[sdiy] Analog bandwidth

[Richard Wentk]

Thanks Richie.

Just to be clear I wasn't thinking purely in terms of absolute bandwidth, but more in terms of bandwidth artefacts, such as phase shifts, and how necessary they are for good modelling. 

> That really depends on the complexity of what the simulation is doing.  It's a big subject, but 44.1kHz can be more than adequate for a lot of "Analogue Modelling" stuff, like modelling a TR-808's damped resonator drum sounds or some analogue synth sawtooth oscillators.  However, you might need to temporarily go up to 96kHz, 192kHz or higher to model things like guitar distortion with acceptable attenuation of aliasing.

That was the point. E.g. it's not unusual to add harmonics with a Chebyshev wave shaper. But of course if you start with a signal with 20k bandwidth and try to add frequencies at 2x, 3x, etc, you're not going to get what you want unless you upsample.

> 44.1k is clearly a very poor representation of the real thing.
> 
> Everything you listen to on a CD is represented at Fs=44.1kHz, so I would be careful about saying that.  44.1kHz is perfectly adequate for representing the output from an analogue synth that you intend to listen too directly, but it might not be enough to deal with some extreme post-processing like a hard-clipping distortion for example.  (In this case you might choose to up-sample by saw 8 times, process the distortion, filter out all the ultrasonic hash that you can't hear anyway, and then decimate back to Fs=44.1kHz to listen again or burn to CD.)

I've yet to hear alias-free synthesis at 44.1k without upsampling. The aliasing doesn't always sound bad. But it would better to be able to add it as an effect, not have it as a permanent feature.

> Usually op-amps have GBP up in the MHz range, so unless the op-amp is being used with a gain up in the hundreds it's pole won't start dramatically to impact the audio response below 20kHz.  

True, but - as someone pointed out - slew rates of vintage op-amps weren't great to start with, and on the data sheets they're often specified at unity gain. So the actual bandwidth, allowing for slew limiting, may not be quite as high.

> An example you might want to look at is the analogue state-variable filter.  Without compensation the filter is slightly more apt to self-oscillate at high cutoff frequencies because of increased phase-lag in the feedback path at high frequencies.  If you look at some of the discrete analogue Roland SVF designs (one of the Jupiter service notes) you'll see little ceramic caps of a few pF connected across some resistors at the inputs of the summing amps in the feedback path to give lead-compensation and balance out the phase-lag in the feedback path.  This makes the self-resonance more even across the audio range.

Thanks - I'll take a look at that. 

Richard