[sdiy] Making a HPF using a LPF...??

[Magnus Danielson]

On 04/10/2012 08:36 PM, David G Dixon wrote:
>>> Jean-Pierre Desrochers wrote:
>>>> Can I make a High pass filter using a Low pass filter and
>> a summing
>>>> amp using both positive and negative inputs?
>>>
>>> In theory, yes.
>>>
>>> In practice, try it.
>
> Actually, this sort of filter-stage summing is done all the time, and it
> works quite well.  This is, after all, how the highpass response is derived
> in a state variable filter.  It is also how highpass is derived in my
> SSM2164-based MS-20 clone, the Korgasmatron.  The only problem with it is
> that the impedances in the summed stages must be very tightly matched or
> there may be audible input signal bleedthrough in highpass mode at low
> cutoff frequencies (in other words, the signals which are summed must be
> more or less perfectly cancelled out for highpass cutoff to be complete).
> This can be achieved with 0.1% resistors and 2164s, or (even better) with a
> small trimmer in series with one of the summing resistors.

You can make a high-pass filter by summing for a low-pass filter, but...

Let's consider a second degree low-pass filter response

Hlp(s) = b / (s^2 + a*s + b)

If we now subtract the original signal with the output of that, we get

H2(s) = 1 - b / (s^2 + a*s + b) = (s^2 + a*s) / (s^2 + a*s + b)

However, we expect this to be

Hhp(s) = s^2 / (s^2 + a*s + b)

So, you don't get the "pure" HP response, but a variant.

Which variant is the most useful, the "pure" or the difference variant 
is up to you and your application.

Cheers,
Magnus