Are digital reconstruction filters really necessary?

This is something I've wondered for a long long while, but never spent the time to research. The typical digital flow is the analog sound comes into a microphone, into an analog lowpass filter, then an A/D which digitizes it. On playback out of the DAC, the last stage is also a filter to remove images or false frequencies.

I *think* these images are just from the highest frequencies near the sampling frequency. In that case, considering that there is little information up there, it makes me wonder if you really need that filter at all. Those filters were blamed-rightly or wrongly-for early problems with digital sound due to their steepness and time domain behavior. So presumably, if you ditched them entirely, you could improve the time behavior, at the price of distortion from imaged frequencies. But if there is hardly anything to image, maybe it would be OK. Or at least worth trying out.

Now if the images are from ALL the audio, that's a different story.
Reconstruction Filter - an overview | ScienceDirect Topics
under the section "Hardware for Active Control - S.J. ELLIOTT, in Signal Processing for Active Control, 2001 - 10.3 RECONSTRUCTION FILTERS" it discusses this, but having not thought about this stuff to this level of detail in a long time I could not glean if the imaged frequencies are indeed the ones around half the sampling frequency that is around 22 kHz for a CD system. Actually I spent a fair amount of time looking and couldn't find something clearly showing images of various frequencies on the reconstruction side. (This Typical Errors in Digital Audio: Part 6 – Aliasing was interesting but if I understand correctly they are talking about stuff that's already present before the D/A reconstruction).

So back to the topic: what happens with real recordings if there is NO reconstruction filter?

 

"Necessary" is a relative thing .

If you don't use a reconstruction filter, it results in:
1. -3dB roll-off into Nyquist.
2. Imaging/"Aliasing" ultrasonic artifacts that can lead to audible intermodulation I suppose.

Many people like NOS DACs with reconstruction filters turned off. And modern DACs like the Topping DX3 Pro have NOS type filter settings.

Here's an article on this...
NOS vs. Digital Filtering DACs: Exploring filtering turned off, implications, fidelity and subjective audibility.

Have a listen for yourself of course.

 

The reconstruction filter is what keeps PCM waveforms from looking like they are composed of very tiny stair steps (at very low levels only). They also suppress ultrasonic reflections of all of the energy of the entire audio band (which, for CDs, appear beginning at about 24kHz and extends to about 44kHz in the case of an NOS DAC ) from being sent through your amp and speakers.

But despite how badly such a DAC would measure in terms of ultrasonic noise without a reconstruction filter, the lack of this filter must not sound too bad subjectively, or companies like Audio Note would not build their NOS DACs without them. However it surprises me that more tweeters don't get fried from this lack of filtering, and that more Dogs and Cats don't run from the vicinity when such a DAC is used.

 

Ah very interesting article. My brain is still attempting to consider if it answers my question. Surely removing the filter can theoretically cause all manner of ills, but I'm wondering if it's a problem with real music.
AND, I guess I'd add what if you DO oversample, and shift all the filtering to a higher frequency, and then remove the filter. Or something like that, since that statement makes no sense.

 

- keeps PCM waveforms from looking like they are composed of very tiny stair steps
@ well, yes, but that's visual, it doesn't mean that would be audible necessarily...I'm thinking not but that's just offhand

- suppress ultrasonic reflections of all of the energy of the entire audio band
@ Aren't those reflections "backwards"? In other words, the lower frequencies have inaudible higher frequency images (like up around 44), and it's only the highest audio frequencies which would reflect back down into the audio range (down below 22)?
@ Which would be minimized more by oversampling
@ Now the energy level of those images up around 44, is that a problem? Don't know. Those are still full level I guess? Even if so it begs the question, especially if you oversampled, couldn't you then use a very simple reconstruction filter, maybe even 1st order, instead of these complicated constructs with bouncy nulls and peaks.

- However it surprises me that more tweeters don't get fried from this lack of filtering,
@ Exactly, that gets back to the above

- and that more Dogs and Cats don't run from the vicinity when such a DAC is used.
@ Let's get The Gallup Poll on it, survey to find if NOS DAC users on average have far less cats and dogs
@ Or if their cats and dogs are, on average, less happy that oversampling DAC owner's dogs and cats

 

Yes it's an insurmountable problem as for mathematical reasons, you will introduce spurious information into the pass band that was not in the original signal.

The creative way to tackle the problems of filter design is SACD.

It is actually only fairly recently we've been able to measure the effects of different filter designs. In the 80s most major manufacturers applied the closest they could get to a brick-wall filter without any real understanding of what this did to the pass band.

 

Let me see if I can express it from what I remember from my EE classes

In Nyquist math theory, in strict terms what goes into the ADC and then out of the DAC (before the low pass filter) is not the same signal. There are "echoes" or reflections of the original signal centered around multiples of the sampling frequency, but these are of lesser amplitude than the original signal. If you were able to (in theory) have a perfect filter that cuts off all frequencies above half the sampling frequency (in the case of CD, sampling frequency= 44.1 KHZ, so you want to filter out everything above 22.05 kHz), you would be left with the original signal.

But circuits and filters are not perfect in the real world, and each CD player will have a better or worst implementation of the low pass filter, depending on the quality of the engineering and the quality of the circuit components used. And as some have stated, in the real world, filters add problems of their own, again depending on how good or bad they have been implemented.

Does it matter? Well, by definition these echos or reflections are, in theory, above the human hearing range, and at what frequencies they appear depends on the frequencies present in the original signal. The lower the frequency range of the original signal, the farther away (frequency wise) from the desired cut off point these echoes will be and thus more easily filtered out and/or less receptive by the human ear.

But not filtering out the frequencies above 22.05 kHz, while theoretically beyond human hearing (and everybody hears differently, some more sensitive than others) could still affect the the audible signal (albeit to a small degree) by being additive or subtractive to the original signal. And that is called harmonic distortion, but let's keep it simple and stop there.

 

That is all correct. If I am not mistaken (which I very well might be in this thought experiment), the stair-stepped waveforms could actually be thought of as a microscopic construction of 22kHz square waves. In theory I believe that this would also mean that the first of the odd-order harmonics which composed these microscopic square-waves would begin at about 66kHz (the third harmonic of 22kHz), and that these would extend higher in frequency for each of the successive odd-order harmonic.

For the simplicity of discussion above I have looked only at the case of a NOS DAC. An oversampling DAC extends all of these artifacts much higher into the ultrasonic range, just as you state.

 

Man, if my wife’s cat ran out of the room every time I fired up my Audio Note DAC I’d be one happy man. Unfortunately the pesky animal sticks around and provides just enough uncomfortable tension to stifle any relaxation I might have hoped to gain from the music. But the DAC does sound very nice...