Amplitude Time Ave. w/o Rectification

Bret Cahill wrote:

Why the concern over whether a method is a form of
"rectification" or not? =A0What are you really trying to
measure?

The magnitude of a randomly fluctuating signal over a period of time.
This doesn't include the trivial case where the time the signal is
positive is integrated along with the time the signal is negative.

Peak to peak will only work with a known waveform so it looks more and
more like it must involve taking absolute values or sqrts of sum of
squares at some point which would ordinarily be considered
"rectification" even in a relatively narrow sense of the word.

You haven't explained what's wrong with "rectification",


Nothing is wrong with rectification. It's not only the best way.
It's the only way.
Did you look at the precision rectifier links I gave you ?

I haven't seen any reference to what BW you are interested in?


Jamie.
 
Why the concern over whether a method is a form of
"rectification" or not? =A0What are you really trying to
measure?

The magnitude of a randomly fluctuating signal over a period of time.
This doesn't include the trivial case where the time the signal is
positive is integrated along with the time the signal is negative.

Peak to peak will only work with a known waveform so it looks more and
more like it must involve taking absolute values or sqrts of sum of
squares at some point which would ordinarily be considered
"rectification" even in a relatively narrow sense of the word.

You haven't explained what's wrong with "rectification",
Nothing is wrong with rectification. It's not only the best way.
It's the only way.

and
especially true RMS for this purpose.

Best regards,

Bob Masta

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On Nov 10, 11:43 am, Bret Cahill <Bret_E_Cah...@yahoo.com> wrote:
As pointed out above amplitude is always positive.  A Fourier
transform is always positive so that might be one way to determine the
magnitude of the signal over time.

Huh?  A Fourier transform produces real and imaginary
arrays, any component of which may be negative.  

If the only information displayed in the FFT is an amplitude and a
phase angle for each frequency, and if amplitude is always positive as
suggested above, then amplitudes are always positive in an FFT.

Even a negative dc offset could be represented as a positive 0 Hz
spike with a 180 degree phase angle.

It is
common to display the *magnitude* at each frequency bin, but
that involves a separate step (square root of
sum-of-squares), which I assume you would call
rectification.

In that case there seems to be no way to end run rectification.

It might be hard to argue that a FFT is rectification.  When you
rectify by diode or resistor you lose some information.  You no longer
know when the unrectified signal was positive or negative.
Not true for the FFT.
If you only take the magnitude, to get the "always positive"
result you mention, then that of course has no information
about the original polarity.  

A phase angle for each frequency would allow recovery the sign of the
signal in the time domain.

You can also compute the phase
at each frequency bin, as a separate operation on the same
real and imaginary arrays.  Is that what you are talking
about?

Yes.

Why the concern over whether a method is a form of
"rectification" or not?  What are you really trying to
measure?

The magnitude of a randomly fluctuating signal over a period of time.
This doesn't include the trivial case where the time the signal is
positive is integrated along with the time the signal is negative.

Peak to peak will only work with a known waveform so it looks more and
more like it must involve taking absolute values or sqrts of sum of
squares at some point which would ordinarily be considered
"rectification" even in a relatively narrow sense of the word.

Bret Cahill
I haven't read the whole thread as it seems rather long and possibly
contentious. But if you are saying that an FFT performs rectification
in any sense, I don't think that is true. Maybe I misunderstand what
you are saying.

BTW, why do you want to avoid rectification when performing this
measurement? Also, how exactly do you define "rectification"? If you
want a magnitude off the signal, by definition that will be always
positive and like would be considered rectification. The FFT does not
inherently calculate the magnitude, rather it results in a complex
number allowing both phase and magnitude to be calculated.

Rick
 
On Nov 5, 5:10 pm, Bret Cahill <BretCah...@peoplepc.com> wrote:
Is there anyway to get an amplitude of an ac signal averaged over time
w/o some kind of rectification?

This doesn't include the trivial, i.e., dc offsets or partial cycles.

The rectification could be analog, digital or software.

Bret Cahill

You need a precision rectifier..
   couple of op-amps and maybe 1 diode ..

http://sound.westhost.com/appnotes/an001.htm

Poorly written OP.  The goal is getting the amplitude _without_
rectification.  Rectification" is to be very broadly construed and
includes anything that results in the final "signal" being positive at
all times.

Maybe peak to peak wil work if you know the wave form.

Bret Cahill
Ok, this is making some sense. If you want to measure amplitude, by
definition this is always going to be a positive number, right? Even
your peak to peak measurement should provide a positive value which is
rectification according to your definition I believe.

Rick
 
As pointed out above amplitude is always positive.  A Fourier
transform is always positive so that might be one way to determine the
magnitude of the signal over time.

