Joined: Nov 20, 2007 Posts: 1988 Location: West Red Spot, Jupiter
Audio files: 224
Posted: Wed Dec 19, 2012 12:39 pm Post subject:
HexInverter wrote:
Aliasing is the "stepping" that occurs when reading (or generating) any analogue signal with a digital device (in this case, a microcontroller). Basically, the ADC (analogue -> digital converter) on a microcontroller is typically 1024 (10 bit) step resolution, so, as you turn the CV knob on a digital device, or input a control voltage, the device actually only has 1024 steps on the control.
In audio, the stepping you refer to is quantization, specificially of the signal's amplitude. This is not aliasing.
Aliasing or production of alias artifacts occurs when a signal contains one or more harmonics which have frequencies above the Nyquist limit. The Nyquist limit is a frequency 1/2 the sample rate. What happens with signals that have such harmonics is that they are "folded" back into the spectrum below Nyquist and will not sound good because they are no longer harmonics, they might be subharmonics, or inharmonic partials. Remember that periodic waveforms have a harmonic series that extends to infiinty. This is why antialiasing filters are used - they remove the harmonics above the Nyquist limit so that the signal sounds as it should without nasty alias artifacts.
An example would be: Assume a sample rate of 10 kHz that is attempting to reproduce a sinewave signal of 11 kHz. When the 11 kHz signal is captured at 10 kHz sample rate, the reproduced signal will be 1 kHz - an "alias" of the original signal which is completely different from the actual input signal. It takes at least 2 samples per cycle of a given waveform to come even close to reproducing the frequency of a sampled signal - and that's only "half ass" accurate. The 2 sample requirement is what gives rise to the Nyquist 1/2 sample rate figure. The more samples per cycle, the more accurate will be the reproduction.
In audio, the stepping you refer to is quantization, specificially of the signal's amplitude. This is not aliasing.
Aliasing or production of alias artifacts occurs when a signal contains one or more harmonics which have frequencies above the Nyquist limit. The Nyquist limit is a frequency 1/2 the sample rate. What happens with signals that have such harmonics is that they are "folded" back into the spectrum below Nyquist and will not sound good because they are no longer harmonics, they might be subharmonics, or inharmonic partials. Remember that periodic waveforms have a harmonic series that extends to infiinty. This is why antialiasing filters are used - they remove the harmonics above the Nyquist limit so that the signal sounds as it should without nasty alias artifacts.
An example would be: Assume a sample rate of 10 kHz that is attempting to reproduce a sinewave signal of 11 kHz. When the 11 kHz signal is captured at 10 kHz sample rate, the reproduced signal will be 1 kHz - an "alias" of the original signal which is completely different from the actual input signal. It takes at least 2 samples per cycle of a given waveform to come even close to reproducing the frequency of a sampled signal - and that's only "half ass" accurate. The 2 sample requirement is what gives rise to the Nyquist 1/2 sample rate figure. The more samples per cycle, the more accurate will be the reproduction.
Yes, I understand the difference Sorry, I did mean stepping. Specifically, on the CV input and the oscillator's response to CV.
I am speaking from a lot of weird backgrounds that use words differently so I get terminology crossed sometimes!
In particular, I think I was thinking about how the word pertains to visual/graphic design in my head (which can also be seen on the image example of the letter "A" at the right of the Wiki page you linked). If you imagine a sloped CV input as a function of time vs. the uP's output frequency, the output frequency would resemble an aliased image.
Thanks for the explanation. I hope I did not confuse anyone too much ^__^ _________________ hexinverter.net -- Shop DIY projects and modules for modular synthesis
sympleSEQ -- the simple to build analog step-sequencer
Joined: Nov 20, 2007 Posts: 1988 Location: West Red Spot, Jupiter
Audio files: 224
Posted: Wed Dec 19, 2012 5:09 pm Post subject:
Yeah, the wikipedia article is more broad than just the consideration of digitally reproduced sampled audio signal alias artifacts (that's a mouthful), which is why I used the word audio to prevent any confusion with the other kinds of alias artifacts that are described there.
