Question about FFT phase

Hi.

I understand that in FFT, we will get both the amplitude and the phase
components. Is it possible to get the same phase value but yet the
amplitudes of the FFT result are different? For example, a signal input
produces a FFT amplitude of 10 and the phase computed is pi/4. If because
of some noise, the FFT amplitude gets influenced and become 4 or 5 or just
some values, and yet the phase could still report as pi/4?

Thanks!
Marc

On Nov 28, 9:37&#4294967295;pm, "Marc2050" <maarcc@n_o_s_p_a_m.gmail.com> wrote:
> Hi.
>
> I understand that in FFT, we will get both the amplitude and the phase
> components. Is it possible to get the same phase value but yet the
> amplitudes of the FFT result are different? For example, a signal input
> produces a FFT amplitude of 10 and the phase computed is pi/4. If because
> of some noise, the FFT amplitude gets influenced and become 4 or 5 or just
> some values, and yet the phase could still report as pi/4?
>
> Thanks!
> Marc

I think in this case you are better off to think of cosine/sine
representation rather than amplitude/phase.  If both the sine
component and cosine component were both exactly reduced to 4 (or
five) together, then you would retain the same phase.  But that is
probably unlikely. That much noise would almost certainly be moving
the phase around.

>On Nov 28, 9:37=A0pm, "Marc2050" <maarcc@n_o_s_p_a_m.gmail.com> wrote:
>> Hi.
>>
>> I understand that in FFT, we will get both the amplitude and the phase
>> components. Is it possible to get the same phase value but yet the
>> amplitudes of the FFT result are different? For example, a signal input
>> produces a FFT amplitude of 10 and the phase computed is pi/4. If
because
>> of some noise, the FFT amplitude gets influenced and become 4 or 5 or
jus=
>t
>> some values, and yet the phase could still report as pi/4?
>>
>> Thanks!
>> Marc
>
>I think in this case you are better off to think of cosine/sine
>representation rather than amplitude/phase.  If both the sine
>component and cosine component were both exactly reduced to 4 (or
>five) together, then you would retain the same phase.  But that is
>probably unlikely. That much noise would almost certainly be moving
>the phase around.
>

So in practical term, is this possible to happen? That is, in practice, is
it possible for us to encounter cases where the phase remains more or less
in synchrony (ie. they didnt seem to vary much from, e.g., pi/4) while the
amplitudes seem to be random sort of values (or lies within quite a wide
range, say between 2 to 10)?

Thanks!

>On Nov 28, 9:37=A0pm, "Marc2050" <maarcc@n_o_s_p_a_m.gmail.com> wrote:
>> Hi.
>>
>> I understand that in FFT, we will get both the amplitude and the phase
>> components. Is it possible to get the same phase value but yet the
>> amplitudes of the FFT result are different? For example, a signal input
>> produces a FFT amplitude of 10 and the phase computed is pi/4. If
because
>> of some noise, the FFT amplitude gets influenced and become 4 or 5 or
jus=
>t
>> some values, and yet the phase could still report as pi/4?
>>
>> Thanks!
>> Marc
>
>I think in this case you are better off to think of cosine/sine
>representation rather than amplitude/phase.  If both the sine
>component and cosine component were both exactly reduced to 4 (or
>five) together, then you would retain the same phase.  But that is
>probably unlikely. That much noise would almost certainly be moving
>the phase around.
>

So in practical term, is this possible to happen? That is, in practice, is
it possible for us to encounter cases where the phase remains more or less
in synchrony (ie. they didnt seem to vary much from, e.g., pi/4) while the
amplitudes seem to be random sort of values (or lies within quite a wide
range, say between 2 to 10)?

Thanks!

Marc2050 <maarcc@n_o_s_p_a_m.gmail.com> wrote:

> I understand that in FFT, we will get both the amplitude and the phase
> components. Is it possible to get the same phase value but yet the
> amplitudes of the FFT result are different? For example, a signal input
> produces a FFT amplitude of 10 and the phase computed is pi/4. If because
> of some noise, the FFT amplitude gets influenced and become 4 or 5 or just
> some values, and yet the phase could still report as pi/4?

The output of the FFT is the real and imaginary parts.  

From those, you can generate magnitude and phase.

