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Topic: Some of you literate types help me.. (Read 4336 times) previous topic - next topic
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Some of you literate types help me..

I am a recording engineer and am intrigued by the excerpt is from This Threadin which I posted a clip from an interview with Mr. Bruno Putzeys. At the time he was the Chief Engineer at Phillips.

Recipe for perfect PCM:

Specify all interpolation/decimation filters as halfband, 0.4fs to 0.6fs transition.
Put exactly one non-halfband lowpass filter in the chain (e.g. at replay or before final dithering) that enters stopband at 0.4fs. Specifying its passband at 20kHz will allow for a very smooth roll-off and hence very short and practically ringing-free impulse response.

Can someone tell me just what that last bit means? IEE Speak makes my brain hurt.

If there is such a thing, Id love to know how to achieve it.....

Some of you literate types help me..

Reply #1 –
Halfband filter: frequency response posesses certain symmetry properties about Fs/4. The upside is that half the FIR filter coefficients go to 0 in this case so the filter runs twice as fast as it otherwise might. The downside is that because of the symmetry, the response at Fs/4 must be exactly -6db. If this filter is running at 2x the original Fs this means that aliasing will occur within the transition band, and in Bruno's view this is an unacceptable violation of the Nyquist criterion. (I'm willing to disagree with him on that, though.)

So by specifying a non-halfband filter, Bruno is saying that you can't "cheat" in your filter design and have the response be symmetric about 22khz. At some point in the filter stages, you must have some kind of lowpass filter that has a frequency response of 0 (or -100db or what have you) at 22khz. But all the other subfilters that comprise the complete digital filter design might be halfband if need be.

And, along with that, a wide transition band, say from 18khz to 22khz is needed in this non-halfband lowpass filter, to optimize the transient response. (Rule of thumb: The wider the transition band, the less the ringing.)

Clear as mud?

Good link, btw!

Some of you literate types help me..

Reply #2 –
Quote from: Axon on
Rule of thumb: The wider the transition band, the less the ringing.


Beware that this rule is the source of endless misinterpretations.

Rule of thumb 2 : the ringing occurs at the transition frequency and nowhere else.

For example, on a CD, you have a filter around 20 or 22 kHz. Thus you have a ringing made of a 20 or 22 kHz sine, which is inaudible, except for a very few gifted people.

Very often, it is said that transient are less sharp if you use a sharp filter, with a lot of ringing, because the impulse response is widened. This is false. Transients, in the musical frequency band, remain exactly as sharp as with any other filter. You can see a graphic analysis of the phenomenon here : http://www.head-fi.org/forums/f133/importa...tml#post5517013

In the experiment, I introduce a very long ringing using a very sharp filter. Then, I show that the ringing is strictly restricted to the frequency of my filter, and that the frequencies below that one remain razor-sharp in the time domain.

One last thing : here is a successful ABX of the simulation of the effect of removing filters in a DAC (french link) : http://www.homecinema-fr.com/forum/viewtop...t=60#p170435302
According to some documents posted in the other discussion, where I posted my graphics, the treble roll-off introduced in high end CD players in order to restore a "sharp impulse response" (Wadia, Corda...) are of the same order of magnitude. Therefore trading flat frequency response for impulse response is likely a bad idea.

Some of you literate types help me..

Reply #3 –
Quote from: Axon on
Halfband filter: frequency response posesses certain symmetry properties about Fs/4. The upside is that half the FIR filter coefficients go to 0 in this case so the filter runs twice as fast as it otherwise might. The downside is that because of the symmetry, the response at Fs/4 must be exactly -6db. If this filter is running at 2x the original Fs this means that aliasing will occur within the transition band, and in Bruno's view this is an unacceptable violation of the Nyquist criterion. (I'm willing to disagree with him on that, though.)

So by specifying a non-halfband filter, Bruno is saying that you can't "cheat" in your filter design and have the response be symmetric about 22khz. At some point in the filter stages, you must have some kind of lowpass filter that has a frequency response of 0 (or -100db or what have you) at 22khz. But all the other subfilters that comprise the complete digital filter design might be halfband if need be.

