[sdiy] All-pass filters, was: Screwing with Square Waves

[Phil Macphail]

On 02/11/2013 09:15, "cheater00 ." <cheater00 at gmail.com> wrote:

>Phil,
>
>On Fri, Nov 1, 2013 at 4:10 PM, Phil Macphail
><phil.macphail at liivatera.com> wrote:
>> That depends on what you want - do you want a 90-degree shift on the
>>harmonics too?
>
>Yes, definitely. Can you see any other options? Or do you mean the
>alternative would be to shift the starting phase of the oscillator by
>tau/4, i.e. a quarter cycle? That's not what I had meant.
>
>> If so then a polyphase network will do that. There is a trade-off
>>between bandwidth, ripple and number of stages so these days they are
>>probably best implemented digitally.
>
>I'm kind of hoping there's a way to do this with and have it work well
>even when the oscillator changes pitch rapidly. Naturally it has to be
>analogue, otherwise we cannot use the oscillator for many things that
>require immediate reaction time.
>
>I wonder if shaping a triangle wave might create a wave that's good
>enough an approximation of the "hilbert wave".
>
>Cheers,
>D.

Well immediate reaction time isn't something you will get from any
filter.... A polyphase filter will phase-shift the frequency components by
90 degrees, but the whole signal will be delayed relative to the input
signal by more than this.
The best papers are from the IEEE, so without subscription you can't
access them. The following links should give you enough idea of how to
make a polyphase filter (and the limitations of analogue circuits) -

http://homepage.ntlworld.com/johngduffy/Project/Chapter3.htm
http://www.hanssummers.com/gallery4.html

With careful design you can get around 8 octaves of bandwidth with around
1-2dB ripple through the passband from a reasonable number of stages
(<10), but it isn't a trivial exercise. The best way to design these
filters is with some kind of synthesis step to solve the design equations
and circuit simulator to verify the solution.

Phil.