I did an experiment with a sawtooth waveform naively generated in an FPGA into a 24 bit DAC. I used a sample rate of 44.1 kHz and the design would sweep the frequency of the sawtooth when a button was pushed. While the sawtooth wave was static at one frequency, the alias artifacts were not noticable, but when the sweep button was pushed, you could hear the sawtooth sweep, but you could also hear the aliased harmonic frequencies sweeping as well, often in the opposite direction of the fundamental tone sweep. If you're ever going to hear aliasing, that's when it will become boldly apparent - when you sweep the waveform's fundamental frequency (as in portamento). There are two ways (that I know of) to deal with that - one is to band limit the sawtooth which can be done (among several ways) by adding up sinewaves up to but less than the sample rate frequency divided by two to build the sawtooth from it's harmonic series. This won't alias, because there is no violation of the Nyquist limit. The other way is a bit sneakier; which is to use a very high sample rate. As you may know, periodic waveforms have harmonics that go to infinity in frequency, but they also are more and more attenutated as the harmonic number is increased. If a very high sample rate is used with a naively generated waveform like sawtooth, there will still be alias artifacts, but the amplitudes of those harmonics above the Nyquist limit are so small that they are imperceptible and you don't hear them.
As for stepping or quantization, it can certainly be a problem especially when fewer bits are used to represent signal values. When an envelope is generated with only a few bits, it will certainly have what is call "the zipper effect" when it slews from one value to the next. This is often handled in circuitry by a simple lowpass filter (resistor and capacitor) to smooth it out.
Yeah, the wikipedia article is more broad than just the consideration of digitally reproduced sampled audio signal alias artifacts (that's a mouthful), which is why I used the word audio to prevent any confusion with the other kinds of alias artifacts that are described there.
I did an experiment with a sawtooth waveform naively generated in an FPGA into a 24 bit DAC. I used a sample rate of 44.1 kHz and the design would sweep the frequency of the sawtooth when a button was pushed. While the sawtooth wave was static at one frequency, the alias artifacts were not noticable, but when the sweep button was pushed, you could hear the sawtooth sweep, but you could also hear the aliased harmonic frequencies sweeping as well, often in the opposite direction of the fundamental tone sweep. If you're ever going to hear aliasing, that's when it will become boldly apparent - when you sweep the waveform's fundamental frequency (as in portamento). There are two ways (that I know of) to deal with that - one is to band limit the sawtooth which can be done (among several ways) by adding up sinewaves up to but less than the sample rate frequency divided by two to build the sawtooth from it's harmonic series. This won't alias, because there is no violation of the Nyquist limit. The other way is a bit sneakier; which is to use a very high sample rate. As you may know, periodic waveforms have harmonics that go to infinity in frequency, but they also are more and more attenutated as the harmonic number is increased. If a very high sample rate is used with a naively generated waveform like sawtooth, there will still be alias artifacts, but the amplitudes of those harmonics above the Nyquist limit are so small that they are imperceptible and you don't hear them.
As for stepping or quantization, it can certainly be a problem especially when fewer bits are used to represent signal values. When an envelope is generated with only a few bits, it will certainly have what is call "the zipper effect" when it slews from one value to the next. This is often handled in circuitry by a simple lowpass filter (resistor and capacitor) to smooth it out.
Nice board, by the way
Cool read! Thanks for the information _________________ hexinverter.net -- Shop DIY projects and modules for modular synthesis
sympleSEQ -- the simple to build analog step-sequencer
Short video demo of FM with Make Noise Pressure Points and Intellijel PLANAR mixing FM sources!
I will make a more formal video demo with some spoken explanation eventually...just gotta finish make a couple more vcNOIZ modules so I can have some chaotic fun with it
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sympleSEQ -- the simple to build analog step-sequencer
Very cool sounds and lovely PCB design. Wish I could afford the Eurorack boards as it looks like fun. Any chance you'd offer the PCBs without the SMT already mounted, for those of us comfortable with SMT soldering?
Sorry! I missed this post until now, somehow.
Unfortunately I only ordered the PCBs with SMT done on them (there are not any extras), so, I won't have any to offer without SMT done, nope!
You can however build a universal PCB set into eurorack no problem! You just have to mount the board like any other DIY module (at a right angle to the panel) and handwire the jacks and pots!
I am doing this myself for a couple of them as we speak, since I don't have any complete SMT boards here yet and need a couple more modules done for video demos! _________________ hexinverter.net -- Shop DIY projects and modules for modular synthesis
sympleSEQ -- the simple to build analog step-sequencer
The euro SMT assembly order arrived today from the manufacturer! As you can see, I still have to hand assemble all of the through hole components. These are the boards that Option #3 and #4 preorders will receive.
I am still waiting on the panel order before I can ship any of these, so, it may be a few weeks still!
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sympleSEQ -- the simple to build analog step-sequencer
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