Filter phase response

Hello,

I would like to know the effect of phase response in filters, in practical
applications. 

For example, when dealing with audio signals, if audio signal is passed
through a filter in order to filter out undesired frequency component(s)
and if the filter has linear phase response, I would assume that output
after filtering is equivalent to adding individual frequeny components back
to create filtered output. Now in this case, since each individual
frequencies have undergone unequal phase change, when they are combined
back, the shape of the output would totally change leading to an audio
output which is nowhere near original one.

I will try out an example on this myself but I am not yet fluent in
Matlab.

Thank you,	 

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On Saturday, August 2, 2014 6:32:15 PM UTC+12, SBR123 wrote:
> Hello,
> 
> 
> 
> I would like to know the effect of phase response in filters, in practical
> 
> applications. 
> 
> 
> 
> For example, when dealing with audio signals, if audio signal is passed
> 
> through a filter in order to filter out undesired frequency component(s)
> 
> and if the filter has linear phase response, I would assume that output
> 
> after filtering is equivalent to adding individual frequeny components back
> 
> to create filtered output. Now in this case, since each individual
> 
> frequencies have undergone unequal phase change, when they are combined
> 
> back, the shape of the output would totally change leading to an audio
> 
> output which is nowhere near original one.
> 
> 
> 
> I will try out an example on this myself but I am not yet fluent in
> 
> Matlab.
> 
> 
> 
In a mono recording the ear has no sensitivity to phase. For stereo it may change the position of the stereo image. Audio is not like digital pulses where you need linear phase. I am sure though there are people who talk of peak power and golden connectors who would disagree.

The unequal phase shift you speak of will delay the signal by half the filter length. So it's not really true that it looks nothing like the original. 

Regarding the audibility of phase shift, the ear is insensitive to absolute phase shift (within reason) above a certain frequency (around 1-2 kHz). But below these frequencies it's easy to show you can hear the difference. To prove this to yourself, just cascade a few hi-Q allpass filters with a center frequency around 500 hz and A/B the results. No golden ears are required to hear the difference. 

When designing crossover filters, it is common to use so-called Linkwitz- Riley designs which sum to an allpass response. Unfortunately this can change the sound if the crossover occurs in the low- frequency range. 

Bob

Also the op speaks of a linear phase shift.
This of course means that all the frequencies are delayed by an equal amount of time. 
This is the same as passing the signal through a wire.
But i also agree, phase shift is not audible.
It is an easy experiment to prove to ypurself.
Get two signal generators and set one to 1 kHz and the second to 2.0001 kHz.
Listen to the signal as the harmonic drifts in phase relative to the fundamental.
You will, at least i can,t hear the difference.
Also observe the combined signal on a scope. The waveform changes drasticallly as the phase changes.
You can add more generators if you have them.
Mark

On Sat, 02 Aug 2014 01:32:15 -0500, "SBR123" <100967@dsprelated>
wrote:

>Hello,

Hello mysterious Mr. SBR123,

>I would like to know the effect of phase response in filters, in practical
>applications. 

That's a big subject.  There's much to consider.

>
>For example, when dealing with audio signals, if audio signal is passed
>through a filter in order to filter out undesired frequency component(s)
>and if the filter has linear phase response, I would assume that output
>after filtering is equivalent to adding individual frequeny components back
>to create filtered output. 

Whoa, wait!   Digital filtering does NOT add anything 
to a filter's input signal.   Think about the 
word "filtering."  What does it mean?  What does 
the paper filter in your coffee maker do?  What does 
the engine air filter in your automibile do?

       "First principles, Clarice. SIMPLICITY! 
        Read Marcus Aurelius. Of each particular thing 
        ask: What is it in itself?  What is its nature? 
                           -- Hannibal Lecter

>Now in this case, since each individual
>frequencies have undergone unequal phase change, when they are combined
>back, the shape of the output would totally change leading to an audio
>output which is nowhere near original one.

You've just made one correct statement and then you 
came to a wildy incorrect conclusion!!

I'm too lazy to type a long discourse here on the 
"phase shift" and "time delay" behavior of linear 
phase filters.

SBR123, you have some studying to do.  Seach the web for 
"filter phase response" and "filter group delay."
Study, study, study!  And when you're finished 
studying, ...study some more.
It won't take you too long to learn what you 
need to know about linear-phase filters.

>I will try out an example on this myself but I am not yet fluent in
>Matlab.

The sooner you become familiar with Matlab, 
the sooner you will learn the basics of 
what you need to know about linear-phase filters.

Good Luck,
[-Rick-]

The audibility of low- frequency phase shifts has been well- studied and is no longer a subject of debate. 

Bob

On Saturday, August 2, 2014 10:19:49 PM UTC+12, radam...@gmail.com wrote:
> The unequal phase shift you speak of will delay the signal by half the filter length. So it's not really true that it looks nothing like the original. 
> 
> 
> 
> Regarding the audibility of phase shift, the ear is insensitive to absolute phase shift (within reason) above a certain frequency (around 1-2 kHz). But below these frequencies it's easy to show you can hear the difference. To prove this to yourself, just cascade a few hi-Q allpass filters with a center frequency around 500 hz and A/B the results. No golden ears are required to hear the difference. 
>

Hi-Q all-pass? What the hell do you mean? An all-pass has a flat magnitude response and no Q at all! Do you mean a resonant phase characteristic and flat frequency response? Interesting, but when would that become a problem in a physical system?

Sigh... 


Second - order allpass filters have poles and zeroes that come in pairs. In the Z domain the pairs are at the same angle, with the zeros outside the unit circle and the poles inside. When the poles and zeros are close to the unit circle they are high- q, and exhibit time- domain ringing that can go on for long periods of time. In this case the phase shift can change rapidly. Yes the amplitude is still flat. 

You can't prove audibility of phase shift by playing 2 sine waves. Listen to short pulses instead. 

Bob

On Sunday, August 3, 2014 11:49:24 AM UTC+12, radam...@gmail.com wrote:
> Sigh... 
> 
> 
> 
> 
> 
> Second - order allpass filters have poles and zeroes that come in pairs. In the Z domain the pairs are at the same angle, with the zeros outside the unit circle and the poles inside. When the poles and zeros are close to the unit circle they are high- q, and exhibit time- domain ringing that can go on for long periods of time. In this case the phase shift can change rapidly. Yes the amplitude is still flat. 
> 
> 
> 
> You can't prove audibility of phase shift by playing 2 sine waves. Listen to short pulses instead. 
> 
> 
> 
> Bob

So that maybe proves that the ear can detect such differences, but what is the practical demonstration of this? When do you ever phase-shift speech in this way or does it occur naturally? I think it is a little contrived.

Crossover networks often introduce allpass phase shifts. There's a lot of research out there that shows it is audible especially on headphones, but is it a huge deal? Depends on who is doing the listening. 

Of course if the Q of your allpass is so high that the ringing goes beyond 20ms or so, you would start to hear time-domain effects. 

Bob