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AN1x filters are not correctly modeled


Don Solaris

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Yep. The 303 is a 4-pole diode ladder with 1 of the rungs offset giving it a 18db/oct around cutoff then a 24 db/oct slope higher up. The last rung participates in the resonance feedback but I'm not sure what would happen with resonance. My guess is that you _would_ get a slight peak one octave up. It's been a while since I could do that kind of math. I quickly purged all that knowledge after college.

 

Larry

 

 

 

Seriously? I never knew that. Does the higher filter resonate along with the lower one when you turn up that knob? I wouldn't imagine so.

 

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Don:

 

 

Interesting work. I wonder if the filters in the A-series samplers are likewise mislabeled. Given the sound, I do not think so, but I could be wrong. I always quite liked the filters on my A5K, especially because the 3-pole was the perfect sound between the 2- and 4-pole filters, and for me was so useful for basses and darker strings.

 

I love the sound of the 8-pole filters in the effects section too. Stacking 6 of those in bandpass and then sweeping the cutoff always leads to interesting sounds.

 

 

cheers,

Ian

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Yep. The 303 is a 4-pole diode ladder with 1 of the rungs offset giving it a 18db/oct around cutoff then a 24 db/oct slope higher up. The last rung participates in the resonance feedback but I'm not sure what would happen with resonance. My guess is that you _would_ get a slight peak one octave up.

Probably why it doesn't sound like it's just mid way between a 12 and 24 but has some extra bite instead.

 

Don, if I put up a sample of a will you generate a graph for it? I'm really curious about the varios-303 which sounds way to weak to be an 18.

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That is ok: +/- 0.5 dB or even +/- 1 dB is not big deal, but placing 24 dB label and putting 19 dB filter, is. Sorry but for such value a 18 dB label would be far more appropriate.

 

 

The label may not be inappropriate if the filter has a slope greater than 24 db at the upper end of the "feedback" spectrum, and a slope less than 24 db at the lower end of the spectrum.

 

Jerry

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The label may not be inappropriate if the filter has a slope greater than 24 db at the upper end of the "feedback" spectrum, and a slope less than 24 db at the lower end of the spectrum.

 

Well this is actually simple engineering. When you build a filter with a slope of 19 dB, you will more probably call it a 18 dB filter. Because if you claim it is 24 dB, yet it gives only 19 dB, then it shows your filter design skills are pretty low and buyers will avoid you.

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I thought it was generally understood that analog filters rarely reach their "ideal" slope. IIRC, it's actually impossible for them to do so, although a good filter design can come very close. To demonstrate this, I did a similar experiment with my Ensoniq Mirage, which uses CEM3328 VCF ICs for it's filters. The stated specification for the filters is a -24dB/8ve slope. In reality, it's more like -18dB/8ve. There's a little more variance in the data (apparently the AN1x produces a very smooth noise spectrum - I used the "white noise" generator in wavelab as the source for the Mirage), but it's clear that the slope is fairly constant. I can provide the source data if you'd like to draw your own conclusions.

 

MirageFilterSlope.jpg

 

It would be interesting to see how other analog synths perform in this area - I would assume that many do not show such drastic discrepancies as the Mirage or the AN1x, but on the other hand, some are probably even worse! One thing to note for anybody who'd like to try this experiment - make sure that your noise has an even spectrum with the filter wide open (or better, bypassed). Many synths have a noise spectrum which is not "white", but closer to "pink", or other colors. This will distort your measurement if you do not take it into account, the result being that the overall filter slope will appear steeper than what it actually is.

 

At any rate, I really doubt the AN1x's filter's slope characteristics are an accident. It's not difficult to create simple, bog standard 4-pole LPF which will perform at -24db/8ve. For whatever reason, Yamaha's engineers didn't want to do it like that. If I had to guess, I'd say they took real world measurements and concluded that most "-24dB" filters do not perform as such, so they modeled that characteristic. If that's the case, they actually modeled their filter pretty accurately.

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Did Yamaha call the filter 2/3/4 poles or their "rough" dB/octave equivalents?

 

Please look at the bottom of the page. All 4 are single pole/first order.

 

http://en.wikipedia.org/wiki/Chebyshev_filter

 

Unless Yamaha specified the filters in dBs they are "legit".

 

What we really need is some samples from other synths to compare.

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Many synths have a noise spectrum which is not "white", but closer to "pink", or other colors.

You have a point but I doubt most synths have pinker rather than white noise.

 

pink noise = 1/f response (or 3dB/octave)

 

white noise = constant response to cosmicrays Hz.

 

The 3dB/octave isn't trivial to design.

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I dunno. The Waldorf Pulse has a pink noise generator. A lot of noise generators sound more pink than white to me.

 

Here's a pretty simple design for an analog pink noise generator - http://www.techlib.com/electronics/pinknoise.htm

 

I've never tested or built it so I'll just have to take the author's word that it really does produce pink noise. I'm curious as to whether it's spectrum can be shifted so that it produces a -3dB/8ve slope over a more reasonable range for audio, like 20Hz-20kHz.

