[music-dsp] Group Delay, Step Response from Cascade?

[robert bristow-johnson]

On Jun 11, 2009, at 8:11 AM, Vinnie wrote:

>
> I would like to graph the group delay and step response for a  
> cascade of second order stages (I have all the coefficients). Is  
> this possible and if so, what is the formula?
>


step response is a problem.  group delay is easy (just add up the  
groupd delays for each stage).  but with step response, you can't  
simply do that.

for step response, first get your impulse response.  to get that for  
IIR, you have to break your cascade of 2nd-order sections into a  
"cascode" (that word i have rarely used) of 2nd-order sections.  by  
"cascode", i mean in parallel; the section that have a common input  
and the output from each is summed.  to do *that*, assuming none of  
the poles of the sections lie directly on top of each other, then you  
*might* be able to do it automatically (with a computer program)  
using the Heaviside expansion theorem.  this is *not* a small deal.   
i might suggest getting a good book (or maybe Wikipedia) to tell you  
about that.

--

r b-j                  rbj at audioimagination.com

"Imagination is more important than knowledge."