Detecting if a notch filter is 'notching' something!

Greg Berchin wrote:
> On Fri, 29 Jan 2010 17:35:11 +1100, John Monro <johnmonro@optusnet.com.au>
> wrote:
> 
>> For subtraction to work the filter must 
>> have a linear phase.
> 
> A generic 2nd-order notch filter:
> 
> .     s&#4294967295; + A&#4294967295;
> .   ------------
> .   s&#4294967295; + Bs + A&#4294967295;
> 
> "One minus a generic 2nd-order notch filter":
> 
> .         s&#4294967295; + A&#4294967295;
> .   1 - ------------
> .       s&#4294967295; + Bs + A&#4294967295;
> .
> .     s&#4294967295; + Bs + A&#4294967295; - (s&#4294967295; + A&#4294967295;)
> .   = ------------------------
> .          s&#4294967295; + Bs + A&#4294967295;
> .
> .          Bs
> .   = ------------
> .     s&#4294967295; + Bs + A&#4294967295;
> 
> ... which is a bandpass filter.
> 
> Neither the notch filter nor the bandpass filter is linear phase.
> 
> Greg

You are quite right Greg.  What I was thinking of was the 
situation where the 'notch' filter is a reasonably flat 
band-reject filter, but of course this would have a much 
higher order than the second-order filter mentioned by the OP.

With a nice flat higher-order band-reject filter the 
subtraction scheme would not work well because the phase 
shift either side of centre frequency would mess up the 
amplitude response when the subtraction was carried out.


Regards,
John