The rounding properties of the FFT are usually better than
the direct DFT, but you could be unlucky.  It is possible that in 
some cases the magnitude might be very small, mostly rounding noise.

In that case, it is hard to say much about the phase, but possibly
it could still come out close to an expected value like pi/4.

I could imagine cases where both the real and imaginary parts
were the result of subtracting nearly equal values, and so have
very few, maybe only one, significant bit.  They could be equal,
and so generate a pi/4 phase term.

Otherwise, it would be rare to accidentally get a similar phase
when the real and imaginary parts changed independently.
Unexpected dependence, more commonly known as systematic error,
can cause surprising results, though.

-- glen

On 11/28/2011 6:59 PM, Marc2050 wrote:
>> On Nov 28, 9:37=A0pm, "Marc2050"<maarcc@n_o_s_p_a_m.gmail.com>  wrote:
>>> Hi.
>>>
>>> I understand that in FFT, we will get both the amplitude and the phase
>>> components. Is it possible to get the same phase value but yet the
>>> amplitudes of the FFT result are different? For example, a signal input
>>> produces a FFT amplitude of 10 and the phase computed is pi/4. If
> because
>>> of some noise, the FFT amplitude gets influenced and become 4 or 5 or
> jus=
>> t
>>> some values, and yet the phase could still report as pi/4?
>>>
>>> Thanks!
>>> Marc
>>
>> I think in this case you are better off to think of cosine/sine
>> representation rather than amplitude/phase.  If both the sine
>> component and cosine component were both exactly reduced to 4 (or
>> five) together, then you would retain the same phase.  But that is
>> probably unlikely. That much noise would almost certainly be moving
>> the phase around.
>>
>
> So in practical term, is this possible to happen? That is, in practice, is
> it possible for us to encounter cases where the phase remains more or less
> in synchrony (ie. they didnt seem to vary much from, e.g., pi/4) while the
> amplitudes seem to be random sort of values (or lies within quite a wide
> range, say between 2 to 10)?
>
> Thanks!

Lots of things are possible.  Consider classical FM modulation - which 
is just a form of phase modulation.  In practice the received amplitudes 
can vary quite a bit.  But, that doesn't affect the phase (in the 
passband) all that much and the detected signal is still solid as long 
as there's adequate SNR.  Often the "carrier" is clipped in the receiver 
before phase/frequency detection .. so amplitude is unimportant.  This 
is sort of important to your question because it brings "bandwidth" into 
the picture.  Yet, your FFT question limits bandwidth and, it seems, you 
are really referring to a single pair of complex samples at a single 
frequency ... so not much in the way of "bandwidth", eh?

I don't think it matters much whether you consider sin and cos or 
amplitude and phase as they are so closely related.  But maybe sin and 
cos components help you envision the situation and that's a help.  So, I 
agree with Brent.

You might want to ponder what happens in the FM case.  I think you'll 
find that individual frequency values change all over the place 
(depending on the time window).  Phase and amplitude changes imply some 
bandwidth.

I hope this helps move you in a useful direction with your question.

