🚀 go-pugleaf

Hello -

There are methods and there are methods.  This one escapes me.

All the courses I had in my undergraduate EE days said that analog filters
with an even number of poles or zeros in the transfer function NOT all on
the real axis were always complex-conjugate pairs reflected across the real
axis.

The last day of an active filters course the professor hints that there
is a way to make the reflection axis selectable across the origin or
across the imaginary axis... like:

		 +jw				 +jw
		|				|
	   x	|			    x	|   x
		|				|
	--------+------- (sigma)	--------+--------- (sigma)
		|				|
	    -jw	|    x			    -jw	|

	 (across the origin)		(across the imaginary axis)

		 +jw				 +jw
		|				|
	   o	|			    o	|   o
		|				|
	--------+------- (sigma)	--------+--------- (sigma)
		|				|
	    -jw	|    o			    -jw	|

	 (across the origin)		(across the imaginary axis)

 (Real axis reflections omitted for clarity)

That complex poles and zeros exist as pairs I think is required.  But I
haven't the foggiest idea of how to move _just_ one of them across an
axis, never mind through the origin.

I don't know of any way for an analog circuit to do this so maybe it's
done digitally (digital methods were not covered in the course).  Can
anyone point me to an article somewhere as to the method used to
implement such a transfer function?

Mark