# [sdiy] Different pole notches and phasers

ColinMuirDorward colindorward at gmail.com
Mon Apr 13 15:24:43 CEST 2020

```This is a conversation I've been waiting to have! Thanks for bringing it
up, Tom.

In the simplest instance, if you take a signal, delay it and mix it back in
with the original, you will get notches.  This is the classic comb filter.

In this case, are the notches distributed evenly? Is the space between each
notch determined by the delay time? What sort of db/oct gain do we see?

In the classic 4pole cascaded OTA phaser design, my ears tell me there is
only one notch, but I'm not sure I'm hearing it right.
I see that a one-pole allpass gives you 180degree phase rotation around the
cutoff. So I suppose if we have two of them, then we get 360degree phase
shift. As we add more poles, and increase that phase shift, doesn't that
start looking more like delay? Does that mean we get classic comb filtering
effects, ie a spread of notches above the APF's cutoff? Am I making *any *
sense?

Cheers,
Colin

On Mon, Apr 13, 2020 at 10:21 AM Richie Burnett <
rburnett at richieburnett.co.uk> wrote:

> I think one of the things that is confusing is that mathematically
> "notches"
> don't come from poles.  They come from zeros.  And zeros in a transfer
> function often arise from a signal taking two parallel paths through a
> circuit.  Like in the classic cascaded all-pass phaser, or those
> combinations of the Expander filter outputs that result in responses with
> notches.  You don't get notches until you start to combine the input with
> a
> phase-shifted version,  or combine outputs that have different phase
> relationships.
>
> In the simplest instance, if you take a signal, delay it and mix it back
> in
> with the original, you will get notches.  This is the classic comb filter.
> And the notches result from destructive interference between the original
> and the delayed (phase shifted) version.
>
> If you actually wanted to design a digital notch filter to remove
> something
> like an annoying 1kHz tone, you would do this by placing a pair of zeros
> right on the unit circle at the angle that corresponds to 1kHz.  And this
> would annihilate anything at 1kHz (to the limits of numerical precision.)
> You can alter the width of the notches by placing poles close to them but
> just in from the unit circle.  The closer you put the poles to the zeros
> the
> narrower the notch width will be.  (A narrow digital 1kHz notch filter at
> 8kHz sample rate would have a pair of complex zeros at 0.7071+j0.7071 and
> 0.7071-j0.7071, and a pair of poles just inward from the unit circle at
> something like 0.69+j0.69 and 0.69-j0.69.  If you move the poles closer to
> the origin the notches will get wider.)
>
> Stay healthy everyone!
>
> -Richie,
>
>
>
> -----Original Message-----
> From: Tom Wiltshire
> Sent: Monday, April 13, 2020 11:58 AM
> To: SDIY List
> Subject: [sdiy] Different pole notches and phasers
>
> Hi all,
>
> Could someone explain something I don’t understand clearly to me?
>
> What does it mean to talk about the number of poles when discussing a
> notch
> filter?
>
> Additionally, what’s the difference between a notch filter and a notch
> created with an allpass filter and the input added together? Is there a
> difference?
>
> It seems to me there is, since multiple stages of allpass filters with the
> input added together (a phaser) creates multiple notches, whereas a
> multi-pole notch would just be a deeper/narrower notch. Is that right? Or
> could a 4-pole notch filter have two notches?
>
> There’s something I don’t quite get here, and I’m struggling to find
> exactly
> what it is, hence the rather confused questions. Any clarification anyone
> can offer would be greatly appreciated.
>
> Thanks,
> Tom
>
> ==================
>        Electric Druid
> Synth & Stompbox DIY
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