Fred

>On 11/28/2011 6:59 PM, Marc2050 wrote:
>>> On Nov 28, 9:37=A0pm, "Marc2050"<maarcc@n_o_s_p_a_m.gmail.com>  wrote:
>>>> Hi.
>>>>
>>>> I understand that in FFT, we will get both the amplitude and the
phase
>>>> components. Is it possible to get the same phase value but yet the
>>>> amplitudes of the FFT result are different? For example, a signal
input
>>>> produces a FFT amplitude of 10 and the phase computed is pi/4. If
>> because
>>>> of some noise, the FFT amplitude gets influenced and become 4 or 5 or
>> jus=
>>> t
>>>> some values, and yet the phase could still report as pi/4?
>>>>
>>>> Thanks!
>>>> Marc
>>>
>>> I think in this case you are better off to think of cosine/sine
>>> representation rather than amplitude/phase.  If both the sine
>>> component and cosine component were both exactly reduced to 4 (or
>>> five) together, then you would retain the same phase.  But that is
>>> probably unlikely. That much noise would almost certainly be moving
>>> the phase around.
>>>
>>
>> So in practical term, is this possible to happen? That is, in practice,
is
>> it possible for us to encounter cases where the phase remains more or
less
>> in synchrony (ie. they didnt seem to vary much from, e.g., pi/4) while
the
>> amplitudes seem to be random sort of values (or lies within quite a
wide
>> range, say between 2 to 10)?
>>
>> Thanks!
>
>Lots of things are possible.  Consider classical FM modulation - which 
>is just a form of phase modulation.  In practice the received amplitudes 
>can vary quite a bit.  But, that doesn't affect the phase (in the 
>passband) all that much and the detected signal is still solid as long 
>as there's adequate SNR.  Often the "carrier" is clipped in the receiver 
>before phase/frequency detection .. so amplitude is unimportant.  This 
>is sort of important to your question because it brings "bandwidth" into 
>the picture.  Yet, your FFT question limits bandwidth and, it seems, you 
>are really referring to a single pair of complex samples at a single 
>frequency ... so not much in the way of "bandwidth", eh?
>
>I don't think it matters much whether you consider sin and cos or 
>amplitude and phase as they are so closely related.  But maybe sin and 
>cos components help you envision the situation and that's a help.  So, I 
>agree with Brent.
>
>You might want to ponder what happens in the FM case.  I think you'll 
>find that individual frequency values change all over the place 
>(depending on the time window).  Phase and amplitude changes imply some 
>bandwidth.
>
>I hope this helps move you in a useful direction with your question.
>
>Fred
>

The FM idea is very interesting...
The background of my question is really more related to classifying neural
signals. If I understand correctly, therefore, it is better to use phase
component of the FFT to classify neural signal than it is to use
amplitude to classify. Is this right?
Thank you.

On 12/1/11 10:39 PM, Marc2050 wrote:

> The background of my question is really more related to classifying neural
> signals. If I understand correctly, therefore, it is better to use phase
> component of the FFT to classify neural signal than it is to use
> amplitude to classify. Is this right?

uhhh, i think that would be a question to ask the person researching 
neurophysiology.  your question (which is "better") about a class of 
signals where a neurologist would know a lot more about the origin than 
an assemblage of mostly electrical engineers and physicists who like to 
discuss signal processing methods.

what little i have gathered is that neural firing is a little bit like a 
sequence of impulses spaced apart in time according to some p.d.f. 
function that might look like a Raleigh distribution.  now, i dunno how 
one might translate that to a frequency-domain model and make some guess 
about whether the variation of magnitude stands out more than the 
variation of phase, or which of the two somehow couple statistically to 
some parameter of salience to the neurology guys.  thems are the guys 
who would know.

-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

On 12/1/2011 7:39 PM, Marc2050 wrote:

>>
>
> The FM idea is very interesting...
> The background of my question is really more related to classifying neural
> signals. If I understand correctly, therefore, it is better to use phase
> component of the FFT to classify neural signal than it is to use
> amplitude to classify. Is this right?
> Thank you.
>

No.  That's not what I was implying at all.  It's just that FM is sort 
of an example of what you asked about but is also different because of 
the bandwidth.  So, maybe that makes it a counter-example?

When you said:
"For example, a signal input produces a FFT amplitude of 10 and the 
phase computed is pi/4. If because of some noise, the FFT amplitude gets 
influenced and become 4 or 5 or just some values, and yet the phase 
could still report as pi/4?"

That rather reminded me of FM where the amplitude can vary a lot, 
including due to additive noise, but where the phase is the important 
information.  That's all .....

I think this idea of separating phase and amplitude is likely a dead end 
and see no strong reason for doing so anyway.

Fred

On 2 Des, 04:39, "Marc2050" <maarcc@n_o_s_p_a_m.gmail.com> wrote:

> The FM idea is very interesting...
> The background of my question is really more related to classifying neural
> signals. If I understand correctly, therefore, it is better to use phase
> component of the FFT to classify neural signal than it is to use
> amplitude to classify. Is this right?

Don't confuse Phase / Frequency Modulation with
the phase spectrum!

PM/FM is a non-linear modulation technique which
has nothing to do with the linear FT at all. What
happens in PM/FM is that the baseband source signal
is nonlinearly transformed to a signal at RF which
has far greater bandwidth than the source signal
itself.

Forget about phase spectra at all. They have very
little use, and are extremely sensitive to noise.
There is nothing to be learned from studying
phase spectra.

Rune