I guess the answer will be no, but I'll ask anyway. Is it possible to build an analogue low pass filter that doesn't cause phase shift while still in the (almost)flat gain region?

Let's say a filter with a cutoff frequency of 200Hz will start changing the output signal phase well before 200Hz, an undesired behaviour. This is even worse with higher order filters.

With inductors maybe?

 

I don't think so. IIRC the phase is controlled by the bandwidth and the number of poles. Increasing the number of poles is equivalent to increasing the order of the filter. What are you actually trying to do?

 

I want to understand how noise cancelling headphones work, especially why they have to be so expensive. Maybe they use DSPs, but I was thinking, can't it be done with less? I understand that most effectively low frequencies can be cancelled because the wavelength is quite long. However, how do they account for this phase shift when inverting the incoming signal?

There is a region where there is almost no attenuation and a phase shift.

edit: I see why it's not easily possible. I would to know what will happen in the future to be able to compensate for the phase shift... At least for a simple RC

 

It might be that noise canceling headphones are a scam. You need to start by understanding the characteristics of different kinds of noise.

 

Yes , some are scam. The high-end headphones from Bose for example are not. The over-the-ear headphones rely on absorption for higher frequencies and destructive interference for lower frequencies. Since they apparently work better for continuous (predictable) low frequency patterns I could imagine they "predict" the next period and could adapt the compensation signal phase accordingly.

The concept has been proposed decades ago. It is difficult to implement in real-world situations due to unpredictable diffraction etc... It kind of really works, within certain limits. It does not account for sound conducted through the body/scull though.

 

I think any scheme based on prediction is doomed to produce marginal results. Elimination at the source seems to provide greater bang for the buck. What is the noise source you are concerned about? Is it in the signal or is it external?

 

I think any scheme based on prediction is doomed to produce marginal results. Elimination at the source seems to provide greater bang for the buck. What is the noise source you are concerned about? Is it in the signal or is it external?

It is varying noise sources from the outside of my home. Mainly low frequency noise (up to about 400Hz, but in general lower) from vehicles. A common exterior wall absorbs a lot of higher frequency noise, the lows pass through.
I know, the walls can be modified to absorb more sound energy but that's expensive too.

I'd prefer an electronic solution but I am still a little unclear about all the phase shifts involved.

 

Just don't put the pole to close to your 400Hz. target.

 

Just don't put the pole to close to your 400Hz. target.

Can you elaborate?

A simple 2nd order opamp filter may have a more or less flat gain response until 200Hz. It's output phase starts shifting well before that. At 200Hz it can be 70 to 90 degree depending on the type of filter... How do the handle this?

 

So let me get this straight. You have a noise source in the low audio range of 20-400Hz and you want to eliminate the noise electronically on the basis of frequency (you said low pass filter). I don't see what phase has to do with anything at all since the filter cannot distinguish between signal and noise under any conceivable conditions that I can imagine.

 

So let me get this straight. You have a noise source in the low audio range of 20-400Hz and you want to eliminate the noise electronically on the basis of frequency (you said low pass filter). I don't see what phase has to do with anything at all since the filter cannot distinguish between signal and noise under any conceivable conditions that I can imagine.

As I explained they use destructive interference. A noise signal is captured with a microphone, amplified and given exactly phase inverted to the headphone speaker. The result is an attenuated signal. In a headphone there is only one speaker, which has to be broadband since you still will want to hear music. Since destructive interference doesn't work well with higher frequencies the low noise part has to be filtered out. If the phase of the the low pass filter output signal is not steady then how to compensate the signal correctly so that the sum of noise plus compensating signal will be zero. (or almost zero).

That's why I think they maybe use a fixed group delay for the whole range up to the cutoff frequency. Not considering other phase shifts in the system this would have to be 360 degrees phase shift.

 

Ok, so it is not prediction. It delays everything by a constant amount, signal, noise, and cancelation signal. So why do you need a low pass filter?

 

So why do you need a low pass filter?

Good question. I think it has to do with the fact that the noise signal is not measured where it should be canceled; at the eardrum. It is measured a few centimeters away from it. At e.g. 10kHz the wavelength is 3.4cm, I assume the cancellation signal cannot be precisely predicted at this higher frequency for a variety of users. So they limit the cancellation to lower frequencies. Therefore the filter.

It looks easy at first but the deeper you dig the more complex it becomes.

 

Not sure why you need a filter either, but if you put the pole at say 10KHz there would only be a few degrees at 400 Hz. I think if I did a filter at all I would just use a 1st order since you don't need to subtract anything above 400Hz. anyway

 

Not sure why you need a filter either,

Because without filter ALL frequencies would be treated (inverted) even the higher once that are not supposed to be part of the compensating signal sent to the headphone speaker.

 

Well, it won't work both ways. You can't roll it off and still use it to cancel something. Since you said there is not outside noise above 400Hz. you don't care what the phase is above 400 Hz. because there is no signal to subtract from the music.

 

Well, it won't work both ways. You can't roll it off and still use it to cancel something. Since you said there is not outside noise above 400Hz. you don't care what the phase is above 400 Hz. because there is no signal to subtract from the music.

Little misunderstanding here I guess. The high frequency part of the outside noise is absorbed by the exterior wall. That doesn't mean that inside the house there do not exist other noise sources. The goal is to ignore the high frequency part of that noise.

That clearly means that a noise signal needs to pass through a low pass, one that doesn't shift the phase while still in a region where it doesn't have enough attenuation.

 

So just open up the bandwidth to where you still have good phase.

Or why not no filter?