Huh?  A Fourier transform produces real and imaginary
arrays, any component of which may be negative.  

If the only information displayed in the FFT is an amplitude and a
phase angle for each frequency, and if amplitude is always positive as
suggested above, then amplitudes are always positive in an FFT.

Even a negative dc offset could be represented as a positive 0 Hz
spike with a 180 degree phase angle.

It is
common to display the *magnitude* at each frequency bin, but
that involves a separate step (square root of
sum-of-squares), which I assume you would call
rectification.

In that case there seems to be no way to end run rectification.

It might be hard to argue that a FFT is rectification.  When you
rectify by diode or resistor you lose some information.  You no longer
know when the unrectified signal was positive or negative.
Not true for the FFT.
If you only take the magnitude, to get the "always positive"
result you mention, then that of course has no information
about the original polarity.  

A phase angle for each frequency would allow recovery the sign of the
signal in the time domain.

You can also compute the phase
at each frequency bin, as a separate operation on the same
real and imaginary arrays.  Is that what you are talking
about?

Yes.

Why the concern over whether a method is a form of
"rectification" or not?  What are you really trying to
measure?

The magnitude of a randomly fluctuating signal over a period of time.
This doesn't include the trivial case where the time the signal is
positive is integrated along with the time the signal is negative.

Peak to peak will only work with a known waveform so it looks more and
more like it must involve taking absolute values or sqrts of sum of
squares at some point which would ordinarily be considered
"rectification" even in a relatively narrow sense of the word.

Bret Cahill

I haven't read the whole thread as it seems rather long and possibly
contentious.  But if you are saying that an FFT performs rectification
in any sense, I don't think that is true.  
The always positive frequency domain graph is apparently generated by
taking the square root of the sum of the square of the real and the
square of the imaginary components of each frequency.

That seems like rectification.

Maybe I misunderstand what
you are saying.

BTW, why do you want to avoid rectification when performing this
measurement?  
Just checking to make sure that is the only way.

Also, how exactly do you define "rectification"?  
Absolute value and sqrt of sum of squares.

If you
want a magnitude off the signal, by definition that will be always
positive and like would be considered rectification.  
Maybe by definition.

The FFT does not
inherently calculate the magnitude, rather it results in a complex
number allowing both phase and magnitude to be calculated.
By taking the sqrt of the sum of the squares which is rectification.


Bret Cahill
 
Why the concern over whether a method is a form of
"rectification" or not? =A0What are you really trying to
measure?

The magnitude of a randomly fluctuating signal over a period of time.
This doesn't include the trivial case where the time the signal is
positive is integrated along with the time the signal is negative.

Peak to peak will only work with a known waveform so it looks more and
more like it must involve taking absolute values or sqrts of sum of
squares at some point which would ordinarily be considered
"rectification" even in a relatively narrow sense of the word.

You haven't explained what's wrong with "rectification",

Nothing is wrong with rectification.  It's not only the best way.
It's the only way.

  Did you look at the precision rectifier links I gave you ?
I've been using the ones provided by LT SPICE.

  I haven't seen any reference to what BW you are interested in?
This is just a general question.


Bret Cahill
 
Is there anyway to get an amplitude of an ac signal averaged over time
w/o some kind of rectification?

This doesn't include the trivial, i.e., dc offsets or partial cycles.

The rectification could be analog, digital or software.

Bret Cahill

You need a precision rectifier..
   couple of op-amps and maybe 1 diode ..

http://sound.westhost.com/appnotes/an001.htm

Poorly written OP.  The goal is getting the amplitude _without_
rectification.  Rectification" is to be very broadly construed and
includes anything that results in the final "signal" being positive at
all times.

Maybe peak to peak wil work if you know the wave form.

Bret Cahill

Ok, this is making some sense.  If you want to measure amplitude, by
definition this is always going to be a positive number, right?  Even
your peak to peak measurement should provide a positive value which is
rectification according to your definition I believe.
I was thinking that myself.


Bret Cahill
 
In comp.dsp Bret Cahill <Bret_E_Cahill@yahoo.com> wrote:
(big snip regarding FFT and rectification)

The always positive frequency domain graph is apparently generated by
taking the square root of the sum of the square of the real and the
square of the imaginary components of each frequency.

That seems like rectification.
Well, it is usual to also keep atan2(y,x), in which case no
information is lost. You have to somehow lose that information.

Consider a DVM where the minus LED is broken. There is no
rectification, but the information regarding the sign is lost.

I tend to think of rectification as a physical process, applied
to analog signals. As far radio receivers, it is normally followed
by a low-pass filter. If one does the same with a digitized
version, then I would have to agree that it is rectification.

-- glen
 

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