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There's a little more variance in the data (apparently the AN1x produces a very smooth noise spectrum

 

Oh, i know what you mean. Actually i did analysis on exactly the same white noise as yours (if it would be so smooth as it looks on my pic, there would be no sound at all). But here is the catch...

 

Filter analysis based on a white noise cannot be performed without a data normalization. Otherwise, the graph is unreadable. To see what i mean, zoom your graph in the region of one octave like i did (450-900 Hz) and there is no way you will be able to read the slope.

 

But if you normalize the data for every 100 values, spotting the slope will be piece of cake. I use Microsoft Excel for this job. Unfortunately there is a small bug (of course, a Microsoft product!) the output data is not moved in the middle (say average from 1-100 is not placed on 50 but on 100). You need to cut the output data, and move it 50 rows above. After saving file, don't forget to replace "," with "." (as Gnuplot can go crazy if you give it "," as a decimal separator).

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It's not difficult to create simple, bog standard 4-pole LPF which will perform at -24db/8ve. For whatever reason, Yamaha's engineers didn't want to do it like that. If I had to guess, I'd say they took real world measurements and concluded that most "-24dB" filters do not perform as such, so they modeled that characteristic. If that's the case, they actually modeled their filter pretty accurately.

 

 

There is a great deal of intention behind the design. Apart from the slope, the resonance characteristics are different between (24db, 12db, bpf etc) and more importantly they respond differently to feedback. My theory is that Yamaha concluded that at feedback settings of approximately 60, it came pretty close to the slope of a 24db ladder filter. They didn't count on us saying that the feedback parameter is part of the amp (it's coupled feedback) and therefore not relevent to the filter. Perhaps with hindsight they should have labelled it feedback to filter instead of feedback from amp. Here's a clip from sos that explains how the "amp feedback" relates to the filter:

 

The final input to the filter is an unusual one: the output of the VCA. Feedback is normally the province of modular synthesizers, and certainly not polysynths. As a nod to the monosynths of old, the VCF is preceded by a high-pass filter -- which allows you to remove the low frequencies which can so easily muddy the sound when you mix together lots of low-pass filtered synth sounds.

 

Filters are personal things. Ladders, state-variable loops, 2-pole, 4-pole and 6-pole variants all go together to produce the characteristic thin and buzzy or dark and moody feels of the analogue filters of old. Yamaha have provided 2-, 3- and 4-pole low-pass filters, plus band-pass, high-pass and band-reject ones. The VCF sounds that most people remember are the strident and synthetic 2-pole 12dB/octave type, and the 4-pole, resonant 24dB/octave type. The AN1x sounds very similar to the real thing in both cases -- by which I mean that if I do an A/B comparison with my analogue 24dB ladder filter, I can detect some differences but I'm not sure exactly what they are.

 

http://www.soundonsound.com/sos/1997_articles/aug97/yamahaan1x.html

 

Which is why judging the slope of the filter without including several feedback variations is interesting but inconclusive.

 

Jerry

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My engineering training tells me that the frequency axis should be a log scale to enhance understanding.

All cool. ;)

 

However, for the frequency range 450-900 there is practically no difference between logarithmic and linear scale on the x axis. In fact the linear one is much easier to read and better for precise observations of the filter slope.

 

Ideally would be a logarithmic scale with a base of 2, because that is exactly what filter slope is. However, a base of 10 (a classic log scale) is a little bit too large for precise filter measurements (to spot the slope).

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Filter analysis based on a white noise cannot be performed without a data normalization. Otherwise, the graph is unreadable. To see what i mean, zoom your graph in the region of one octave like i did (450-900 Hz) and there is no way you will be able to read the slope.

This is true and due to the fact that white noise has a Gaussian distribution ("bell curve"). Its amplitude is not constant, so you have to average some values [think RMS].

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I dunno. The Waldorf Pulse has a pink noise generator. A lot of noise generators sound more pink than white to me.


Here's a pretty simple design for an analog pink noise generator -


I've never tested or built it so I'll just have to take the author's word that it really does produce pink noise. I'm curious as to whether it's spectrum can be shifted so that it produces a -3dB/8ve slope over a more reasonable range for audio, like 20Hz-20kHz.

Cool. I'll try a spectral plot in SPICE.

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Forgive me, for I am neither a master of statistical analysis nor FFT techniques, but (for the purposes of our experiment) what is the advantage of normalizing the data vs just using a smaller FFT size?

See my above comment. White noise has a Gaussian distribution, its not always the same amplitude. That causes a problem if you want to make a nice spectral plot: you have 2 variables, the white noise distribution and the filter slope.

 

To combat this you can average overtime and your white noise amplitude variance is no longer a problem. And then its easier to see the filter slope.

 

In the engineering world noise values can be expressed in terms of sigma [standard deviation]. 3.6 sigma or so means the noise has a 99.9% probability of being less than a certain amplitude.

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. 3.6 sigma or so means the noise has a 99.9% probability of being less than a certain amplitude.

 

 

That I understand. My point is, if you use a smaller FFT sample size, it has the effect of smoothing out the graph (because we are decreasing the spectral line resolution). From my limited understanding of the FFT, this is going to basically average the data, doing the same thing as using a higher FFT size and then normalizing afterward.

 

Is that incorrect, or is there something I'm missing?

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