>On 02/06/2011 01:38 PM, j26 wrote:
>> In Octave:
>>
>> octave:13> [a,b]=butter(2,0.4);
>> octave:14> a
>> a =
>>
>> 0.206572083826148 0.413144167652296 0.206572083826148
>>
>> octave:15> [z,p,g]=butter(2,0.4);
>> octave:16> z
>> z =
>>
>> -1 -1
>>
>> So I can see that the difference equation coefficients are a = [1,2,1];
>> multiplied by a scaling factor. These correspond to two zeros at -1.
But
>> working out the math, I think the difference equation coefficients
should
>> be a = [1,-2,1];
>>
>> (1 - z^-1)(1 - z^-1) = 1 - 2*z^-1 + z^-2
>>
>> Why is octave telling me that the difference equation coefficient a[1] =
2
>> instead of -2?
>
>z^2 + 2 * z + 1 = 0 is zero when z = -1, or when z = -1.
>
>z^2 - 2 * z + 1 = 0 is zero when z = 1, or when z = 1.
>
>--
>
>Tim Wescott
>Wescott Design Services
>http://www.wescottdesign.com
>
>Do you need to implement control loops in software?
>"Applied Control Theory for Embedded Systems" was written for you.
>See details at http://www.wescottdesign.com/actfes/actfes.html
>
Ok, I think I got it, thanks.
Reply by Rune Allnor●February 7, 20112011-02-07
On Feb 6, 10:38�pm, "j26" <ptd26@n_o_s_p_a_m.live.com> wrote:
> In Octave:
>
> octave:13> [a,b]=butter(2,0.4);
> octave:14> a
> a =
>
> � �0.206572083826148 � 0.413144167652296 � 0.206572083826148
>
> octave:15> [z,p,g]=butter(2,0.4);
> octave:16> z
> z =
>
> � -1 �-1
>
> So I can see that the difference equation coefficients are a = [1,2,1];
> multiplied by a scaling factor. �These correspond to two zeros at -1. �But
> working out the math, I think the difference equation coefficients should
> be a = [1,-2,1];
>
> (1 - z^-1)(1 - z^-1)
= (z - 1)(z - 1) = 0 => z = ?
Rune
Reply by bharat pathak●February 6, 20112011-02-06
The Transfer function in matlab and octave are modelled with
numerator and denominator coefficients being all positives.
H(z) = (bo + b1 z^-1 + b2 z^-2 .....)/(a0 + a1 z^-1 + a2 z^-2 + .....)
So when you want to translate this to time domain (difference equation)
the denominator coefficient signs would change. Work out it is simple
math.
Regards
Bharat
Reply by Tim Wescott●February 6, 20112011-02-06
On 02/06/2011 01:38 PM, j26 wrote:
> In Octave:
>
> octave:13> [a,b]=butter(2,0.4);
> octave:14> a
> a =
>
> 0.206572083826148 0.413144167652296 0.206572083826148
>
> octave:15> [z,p,g]=butter(2,0.4);
> octave:16> z
> z =
>
> -1 -1
>
> So I can see that the difference equation coefficients are a = [1,2,1];
> multiplied by a scaling factor. These correspond to two zeros at -1. But
> working out the math, I think the difference equation coefficients should
> be a = [1,-2,1];
>
> (1 - z^-1)(1 - z^-1) = 1 - 2*z^-1 + z^-2
>
> Why is octave telling me that the difference equation coefficient a[1] = 2
> instead of -2?
z^2 + 2 * z + 1 = 0 is zero when z = -1, or when z = -1.
z^2 - 2 * z + 1 = 0 is zero when z = 1, or when z = 1.
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by Tim Wescott●February 6, 20112011-02-06
On 02/06/2011 01:38 PM, j26 wrote:
> In Octave:
>
> octave:13> [a,b]=butter(2,0.4);
> octave:14> a
> a =
>
> 0.206572083826148 0.413144167652296 0.206572083826148
>
> octave:15> [z,p,g]=butter(2,0.4);
> octave:16> z
> z =
>
> -1 -1
>
> So I can see that the difference equation coefficients are a = [1,2,1];
> multiplied by a scaling factor. These correspond to two zeros at -1. But
> working out the math, I think the difference equation coefficients should
> be a = [1,-2,1];
>
> (1 - z^-1)(1 - z^-1) = 1 - 2*z^-1 + z^-2
>
> Why is octave telling me that the difference equation coefficient a[1] = 2
> instead of -2?
z^2 + 2 * z + 1 = 0 is zero when z = -1, or when z = -1.
z^2 - 2 * z + 1 = 0 is zero when z = 1, or when z = 1.
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html