Frequency Domain Ramp

[Bret Cahill]

Taking a time derivative after an FFT would be easy on SPICE if you
had some curve that would FFT into a ramp: Just multiply the function
by the ramp.

The inverse transform of a ramp on Excel is complex, the real part
being a small negative offset with a large positive zero frequency.
The imaginary part may work but it looks like it would be hard to
fashion with a circuit even if the curve was known.

Just builting up 2**n voltage sources where frequency = amplitude = n
is tedious. The FFT is, of course, just 2**n peaks that increase
linearly in height on the linear - linear graph. To get a nice ramp
would require an infinite number of voltage sources & frequencies and
amplitudes.

Is there anyway to get a nice smooth envelope -- "envelope" may have
another technical meaning -- over the time domain curve to get a nice
ramp in the FFT?


Bret Cahill

 

[Phil Hobbs]

Bret Cahill wrote:

Taking a time derivative after an FFT would be easy on SPICE if you
had some curve that would FFT into a ramp: Just multiply the function
by the ramp.

The inverse transform of a ramp on Excel is complex, the real part
being a small negative offset with a large positive zero frequency.
The imaginary part may work but it looks like it would be hard to
fashion with a circuit even if the curve was known.

Just builting up 2**n voltage sources where frequency = amplitude = n
is tedious. The FFT is, of course, just 2**n peaks that increase
linearly in height on the linear - linear graph. To get a nice ramp
would require an infinite number of voltage sources& frequencies and
amplitudes.

Is there anyway to get a nice smooth envelope -- "envelope" may have
another technical meaning -- over the time domain curve to get a nice
ramp in the FFT?


Bret Cahill

I suggest getting a copy of "The Fourier Transform and Its Applications"
by Bracewell. It's a good read and has all of this sort of stuff in it.

Cheers

Phil Hobbs


--
Dr Philip C D Hobbs
Principal
ElectroOptical Innovations
55 Orchard Rd
Briarcliff Manor NY 10510
845-480-2058

email: hobbs (atsign) electrooptical (period) net
http://electrooptical.net

 

[Phil Hobbs]

Bret Cahill wrote:

Taking a time derivative after an FFT would be easy on SPICE if you
had some curve that would FFT into a ramp: Just multiply the function
by the ramp.

The inverse transform of a ramp on Excel is complex, the real part
being a small negative offset with a large positive zero frequency.
The imaginary part may work but it looks like it would be hard to
fashion with a circuit even if the curve was known.

Just builting up 2**n voltage sources where frequency = amplitude = n
is tedious. The FFT is, of course, just 2**n peaks that increase
linearly in height on the linear - linear graph. To get a nice ramp
would require an infinite number of voltage sources& frequencies and
amplitudes.

Is there anyway to get a nice smooth envelope -- "envelope" may have
another technical meaning -- over the time domain curve to get a nice
ramp in the FFT?

Bret Cahill

I suggest getting a copy of "The Fourier Transform and Its Applications"
by Bracewell. It's a good read and has all of this sort of stuff in it.

At $500 / copy it better be a good read. That's what university
libraries pay for Russian books on tech esoterica.

Anyway some nuke medicine page claimed the INV FT of a ramp was just 1/
t.

It's somewhat curious that the INV FFT of a function is equal to the
reciprocal of the function but nevertheless 1/t seemed to approach a
ramp on Excel's FFT, at least at higher frequencies.

I couldn't get anything linear on the SPICE FFT but then, I couldn't
get anything to output a 1/t waveform except a crude 10 point plot.

Five hundred bucks? Where do you find that? Try
http://www.abebooks.com and you'll find a whole pile of the second
edition (which is better than good enough) for about $22 plus shipping.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal
ElectroOptical Innovations
55 Orchard Rd
Briarcliff Manor NY 10510
845-480-2058

email: hobbs (atsign) electrooptical (period) net
http://electrooptical.net

 

[Bret Cahill]

Taking a time derivative after an FFT would be easy on SPICE if you
had some curve that would FFT into a ramp:  Just multiply the function
by the ramp.

The inverse transform of a ramp on Excel is complex, the real part
being a small negative offset with a large positive zero frequency.
The imaginary part may work but it looks like it would be hard to
fashion with a circuit even if the curve was known.

Just builting up 2**n voltage sources where frequency = amplitude = n
is tedious.  The FFT is, of course, just 2**n peaks that increase
linearly in height on the linear - linear graph.  To get a nice ramp
would require an infinite number of voltage sources&  frequencies and
amplitudes.