And, along with that, a wide transition band, say from 18khz to 22khz is needed in this non-halfband lowpass filter, to optimize the transient response. (Rule of thumb: The wider the transition band, the less the ringing.)

Clear as mud?

Good link, btw!



yes, but what does that mean in laymans terms?? something that has to be implemented on the hardware side? not digitally?

Some of you literate types help me..

Reply #4 –
Quote from: ncdrawl on
yes, but what does that mean in laymans terms?? something that has to be implemented on the hardware side? not digitally?


Well it's usually implimented in digital hardware, um, I know, not so useful.

What Bruno is talking about is how to do a high-rate decimation.

What he means about the last stage is that by keeping the sharp transition band in the last stage, you'll have the shortest possible overall impulse response.

There are some issues, though, because the higher-order filters can be much wider than .4 to .6, if you're doing 4 or 8x interpolation/decimation.

Hmm, this is hard to explain without resorting to a great deal of mathematics...

I'll try.

Some facts, in some order:

1) Impulse response is the Fourier transform of frequency response (including both magnitude and phase in the frequency response)
2) The faster the frequency response changes, the longer the big terms in the impulse response will be.
3) The sharper the filter cutoff, the longer the filter impulse response, i.e. for FIR filters (this is what he refers to when he says halfband filters) the filter length. For IIR filters (recursive filters, analog filters for the most part) this means a higher 'Q' in each section, and sensitivity and a variety of filter problemns go as Q^4, which is quite unpleasant when you need to build them with .001% precision parts.

http://i238.photobucket.com/albums/ff228/j...plots/short.jpg

http://i238.photobucket.com/albums/ff228/j.../plots/long.jpg

The two links show a half-band filter (not really QUITE a half-band filter), but notice that every other coef, except for the center one, is very near 0 (half-band filters would be exactly zero, btw), and an optimum FIR of similar rejection on a 20 to 22.05 (at 2x sampling rate, as is the short filter as well) transition band.

Notice the difference in lengths and the sharpness of the filter rolloff. The two are inextricably linked.

Oh, another note, every term in the long filter is non-zero, there are 193 taps, some of which you can't see in the graph  at this resolution. The short filter is 51 taps long, and all even numbered taps except the center are zero.

There are two things going on here, the half-band filter relates to the "every other coefficient zero", and the overall length, which results from the sharpness of the filter.
-----
J. D. (jj) Johnston
 

Some of you literate types help me..

Reply #5 –
Quote from: ncdrawl on
yes, but what does that mean in laymans terms?? something that has to be implemented on the hardware side? not digitally?



(and then he discovers that he does have an account here ...)


The impulse response of a chain, including a PCM chain from ADC in studio to DAC at home), is
determined by the impulse response of the filter in the chain that has the lowest
stopband frequency.

Hence, in order to control the combined impulse response of a PCM chain the recipe
is to have all filters minus one to be halfband filters (meaning: crappy, aliasing,
pre/post-ringing, but cheap and text-book so not too hard to screw up in practice ;-) ),
and then one single filter that imposes the desired impulse response, while literally
undercutting the stopband of the others.


You can put that filter anywhere, but chances are pretty slim that you find such a
thing in any present single-chip ADC's decimator (or DAC chip for replay, for the
matter).

The obvious place to put such a filter would be in the last stage of music
production, i.e. mastering. When doing 96k work a feasible filter would
have its transition band spanning from 20kHz to 38kHz. With CD it is
a bit less clear cut, except when you sacrifice much of the sacred 20kHz
passband.

These things were published many years ago by Peter Craven.

The work (and Craven) were picked up by Meridian, who now have a CD
player with a filter that
1) has a passband to 19kHz
2) stopband at below 22kHz
3) is minimum phase, so as to annihilate the pre-ringing of typical ADCs' decimation filters.

But as said, you can put it anywhere in the system, and today there are software SRCs that
offer many filter variants, have a look at SoX and Izotope RX.

Hope this helps,

Werner