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Why are some signal or waveform generators called "Arbitrary Waveform Generators"? Am I misunderstanding the word arbitrary? This question is not necessarily about the word arbitrary but more about arbitrary signals.

How is a arbitrary waveform generator different from a plain old waveform generator?

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    \$\begingroup\$ Often enough the price... \$\endgroup\$ – PlasmaHH May 18 '15 at 15:16
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    \$\begingroup\$ Usually because you can upload custom waveforms vs. standard ones where all the waveforms are predefined. \$\endgroup\$ – Tom Carpenter May 18 '15 at 15:18
  • \$\begingroup\$ adjective: arbitrary based on random choice or personal whim, rather than any reason or system. \$\endgroup\$ – JIm Dearden May 18 '15 at 15:35
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An AWG is more like a soundcard on steroids, while your POWG contains circuitry for generation of a classical set of waveforms.

The lines are a tiny bit blurry since there are DDS waveform generators that only do a standard configurable set.

Basically for the classical waveform generators and the clunky pushbottons for waveforms (square, sawtooth, sine etc.) you activated a distinct circuit that was responsible for the type of waveform.

In the modern ones, you use DDS (direct digital synthesizers) that are highspeed DACs disciplined by an accurate reference clock. Since they are more or less fed with a waveform (lots of them can take .wav or even .mp3 files and play them back at desired frequencies) the waveforms they can produce are called arbitrary.

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You can upload something like a comma-separated file to the function generator and generate an 'arbitrary' periodic waveform (within the limitations of sample rate and memory depth). Often they will also have pre-programmed (not so) arbitrary waveforms.

For example, here is the relevant section of a Rigol manual:

DG4000 provides 150 kinds of built-in arbitrary waveforms stored in non-volatile memory and allows users to store 10 user-defined arbitrary waveforms in non-volatile memory and 1 user-defined arbitrary waveform in volatile memory. Users can also store the user-defined arbitrary waveform in external memory (such as USB storage device). User-defined waveforms can contain 1 (DC voltage) to 16384 (16k) data points, namely 1pts to 16kpts

(Note that the waveform points have to be loaded into the high-speed RAM to actually be used, the non-volatile memory is just storage and is not fast enough to drive the arb)

Built-in waveforms include things like Gaussian pulses, cardiac and EEG signals, TENS waveforms, and such exotica as the "Protuberant arc hyperbolic cosecant" waveform.

This contrasts with DDS function generators that typically contain only a single look-up table for one quadrant of a sine wave.

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    \$\begingroup\$ Don't forget the voice that says "Rigol" ... \$\endgroup\$ – PlasmaHH May 18 '15 at 15:33
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    \$\begingroup\$ No kidding?! I missed that one! Guess it's this one: "Voice Voice signal". Lol. \$\endgroup\$ – Spehro Pefhany May 18 '15 at 15:34
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    \$\begingroup\$ Its under "Engine" -> "Voice" \$\endgroup\$ – PlasmaHH May 18 '15 at 15:36
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    \$\begingroup\$ Got it! Had to slow the period to ~ 1 second. Made my day, thanks! \$\endgroup\$ – Spehro Pefhany May 18 '15 at 15:42

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