of doing the MAC
twice on one coefficient. You could also consider coding it to work with
1 + a(n). Each of these has their advantages and drawbacks, so you'll
want to look hard at the correct result.

--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html