Is there anyway to get a nice smooth envelope -- "envelope" may have
another technical meaning -- over the time domain curve to get a nice
ramp in the FFT?

Bret Cahill

I suggest getting a copy of "The Fourier Transform and Its Applications"
by Bracewell.  It's a good read and has all of this sort of stuff in it..

At $500 / copy it better be a good read. That's what university
libraries pay for Russian books on tech esoterica.

Anyway some nuke medicine page claimed the INV FT of a ramp was just 1/
t.

It's somewhat curious that the INV FFT of a function is equal to the
reciprocal of the function but nevertheless 1/t seemed to approach a
ramp on Excel's FFT, at least at higher frequencies.

I couldn't get anything linear on the SPICE FFT but then, I couldn't
get anything to output a 1/t waveform except a crude 10 point plot.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal
ElectroOptical Innovations
55 Orchard Rd
Briarcliff Manor NY 10510
845-480-2058

email: hobbs (atsign) electrooptical (period) nethttp://electrooptical.net- Hide quoted text -

- Show quoted text -

 

[whit3rd]

On Feb 24, 9:10 am, Bret Cahill <Bret_E_Cah...@yahoo.com> wrote:

Is there anyway to get a nice smooth envelope -- "envelope" may have
another technical meaning -- over the time domain curve to get a nice
ramp in the FFT?

No. The usual FFT for finite sampled sequences is done with circular
boundary conditions, and you must deal with the enormous discontinuity
at that boundary that any frequency-dependent ramp creates.
It isn't a suitable 'test function' in the sense of nicely behaved
functions for the transformation, so it is going to look very nasty in
the time domain (after the inverse transformation of the 'ramp').

 

[Bret Cahill]

Is there anyway to get a nice smooth envelope -- "envelope" may have
another technical meaning -- over the time domain curve to get a nice
ramp in the FFT?

No.  The usual FFT for finite sampled sequences is done with circular
boundary conditions, and you must deal with the enormous discontinuity
at that boundary that any frequency-dependent ramp creates.

Would this be true if every point used by the FFT -- SPICE has a 256
minimum -- was plotted and used by the FFT?

It isn't a suitable 'test function' in the sense of nicely behaved
functions for the transformation, so it is going to look very nasty in
the time domain (after the inverse transformation of the 'ramp').

Plotting 1/t with about 8 points, (0.125, 8) (.25, 4) . . . (8,
0.125) on SPICE then taking the FFT and then taking the reciprocal --
not sure why this step works or is necessary -- isn't a bad ramp, at
least at the lower frequencies.

It would be really convenient if a time derivative could be taken
mathematically without a derivative circuit in either domain.

You cannot take a FFT of a wave form after you've taken its time
derivative in the time domain -- it won't appear in the box -- and in
the frequency domain you only get a derivative w/ respect to
frequency, whatever that is.

There doesn't seem to be an easy way to create a time signal on SPICE
that equals 1/t.


Bret Cahill

 

[Martin Brown]

On 24/02/2011 22:18, Bret Cahill wrote:

Is there anyway to get a nice smooth envelope -- "envelope" may have
another technical meaning -- over the time domain curve to get a nice
ramp in the FFT?

No. The usual FFT for finite sampled sequences is done with circular
boundary conditions, and you must deal with the enormous discontinuity
at that boundary that any frequency-dependent ramp creates.

Would this be true if every point used by the FFT -- SPICE has a 256
minimum -- was plotted and used by the FFT?

It is always true that an FFT has an implicit assumption of periodic
boundary conditions at the length of the transform which are most
commonly a tiled circular wrap around at the edges, but in some
implementations may be Dirichlet or mirror boundary conditions leading
to a DCT variant. In addition there is also two plausible choices of
origin exactly in the centre of each cell or at the edge.

Bad things happen when this basic assumption of periodic boundary
conditions is for whatever reason invalid. A saw tooth has very obvious
boundary discontinuity problems.

Real applications of FFTs for imaging tend to spend a lot of time and
effort ameliorating this potential aliasing effect at the boundaries.

It isn't a suitable 'test function' in the sense of nicely behaved
functions for the transformation, so it is going to look very nasty in
the time domain (after the inverse transformation of the 'ramp').

Plotting 1/t with about 8 points, (0.125, 8) (.25, 4) . . . (8,
0.125) on SPICE then taking the FFT and then taking the reciprocal --
not sure why this step works or is necessary -- isn't a bad ramp, at
least at the lower frequencies.

It would be really convenient if a time derivative could be taken
mathematically without a derivative circuit in either domain.

You cannot take a FFT of a wave form after you've taken its time
derivative in the time domain -- it won't appear in the box -- and in
the frequency domain you only get a derivative w/ respect to
frequency, whatever that is.

There doesn't seem to be an easy way to create a time signal on SPICE
that equals 1/t.

What are you trying to do?

Regards,
Martin Brown

 

In article <y8L9p.18$aC6.13@newsfe03.iad>,
Martin Brown <|||newspam|||@nezumi.demon.co.uk> wrote:

Bad things happen when this basic assumption of periodic boundary
conditions is for whatever reason invalid. A saw tooth has very obvious
boundary discontinuity problems.

Indeed. In that, it is exactly the same as polynomial fitting of
curves, or any such infinite approximation. Go outside the domain
of validity and things can go badly wrong.

I am often amazed at the things people use Fourier approximations
for - not because they do, but because they seem to work more often
than a naive analysis would expect. But, as you say, you don't get
that by just rushing in, blindly.


Regards,
Nick Maclaren.

 

[Phil Hobbs]

Bob Masta wrote:

On Thu, 24 Feb 2011 09:10:50 -0800 (PST), Bret Cahill
Bret_E_Cahill@yahoo.com> wrote:

Taking a time derivative after an FFT would be easy on SPICE if you
had some curve that would FFT into a ramp: Just multiply the function
by the ramp.

Not sure what you are ultimately trying to do, but note that
you can obtain the FFT of the time derivative by taking the
FFT of the raw waveform and applying a +6 dB/octave
"envelope" to that... essentially, you just tilt the
spectrum up at a 6 dB/octave slope.

This turns out to be very handy for measuring frequency
response of a system. Classically, one can apply an impulse
to the system and take the FFT to get the frequency
response. But an impulse is pretty narrow (one sample, in a
digital system), so it doesn't have much energy. A step
response, on the other hand, has a whole lot more. Since
the derivatve of a step is an impulse, you can get the
frequency response by applying a step, taking the FFT, and
tilting it. This is so handy that I built this feature into
my Daqarta software. See "Frequency Response Measurement -
Step Response" at<http://www.daqarta.com/dw_0a0s.htm>.

Are you windowing the data before taking the DFT? Could get ugly otherwise.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal
ElectroOptical Innovations
55 Orchard Rd
Briarcliff Manor NY 10510
845-480-2058

email: hobbs (atsign) electrooptical (period) net
http://electrooptical.net

 

[Bob Masta]

On Thu, 24 Feb 2011 09:10:50 -0800 (PST), Bret Cahill
<Bret_E_Cahill@yahoo.com> wrote:

Taking a time derivative after an FFT would be easy on SPICE if you
had some curve that would FFT into a ramp: Just multiply the function
by the ramp.

Not sure what you are ultimately trying to do, but note that
you can obtain the FFT of the time derivative by taking the
FFT of the raw waveform and applying a +6 dB/octave
"envelope" to that... essentially, you just tilt the
spectrum up at a 6 dB/octave slope.

This turns out to be very handy for measuring frequency
response of a system. Classically, one can apply an impulse
to the system and take the FFT to get the frequency
response. But an impulse is pretty narrow (one sample, in a
digital system), so it doesn't have much energy. A step
response, on the other hand, has a whole lot more. Since
the derivatve of a step is an impulse, you can get the
frequency response by applying a step, taking the FFT, and
tilting it. This is so handy that I built this feature into
my Daqarta software. See "Frequency Response Measurement -
Step Response" at <http://www.daqarta.com/dw_0a0s.htm>.

Best regards,


Bob Masta

DAQARTA v6.00
Data AcQuisition And Real-Time Analysis
www.daqarta.com
Scope, Spectrum, Spectrogram, Sound Level Meter
Frequency Counter, FREE Signal Generator
Pitch Track, Pitch-to-MIDI
Science with your sound card!

 

[maury]

On Feb 24, 11:10 am, Bret Cahill <Bret_E_Cah...@yahoo.com> wrote:

Taking a time derivative after an FFT would be easy on SPICE if you
had some curve that would FFT into a ramp:  Just multiply the function
by the ramp.

The inverse transform of a ramp on Excel is complex, the real part
being a small negative offset with a large positive zero frequency.
The imaginary part may work but it looks like it would be hard to
fashion with a circuit even if the curve was known.

Just builting up 2**n voltage sources where frequency = amplitude = n
is tedious.  The FFT is, of course, just 2**n peaks that increase
linearly in height on the linear - linear graph.  To get a nice ramp
would require an infinite number of voltage sources & frequencies and
amplitudes.

Is there anyway to get a nice smooth envelope -- "envelope" may have
another technical meaning -- over the time domain curve to get a nice
ramp in the FFT?

Bret Cahill

I'm not sure I understand what you're trying to do. Are you trying to
get a FFT whose "amplitude" is a linear (either positive- or negative-
going) ramp?

 

In article <4d4c208e-fb21-4bfa-9c97-4845cfa6fc85@w9g2000prg.googlegroups.com>,
Bret Cahill <Bret_E_Cahill@yahoo.com> wrote:

What are you trying to do?

Take fractional order derivatives.

Do you know of a reference that explains when that is mathematically
valid? I have seen plenty of references to it, and even done it on
rare occasions, but never seen anything that analyses the problem
properly.

Of course, it may just be an egregious hack that sometimes works, in
which case there may be no such analysis


Regards,
Nick Maclaren.

 

[Bret Cahill]

Taking a time derivative after an FFT would be easy on SPICE if you
had some curve that would FFT into a ramp:  Just multiply the function
by the ramp.

The inverse transform of a ramp on Excel is complex, the real part
being a small negative offset with a large positive zero frequency.
The imaginary part may work but it looks like it would be hard to
fashion with a circuit even if the curve was known.

Just builting up 2**n voltage sources where frequency = amplitude = n
is tedious.  The FFT is, of course, just 2**n peaks that increase
linearly in height on the linear - linear graph.  To get a nice ramp
would require an infinite number of voltage sources & frequencies and
amplitudes.

Is there anyway to get a nice smooth envelope -- "envelope" may have
another technical meaning -- over the time domain curve to get a nice
ramp in the FFT?

Bret Cahill

I'm not sure I understand what you're trying to do. Are you trying to
get a FFT whose "amplitude" is a linear (either positive- or negative-
going) ramp?

Yes.

You can take integer order or fractional order derivatives in the FFT
on Spice if you have something proportional to a ramp.


Bret Cahill

 

[Bret Cahill]

Is there anyway to get a nice smooth envelope -- "envelope" may have
another technical meaning -- over the time domain curve to get a nice
ramp in the FFT?

No.  The usual FFT for finite sampled sequences is done with circular
boundary conditions, and you must deal with the enormous discontinuity
at that boundary that any frequency-dependent ramp creates.

Would this be true if every point used by the FFT -- SPICE has a 256
minimum -- was plotted and used by the FFT?

It is always true that an FFT has an implicit assumption of periodic
boundary conditions at the length of the transform which are most
commonly a tiled circular wrap around at the edges, but in some
implementations may be Dirichlet or mirror boundary conditions leading
to a DCT variant. In addition there is also two plausible choices of
origin exactly in the centre of each cell or at the edge.

Bad things happen when this basic assumption of periodic boundary
conditions is for whatever reason invalid. A saw tooth has very obvious
boundary discontinuity problems.

A frequency ramp would need to start at (0,0) to be useful taking
derivatives.

Real applications of FFTs for imaging tend to spend a lot of time and
effort ameliorating this potential aliasing effect at the boundaries.

It isn't a suitable 'test function' in the sense of nicely behaved
functions for the transformation, so it is going to look very nasty in
the time domain (after the inverse transformation of the 'ramp').

Plotting 1/t with about 8 points, (0.125, 8)  (.25, 4) . . . (8,
0.125) on SPICE then taking the FFT and then taking the reciprocal --
not sure why this step works or is necessary -- isn't a bad ramp, at
least at the lower frequencies.

It would be really convenient if a time derivative could be taken
mathematically without a derivative circuit in either domain.

You cannot take a FFT of a wave form after you've taken its time
derivative in the time domain -- it won't appear in the box -- and in
the frequency domain you only get a derivative w/ respect to
frequency, whatever that is.

There doesn't seem to be an easy way to create a time signal on SPICE
that equals 1/t.

What are you trying to do?

Take fractional order derivatives.


Bret Cahill

 

[Fred Marshall]

On 2/24/2011 9:10 AM, Bret Cahill wrote:

Taking a time derivative after an FFT would be easy on SPICE if you
had some curve that would FFT into a ramp: Just multiply the function
by the ramp.

The inverse transform of a ramp on Excel is complex, the real part
being a small negative offset with a large positive zero frequency.
The imaginary part may work but it looks like it would be hard to
fashion with a circuit even if the curve was known.

Just builting up 2**n voltage sources where frequency = amplitude = n
is tedious. The FFT is, of course, just 2**n peaks that increase
linearly in height on the linear - linear graph. To get a nice ramp
would require an infinite number of voltage sources& frequencies and
amplitudes.

Is there anyway to get a nice smooth envelope -- "envelope" may have
another technical meaning -- over the time domain curve to get a nice
ramp in the FFT?


Bret Cahill

It seems to me that the approach might be something like this:

First, a continous, infinite Fourier Transform pair:

df(t)/dt <-> (jw)*F(w)

So, I expect your "ramp" is the jw term above, eh? Note the "j"

If this is going to be moved into the discrete-periodic world then we
note that the value switches from jW0 to -jW0 where W0=2*pi*fs/2.
Keeping things in the continuous, infinite but periodic world in
frequency then we should recognize immediately that the sawtooth in
frequency will be of infinite extent in time. So, we have to smooth out
that discontinuity.

Take a look at a Parks-McClellan time differentiator design. That has a
ramp in frequency *but* it's bandlimited so the ramp stops and goes to
zero at fs/2.

Fred

 

In article <01a40481-7894-430a-a37f-53c66638ab59@8g2000prb.googlegroups.com>,
Bret Cahill <Bret_E_Cahill@yahoo.com> wrote:

What are you trying to do?

Take fractional order derivatives.

Do you know of a reference that explains when that is mathematically
valid?

It seems to work on Excel. You can check out a lot of different
fractional order derivatives very quickly because you only have to
click 3 times on the FT box.

I.e. it doesn't crash and produces a number. Excel is notorious
for doing that sort of thing.

It might be easier to do electronic circuits on Excel than frequency
ramp functions on SPICE.

Yeah. And it's a lot easier to build faster-than-light spaceships
on Excel, too.

No one will deny it's rigorous elegant civilized orthodox concise
organized kosher nice philosophical thoughtful lofty and often
practical, utilitarian and easy to have a nice formal proof.

It also helps to be able to judge when what you are building
isn't going to work, especially when it comes to minor details
like reliability.

That's why they have witch doctors, aka, "mathematicians" installed at
universities.

And I am one, looking for a grimoire.

All an engineer needs to do, however, is be able to say, "well it w O
R erks."

That's the sales department. A good engineer has solid reasons to
believe that what he has built will work according to the actual
requirements and intent. There are a few of us left

Of course, it may just be an egregious hack that sometimes works, in
which case there may be no such analysis

There's always an analysis. Mathematicians just want a pretty one.

Er, like "Well it probably won't break before we have had time to
cash the cheque"?

The history of engineering is littered with projects which failed
because the analysis was not done properly - and where it was known
what the potential problems were.


Regards,
Nick Maclaren.

 

[Bret Cahill]

What are you trying to do?

Take fractional order derivatives.

Do you know of a reference that explains when that is mathematically
valid?  

It seems to work on Excel. You can check out a lot of different
fractional order derivatives very quickly because you only have to
click 3 times on the FT box.

It might be easier to do electronic circuits on Excel than frequency
ramp functions on SPICE.

I have seen plenty of references to it, and even done it on
rare occasions, but never seen anything that analyses the problem
properly.

No one will deny it's rigorous elegant civilized orthodox concise
organized kosher nice philosophical thoughtful lofty and often
practical, utilitarian and easy to have a nice formal proof.

That's why they have witch doctors, aka, "mathematicians" installed at
universities.

All an engineer needs to do, however, is be able to say, "well it w O
R erks."

Of course, it may just be an egregious hack that sometimes works, in
which case there may be no such analysis

There's always an analysis. Mathematicians just want a pretty one.


Bret Cahill


"Picked up a gal, she was ugly too."

-- Commander Cody

 

[Phil Hobbs]

nmm1@cam.ac.uk wrote:

In article<01a40481-7894-430a-a37f-53c66638ab59@8g2000prb.googlegroups.com>,
Bret Cahill<Bret_E_Cahill@yahoo.com> wrote:
What are you trying to do?

Take fractional order derivatives.

Do you know of a reference that explains when that is mathematically
valid?

It seems to work on Excel. You can check out a lot of different
fractional order derivatives very quickly because you only have to
click 3 times on the FT box.

I.e. it doesn't crash and produces a number. Excel is notorious
for doing that sort of thing.

It might be easier to do electronic circuits on Excel than frequency
ramp functions on SPICE.

