aliasing in D/A conversion?

[Mark-T]

We know aliasing is possible in A to D conversion, but
what about the other direction? Does that make any
sense? It seems to me a non-issue, the signal will naturally
be confined to the baseband, i.e. S/2 Hz, where S is
the signal generation rate, samples/sec.

Am I missing something? Assume we're talking about
a DDS waveform synthesizer.



Mark

 

[[email protected]]

We know aliasing is possible in A to D conversion, but
what about the other direction?  Does that make any
sense?  It seems to me a non-issue, the signal will naturally
be confined to the baseband, i.e. S/2 Hz, where S is
the signal generation rate, samples/sec.

Am I missing something?  Assume we're talking about
a DDS waveform synthesizer.

Read the Analog Devices application notes for their DDS parts.

What you seem to be missing is the insight that the stepwise nature of
the waveform generated by a DAC includes Fourier components up to the
frequency defined by the transition time between each step.

The faster Analog Devices DDS parts are clocked at around 500MHz,
which wouldn't serve any usefulpurpose if the transition times were
greater than 2nsec, which implies the the output waveform is going to
contain harmonic components up to at least 500MHz.

You need an anti-aliasing filter if you don't want your synthesised
waveform to include too much of these components.

A useful way of looking at the situation is to subtract the smooth
sine wave that you would like to be synthesising from the stair-case
approximation to it that you are actually synthesising - the sawtooth
waveform that constitutes the difference is noise, and you want to use
an anti-aliasing filter to minimise the proportion of this noise that
you feed through into the rest of your system.

 

[[email protected]]

We know aliasing is possible in A to D conversion, but
what about the other direction? �Does that make any
sense? �It seems to me a non-issue, the signal will naturally
be confined to the baseband, i.e. S/2 Hz, where S is
the signal generation rate, samples/sec.

Am I missing something? �Assume we're talking about
a DDS waveform synthesizer.

Mark

You dont get aliasing, thats a function of sampling, but you will get
high frequency components in your output waveform. You should filter
it to the bandwidth you require.

 

[Tim Wescott]

We know aliasing is possible in A to D conversion, but what about the
other direction? Does that make any sense? It seems to me a non-issue,
the signal will naturally be confined to the baseband, i.e. S/2 Hz,
where S is the signal generation rate, samples/sec.

Am I missing something? Assume we're talking about a DDS waveform
synthesizer.

Sampled-time data is naturally aliased: there's no difference between cos
(w * n) and cos ((2 * pi + w) * n). It is the transition to sampled time
that causes aliasing in A/D conversion, but the aliasing is there when
you generate a waveform in sampled time. So yes, you have to worry about
it.

There's more in this paper: http://www.wescottdesign.com/articles/
Sampling/sampling.html.

--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html

 

[John Larkin]

We know aliasing is possible in A to D conversion, but
what about the other direction? Does that make any
sense? It seems to me a non-issue, the signal will naturally
be confined to the baseband, i.e. S/2 Hz, where S is
the signal generation rate, samples/sec.

Am I missing something? Assume we're talking about
a DDS waveform synthesizer.



Mark

Suppose you have a dds phase accumulator of, say, 16 bits, and you
clock it at 1 MHz, sinewave map it, DAC the result, and run it through
a good 500 KHz lowpass filter. If you load 0x4000 into the phase
accumulator adder thing, you'll get a nice 250 KHz sine wave out of
the filter.

Poke in 0x7800, and you'll get a 468 KHz sine, just below Nyquist.

Poke in 0x8800, and the output frequency is *still* 468 KHz. This is
aliasing, namely the creation of an unwanted sideband that's a mirror
about the Nyquist frequency. As you poke increasing numbers above
0x8000, the frequency goes *down*

Actually, the 0x8400 case produces *negative* 468 KHz, a
counter-rotating version of +468. You're walking the sine table
backwards.

The other dds artifact to watch for is the sinx/x distortion, which
costs amplitude as you approach Nyquist, roughly down 3 dB close to
Nyquist as I recall.


We did this one recently...

http://www.highlandtechnology.com/DSS/V346DS.html

and my toy version

http://www.highlandtechnology.com/DSS/T340DS.html


and had a lot of fun playing with all these "textbook" things, like
DDS properties, modulation sidebands, stuff like that, that we could
see directly on XY scope traces and spectrum analyzers. All that
theory *works*

John