ThreeFingersOfLove
Joined: Oct 21, 2004 Posts: 162 Location: Greece
Audio files: 3
G2 patch files: 1

Posted: Sun Nov 14, 2004 12:36 pm Post subject:
Filter(Filter(Filter(Filter)))) 


Hello,
OK, let's say we want to make a 4pole lowpass filter out of 4 1pole filters connected in series. We also want to synthesize resonance explicitly by feeding the inverted output of the last filter back to the input. We know that when a signal gets filtered, its output appears 180 degrees phaseshifted. So:
1. First filter> 180 out of phase
2. Second filter > 0
3. Third filter > 180 out of phase
4. Fourth filter > 0 degrees
However, this is not the case. It seems that whenever filters are connected in series, they are regarded as one big filter so someone needs only the last output inverted. Can anyone explain why this happens?
When a signal enters a filter, it gets reversed and added to the original. Frequencies above the cutoff will cancel each other (thus constructing the lowpass) but what about the low registers? How come these don't get filtered?
Also, can anyone explain what do we mean when we say that a lowpass filter acts like an integrator and a high pass filter acts like a diferentiator?
Thanx,
Yannis


Fozzie
Joined: Jun 04, 2004 Posts: 875 Location: Near Wageningen, the Netherlands
Audio files: 8
G2 patch files: 49

Posted: Sun Nov 14, 2004 2:20 pm Post subject:



With these kinds of questions.......
if you got a problem, if no one else can help, and if you can find him, maybe you can hire
the HTeam
tatadataaa tadadaaaa........
Rob??
The only sensible thing I can say, is that I believe the phase shift of a filter is frequency dependent, so you can't say that the whole signal has shifted 180 degrees. But we need some experts here for that, I'm just learning synthesis & stuff for a relatively short time.
Maybe a nice link to this info, anyone? It must have been explained before, I'd say.
EDIT: here's a nice starter http://www.soundonsound.com/sos/aug99/articles/synthsecrets.htm 

jksuperstar
Joined: Aug 20, 2004 Posts: 2495 Location: Denver
Audio files: 1
G2 patch files: 18

Posted: Sun Nov 14, 2004 5:08 pm Post subject:



Quote:  Also, can anyone explain what do we mean when we say that a lowpass filter acts like an integrator and a high pass filter acts like a diferentiator? 
In terms of "graphing" (plotting 2D curves, with X=time, and Y=amplitude), Integration as "the area under the curve", and differentiation is the slope of the curve. Both are true for any given moment.
So, for differentiation, you can think of slope of a curve, seperate from its offset (how far away from "0" it is). In the world of frequencies, this means taking out the superlow frequencies, and the high frequencies left, are equal to the slope back in the time world. So, a hipass filter can do this. It get's rid of the low freq (offset), and leaves the hi freq (slope).
For integration [ED], it is opposite. You want to keep the "offset", or the "area" under a function/curve, not the slope. A lopass does this. There are somewhat long mathematical proofs for this, but this is about as simple as I know how to put it. It works because you are talking about 1 moment in time, not functions that go on forever. That's why it is an approximation. But, it is typically a good aproximation.
Quote:  When a signal enters a filter, it gets reversed and added to the original. Frequencies above the cutoff will cancel each other (thus constructing the lowpass) but what about the low registers? How come these don't get filtered? 
That's only true for 1 specific implementation of 1 type of filter: the comb filter. In general, comb filters are just delayed, then added to themselves.
I don't know if I can explain it in short detail, so I'll give you the "keywords" so you can do some more research. There are two basic types of filters: "IIR", or Infinte Impulse Response, and "FIR", or Finite Impulse Response. "IIR" filters are the classic analog filters, and in digital implementations, get that resonance from a feedback that exists inside the filter, although it is sometimes a feedforward also! So, each stage of the filter (assuming multiple "filters" in serials) also has feedback within itself. By adding 1 more feedback over the *whole* filter, you're adding just one more "pole" to the equation. However, this doesn't need to be a "180 degree shift" (If you find "Discrete Time Domain" in your search, you'll notice in the math equations the feedback part is the 1/x part of equations, where as feedforward is the x/1 part).
FIR Filters are more recently developed (mostly in the last 1 hundred years ) They are based on Fourier's Theorum, that *any* signal can be broken down into a combination of Cosine waves. (This is also the basic concept of Additive synthesis, and convolutional reverb). They are typically designed as a series of delays, where each delay, or "tap", is scaled and added into an output. This is why in the world of DSP, a "multiply and accumulate", (also called "MAC, or "scale & add" in this discussion) is such a big deal. The more "MAC"s a DSP processor can do, the faster it can perform filtering (for more or bigger filter).
So, the ultimate answer is not a flat out "this is what it is for all filters". Each filter get's its characteristics from how it scales the feedback, feedforward, and passthrough conditions. The "frequency" knob on a typical Nord filter probably controls several of these parameters inside the filter. Anyway, you're just scratching the surface on what makes a Moog filter unique vs. other lowpass filters, or what's different about the "Nord" filter vs. the "Classic" filter.
[Editor's note: I changed the word differentiation to integration in the third paragraph. I'm sure that's what you meant. If not, please edit it back and remove this note  mosc] 
