aliasing in D/A conversion?

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.

-- Bill Sloman, Nijmegen

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.

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:

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

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...

and my toy version

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