Why do DACs need filters?

[Paradox.Delta]

Hey guys, I was researching why DACs use oversampling to help with filters and came across a point that I just can’t explain. Hope you can help me out.

What I understood so far:

When audio is made, you record a sound that probably has frequencies above 22kHz and if you sample these in 44,1kHz they are recognized as another audible frequency since there are multiple waves between two samples. This pops up as aliasing in your recording. Or you synthesize a sound with some combined sine-waves that create frequencies like that. So the producer masters his recording, cleans everything above 22kHz in the process and puts these cleaned recordings as discrete 16bit values in 44,1kHz timesteps on a CD.

Now when you play the CD, you want to aproximate the original voltage curve from these 16bit values. So you alter your output voltage according to the 16bit value, wait for the time interval and apply the next voltage. This roughly results in a staircase function for the voltage output. But why is the DAC supposed to add another brickwall filter? The source material on the CD should already be void of anything higher than 22kHz. How is the aliasing reintroduced? Is it because of the staircase form of the voltage? Quantization noise? Or is it another strange mirroring effect that I can’t wrap my head around?

Thank you very much in advance.

 

[Paradox.Delta]

Ok, I came across this old post by Dan Lavry: https://www.head-fi.org/threads/nos-dac-marketing-bs.438220/page-3#post-5965222

The process of "filling the gaps" does involve filtering which is in fact the main part of interpolation. Analog filtering is one way to "connect the dots" into the original shape. Up-sampling is not all that different in theory. Up-sampling does some of the filtering in the digital world, and then you still end up with doing the rest of the "connecting the dots" with an analog filter. But with the digital up-sampling, the analog needs to do only a part of the task, the easier part.
...
Let me just say that the perfect interpolator and the perfect brick wall filter are the SAME THING. Filtering is what gets one to connect the dots and end up with the ORIGINAL WAVEFORM.

If I understand him correctly, the DAC filter isn't there to filter something away but to reconstruct the orginal wave form. Or is both the same thing?

 

[MindsMirror]

The source material on the CD should already be void of anything higher than 22kHz

In Nyquist theory, the discrete samples represent Dirac impulses, which have infinite bandwidth. Due to the infinite bandwidth, the theoretical information on the CD contains aliases from the Nyquist frequency out to infinity. The theoretical sampled signal is not the same as the original band limited signal, it is only the same if you band limit the reconstructed signal as well. You have to filter everything above the Nyquist frequency to remove the aliases.

Similar to a Dirac impulse, a square wave or stair step also has infinite bandwidth. If you interpolate the discrete samples this way, it will also have infinite bandwidth with aliases out to infinity which you'd have to filter.

A real DAC can't have infinite bandwidth so it can't produce perfect impulses or steps, but there are still aliases above the Nyquist frequency which must be filtered.

 

[yage]

You need to watch this...

Digital Show and Tell

Then read these for more detail...

What the Nyquist Criterion Means to Your Sampled Data System Design

Analog Devices Oversampling and Interpolating DACs

You might also need to read this book in case you need a better understanding of digital signals and systems...

The Scientist and Engineer's Guide to Digital Signal Processing

 

[theveterans]

Not all DACs require filters. There are some exotic DACs that don't even use a digital filter at all such as Aqua Formula xHD DAC and instead rely on their clocks, custom implementation and resistor precision to convert the signals to analog accurately

 

[surfgeorge]

This one is also interesting: