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Author Topic: Are linear phase LP and HP filters possible in analogue domain?  (Read 18404 times)

johnR

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Are linear phase LP and HP filters possible in analogue domain?
« on: October 22, 2010, 02:42:33 PM »

I'm inclined to believe not, but enlightenment would be welcome.
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Bogic Petrovic

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Re: Are linear phase LP and HP filters possible in analogue domain?
« Reply #1 on: October 22, 2010, 03:20:36 PM »

This is about delay function realization, if we have delay function in analogue domain, then linear phase HP and LP will be possible in analogue domain.

Pure signal delay in (strictly) analogue domain is possible, and this means that analogue domain linear phase HP and LP filters (FIR generally)  are possible, but digital domain realization is much more practical (especially for audio)

EDIT: here are some information about analog delays I think about:
http://en.wikipedia.org/wiki/Delay_line_memory

Jim Williams

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Re: Are linear phase LP and HP filters possible in analogue domain?
« Reply #2 on: October 23, 2010, 10:39:51 AM »

Here lies the confusion. Linear phase is not the absence of phase shift. It is the linearity of the phase response.

As an example, say you measure -10 degrees at 10k hz. With a linear phase response you will measure -20 degrees at 20k hz, -40 degrees at 40 k hz. If you measure -21 or -19 at 20k hz you have a 1 degree deviation from linear phase. Measure another filter class other than Bessel and you will measure a phase response that is not linear. That causes ringing of the response and a reorientation of the upper harmonics due to a nonlinear group delay. Feed a nonlinear phase filter with a square wave and the top of that waveform is rippled.

I recommend Dean Jensen's excellent papers on the subject available in the AES archives.
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johnR

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Re: Are linear phase LP and HP filters possible in analogue domain?
« Reply #3 on: October 23, 2010, 12:59:04 PM »

There seems to be some disagreement over terminology between analogue and digital filter designers. DSP programmers appear to define linear phase as constant group delay over the whole frequency range. Analogue designers seem to use a more approximate definition that only applies to the passband. It's confusing for sure.
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Jim Williams

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Re: Are linear phase LP and HP filters possible in analogue domain?
« Reply #4 on: October 24, 2010, 10:19:56 AM »

All filters whether digital or analog rely on the same principles. Filter functions were realized in both mathematics and the analog domain decades before the first digital filters were created.

Chicken before the egg? Horse before the cart? I can see those deep into digital may find it hard to understand that these audio functions were around many decades before the first audio converter was built.
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bruno putzeys

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Re: Are linear phase LP and HP filters possible in analogue domain?
« Reply #5 on: October 25, 2010, 03:47:26 AM »

johnR wrote on Sat, 23 October 2010 18:59

There seems to be some disagreement over terminology between analogue and digital filter designers. DSP programmers appear to define linear phase as constant group delay over the whole frequency range.

This is indeed the case.
Jim Williams wrote on Sun, 24 October 2010 16:19

All filters whether digital or analog rely on the same principles. Filter functions were realized in both mathematics and the analog domain decades before the first digital filters were created.

Chicken before the egg? Horse before the cart? I can see those deep into digital may find it hard to understand that these audio functions were around many decades before the first audio converter was built.

Digital is a red herring. The difference is sampled vs continuous time. You can't make an FIR filter without either a tapped delay or a sampler.
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Geoff Emerick de Fake

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Re: Are linear phase LP and HP filters possible in analogue domain?
« Reply #6 on: October 28, 2010, 06:06:42 PM »

I reckon one could make a multi-tap filter using a large number of analog all-pass filters. The linear-phase operation would be restricted to a finite frequency domain, just like digital systems. The overall performance would certainly be somewhat limited, because of the noise and THD build-up.
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Bogic Petrovic

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Re: Are linear phase LP and HP filters possible in analogue domain?
« Reply #7 on: October 28, 2010, 09:19:26 PM »

Geoff Emerick de Fake wrote on Fri, 29 October 2010 00:06

.....The overall performance would certainly be somewhat limited, because of the noise and THD build-up.


Indeed.
One of my first jobs was upgrading/replacing an old FIR filter based on an ultrasonic quartz delay lines, similar to those described in paper http://www.ieee-uffc.org/main/awards/outpapers/t7140201.pdf (paper doesn't have any relations with my early job, I found it with google Smile )
Digital upgrade of this filter with fast 8 or 10-bit (I dont remember now) ADC, DAC, a fixed digital delay lines realized with fast static RAM, digital multipliers and summers (all "discrete" HCMOS gates,  Very Happy  no FPGA! Shocked )... has a wider frequency range and better signal to noise ratio, without too much sweating.... comparison was possible because system must still have interchangeable old and new filters

regards
Boggy

Geoff Emerick de Fake

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Re: Are linear phase LP and HP filters possible in analogue domain?
« Reply #8 on: October 29, 2010, 09:05:36 AM »

bruno putzeys wrote on Mon, 25 October 2010 02:47

johnR wrote on Sat, 23 October 2010 18:59

There seems to be some disagreement over terminology between analogue and digital filter designers. DSP programmers appear to define linear phase as constant group delay over the whole frequency range.

This is indeed the case.
In all practicality, is that really a necessity? Considering cross-overs, for example, phase needs be linear only one octave away of the corner frequency for a 4th-order filter with an attenuation of 20dB at 0.5Fc (HiPass) or 2Fc (Low-pass). Even with phase completely wrong there and away, the recombination error is less than +/-1dB.
OTOH, I never understood how one could justify calling the attached example a linear-phase filter. Even the comment on the left doesn't make sense to me...
index.php/fa/15722/0/
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bruno putzeys

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Re: Are linear phase LP and HP filters possible in analogue domain?
« Reply #9 on: October 30, 2010, 07:33:10 AM »

Geoff Emerick de Fake wrote on Fri, 29 October 2010 15:05

In all practicality, is that really a necessity? Considering cross-overs, for example, phase needs be linear only one octave away of the corner frequency for a 4th-order filter with an attenuation of 20dB at 0.5Fc (HiPass) or 2Fc (Low-pass). Even with phase completely wrong there and away, the recombination error is less than +/-1dB.

Phase linearity in crossover filters is besides the point. The primary requirement of a crossover filter (including the contribution of the drive units) is that it has to add to unity magnitude ie. a "recombination error" of exactly none at all. Butterworth filters do that, and so do double butterworth aka Linkwitz-Reiley filters.

Requirements to the phase shift of the two filters separately only relate to off-axis behaviour. Linkwitz-Riley wins because you can get identical phase shifts from DC to light.

Other than that the only phase requirement one can think of as concerns crossover filters are what the phase shift of the sum is, because anything beyond the physically impossible 1st order crossover will result in an all-pass filter.

Geoff Emerick de Fake wrote on Fri, 29 October 2010 15:05

OTOH, I never understood how one could justify calling the attached example a linear-phase filter. Even the comment on the left doesn't make sense to me...

I don't even see what the problem is. A chebychev filter is a filter in which the magnitude response is allowed to ripple within bounds such as to stretch the "flat" range beyond the asymptotic cut-off. A butterworth filter is a filter which is mathematically maximally flat meaning the first 2n-1 derivatives of the magnitude response at DC are zero.
A Bessel filter is one where the group delay response is maximally flat in the same vein and a filter with equiripple group delay is one where the group delay is allowed to vary within narrow bounds so that it remains more or less constant over a wider range.
Like chebychev and butterworth are two interpretations of "flat magnitude", bessel and equiripple phase error filters are two approximations of "flat group delay".
Provided you allow the definition of linear phase to stretch all the way to its original meaning i.e. approximately constant group delay across the pass band, this new filter is an approximation of the ideal just like a bessel filter is an approximation of the ideal.
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Geoff Emerick de Fake

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Re: Are linear phase LP and HP filters possible in analogue domain?
« Reply #10 on: October 31, 2010, 09:09:28 PM »

bruno putzeys wrote on Sat, 30 October 2010 06:33

Geoff Emerick de Fake wrote on Fri, 29 October 2010 15:05

In all practicality, is that really a necessity? Considering cross-overs, for example, phase needs be linear only one octave away of the corner frequency for a 4th-order filter with an attenuation of 20dB at 0.5Fc (HiPass) or 2Fc (Low-pass). Even with phase completely wrong there and away, the recombination error is less than +/-1dB.

Phase linearity in crossover filters is besides the point. The primary requirement of a crossover filter (including the contribution of the drive units) is that it has to add to unity magnitude ie. a "recombination error" of exactly none at all.
This is a very restrictive view. Primary requirements of crossover filters are: best pressure response, best energy response and best overall phase response. Very often, these are conflicting constraints, so compromises have to be made; in that case "none error at all is somewhat abusive.
Quote:

 Butterworth filters do that, and so do double butterworth aka Linkwitz-Reiley filters.
Agreed for L-R24, but Butterworth 2nd order and LR12 have terrible phase response (drivers must be wired with opposite polarity) and B3 has incorrect energy response.
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 Requirements to the phase shift of the two filters separately only relate to off-axis behaviour. Linkwitz-Riley wins because you can get identical phase shifts from DC to light.

Other than that the only phase requirement one can think of as concerns crossover filters are what the phase shift of the sum is, because anything beyond the physically impossible 1st order crossover will result in an all-pass filter.
You seem to forget that linear-phase FIR filters have the same benefits AND an overall minimum-phase response.
OK, let's forget about crossovers. Then again: In all practicality, is linear phase really a necessity? Let's consider a HPF on a mic, used for attenuating parasitic noise. What is the point of making sure the remnants of noise are still time-aligned with the useful signal?
Or a parametric EQ; is it important that the frequency range that is boosted remains time-aligned with the rest of the spectrum?
If it was such an issue, one would use a phase equalizer to improve a signal without changing its spectral balance.
Quote:



Geoff Emerick de Fake wrote on Fri, 29 October 2010 15:05

OTOH, I never understood how one could justify calling the attached example a linear-phase filter. Even the comment on the left doesn't make sense to me...

I don't even see what the problem is. A chebychev filter is a filter in which the magnitude response is allowed to ripple within bounds such as to stretch the "flat" range beyond the asymptotic cut-off. A butterworth filter is a filter which is mathematically maximally flat meaning the first 2n-1 derivatives of the magnitude response at DC are zero.
A Bessel filter is one where the group delay response is maximally flat in the same vein and a filter with equiripple group delay is one where the group delay is allowed to vary within narrow bounds so that it remains more or less constant over a wider range.
Like chebychev and butterworth are two interpretations of "flat magnitude", bessel and equiripple phase error filters are two approximations of "flat group delay".
Provided you allow the definition of linear phase to stretch all the way to its original meaning i.e. approximately constant group delay across the pass band, this new filter is an approximation of the ideal just like a bessel filter is an approximation of the ideal.
So, in analog, linear-phase means constant over the passband, in digital it means constant from DC to Nyquist. What's the validity of comparison, then? Different design rules!
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bruno putzeys

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Re: Are linear phase LP and HP filters possible in analogue domain?
« Reply #11 on: November 01, 2010, 06:28:00 AM »

*Yes I should've specified odd order butterworth of course.
*A flat on-axis response is the primary requirement of a speaker. A speaker which is "great" except for the on-axis response is not a "great" speaker, is it? The second most important requirement is off-axis behaviour and, linked with that, energy response. A close third is to optimize crossover frequencies and slopes to minimize distortion. Overall phase is almost completely unimportant. If you can fix overall phase without in any way affecting the previous two items, great, do so, and be prepared to hear almost no improvement at all. In analogue systems you cannot improve the overal phase response without seriously affecting the other requirements, so you will gain a tiny improvement at the expense of a serious and much more audible performance loss elsewhere. Overall phase must never be a requirement in analogue speaker design. Linear phase is fantastically overrated.
From the above it follows that a flat sum is the primary requirement to the crossover function, as measured acoustically.
*I am not arguing that linear phase is important, as the above makes clear.
*Why would anyone suddenly differ with a definition. If "linear phase" as applied to analogue and IIR filters means "somehow approximating perfectly linear phase over the pass-band" in precisely the same vain as "flat magnitude response" means "somehow approximating flat over the pass-band", what's wrong with that definition. Just keep in mind that the definition is not the same as that used in FIR filters because symmetrical FIR filters have perfectly linear phase by definition, permitting a more restrictive definition. The meaning of definitions is unrelated to the sensibility of practical applications.
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Geoff Emerick de Fake

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Re: Are linear phase LP and HP filters possible in analogue domain?
« Reply #12 on: November 01, 2010, 06:12:57 PM »

bruno putzeys wrote on Mon, 01 November 2010 05:28

 *A flat on-axis response is the primary requirement of a speaker. A speaker which is "great" except for the on-axis response is not a "great" speaker, is it?
This is certainly true for studio monitors. For SR speakers, the off-axis behaviour is as important as on-axis response.
Quote:


A close third is to optimize crossover frequencies and slopes to minimize distortion.
Although I cannot say that, for SR speakers, it's THE paramount factor, it certainly is the very beginning in the specification phase.
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 Overall phase is almost completely unimportant. If you can fix overall phase without in any way affecting the previous two items, great, do so, and be prepared to hear almost no improvement at all. In analogue systems you cannot improve the overal phase response without seriously affecting the other requirements, so you will gain a tiny improvement at the expense of a serious and much more audible performance loss elsewhere. Overall phase must never be a requirement in analogue speaker design. Linear phase is fantastically overrated.
I agre 100%.
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 *I am not arguing that linear phase is important, as the above makes clear.
Yes, I understand that and also agree 100% with you. I re-read the different posts and it turns out this subject has been raised by someone else.
Quote:

 *Why would anyone suddenly differ with a definition. If "linear phase" as applied to analogue and IIR filters means "somehow approximating perfectly linear phase over the pass-band" in precisely the same vain as "flat magnitude response" means "somehow approximating flat over the pass-band", what's wrong with that definition. Just keep in mind that the definition is not the same as that used in FIR filters because symmetrical FIR filters have perfectly linear phase by definition, permitting a more restrictive definition. The meaning of definitions is unrelated to the sensibility of practical applications.
What I'm trying to carry through is that there are two misconceptions:
One is that some posters are of the opinion that analog linear-phase filters have the same performance as FIR linear-phase filters, i.e. absolutely constant delay from DC to Nyquist. That is the subject of the OP.
Two is that many think that digital linear-phase filters are perfect because they don't tamper with the timing of signals, which is absolutely untrue. Pre-ringing is seriously tampering with timing, IMO.
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Mo Facta

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Re: Are linear phase LP and HP filters possible in analogue domain?
« Reply #13 on: November 02, 2010, 02:22:14 AM »

Anyone remember the Nightpro (NTI) EQ3?  

http://junctionmusic.jp/images/USED/0501_eq3_01.jpg

If I remember correctly, it claimed to be a hardware linear phase EQ (or one with VERY little phase shift and distortion).

Anyone here still use one of these?

Cheers Smile  
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Jim Williams

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Re: Are linear phase LP and HP filters possible in analogue domain?
« Reply #14 on: November 02, 2010, 10:21:46 AM »

I met those fellows at the 1995 AES show in LA. I invited them to my shop afterwards to run it through my Audio Precision System One A as they had no test gear to qualify it.

They brought it by and I ran the sweeps. I found it had the same analog phase response as any quality analog bell EQ. THD ran about .005% and the other tests led me to suspect it was constructed using NE5532 opamps.

Alas, after my generosity, I asked to open the hood. They refused saying it was some sort of secret.

Then I gave them a secret way back to LAX.
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