Yeah. And it's a lot easier to build faster-than-light spaceships
on Excel, too.

No one will deny it's rigorous elegant civilized orthodox concise
organized kosher nice philosophical thoughtful lofty and often
practical, utilitarian and easy to have a nice formal proof.

It also helps to be able to judge when what you are building
isn't going to work, especially when it comes to minor details
like reliability.

That's why they have witch doctors, aka, "mathematicians" installed at
universities.

And I am one, looking for a grimoire.

All an engineer needs to do, however, is be able to say, "well it w O
R erks."

That's the sales department. A good engineer has solid reasons to
believe that what he has built will work according to the actual
requirements and intent. There are a few of us left

Of course, it may just be an egregious hack that sometimes works, in
which case there may be no such analysis

There's always an analysis. Mathematicians just want a pretty one.

Er, like "Well it probably won't break before we have had time to
cash the cheque"?

The history of engineering is littered with projects which failed
because the analysis was not done properly - and where it was known
what the potential problems were.


Regards,
Nick Maclaren.

Don't take Cahill too seriously--he's a fairly well known crank who'd
far rather slag people off than learn anything from them.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal
ElectroOptical Innovations
55 Orchard Rd
Briarcliff Manor NY 10510
845-480-2058

email: hobbs (atsign) electrooptical (period) net
http://electrooptical.net

 

[Bret Cahill]

What are you trying to do?

Take fractional order derivatives.

Do you know of a reference that explains when that is mathematically
valid?

It seems to work on Excel. You can check out a lot of different
fractional order derivatives very quickly because you only have to
click 3 times on the FT box.

I.e. it doesn't crash

That seems to be a bigger problem on SPICE.

and produces a number.

The graphs on Excel check out for a variety of test functions,
certainly for anything as well behaved as the signal to be processed.

.. . .

It might be easier to do electronic circuits on Excel than frequency
ramp functions on SPICE.

Yeah. And it's a lot easier to build faster-than-light spaceships
on Excel, too.

A series capacitor or inductor is easy on Excel. Take the FFT, go to
polar, subtract nu*pi/2 from the phase angles, then back to real &
imaginary and then raise each frequency to ^nu and multiply. Then
take the inverse transform.

Nu => 0+ for the offset block (a large cap) and =>1 for the 1st
derivative (a small cap) circuit.

Nu => -1 to integrate one order with an inductor.

No one will deny it's rigorous elegant civilized orthodox concise
organized kosher nice philosophical thoughtful lofty and often
practical, utilitarian and easy to have a nice formal proof.

It also helps to be able to judge when what you are building
isn't going to work,

That's the reason for using a variety of simulators in addition to
whatever theory you may have.

especially when it comes to minor details
like reliability.

No one is 100% sure FEA is always reliable but that doesn't stop air
frame engineers from using it as a double check for . . . reliability.

That's why they have witch doctors, aka, "mathematicians" installed at
universities.

And I am one, looking for a grimoire.

All an engineer needs to do, however, is be able to say, "well it w O
R erks."

That's the sales department.

The only way to make any money off of a simulator method is to do a
full blown investigation and write a book on it.

A good engineer has solid reasons to
believe that what he has built will work according to the actual
requirements and intent. There are a few of us left

Even if he "proves" it in a peer reviewed paper with any combination
of first principles and simulators he'll still need to actually build
and test the thing.

But it's not necessary to fully understand a theory to get a patent on
something dependent upon the theory. Many blamed Newton's defective
lift equation for delaying aviation, but as von Karmen pointed out,
that wouldn't deter inventors.

Of course, it may just be an egregious hack that sometimes works, in
which case there may be no such analysis

There's always an analysis. Mathematicians just want a pretty one.

Er, like "Well it probably won't break before we have had time to
cash the cheque"?

RR just tried that with their new wide body turbo fan. Whether some
engineer should have been fired over it is irrelevant. There isn't
any way to ever be 100% risk free, no matter the endeavor.

The real issue is a reasonable cost benefit risk analysis.

The history of engineering is littered with projects which failed
because the analysis was not done properly - and where it was known
what the potential problems were.

That's the purpose of getting a ramp into SPICE's FFT.



Bret Cahill


"You can't get there . . . from here."

-- Maine expression

 

[Bob Masta]

On Fri, 25 Feb 2011 08:05:00 -0500, Phil Hobbs
<pcdhSpamMeSenseless@electrooptical.net> wrote:

Bob Masta wrote:
On Thu, 24 Feb 2011 09:10:50 -0800 (PST), Bret Cahill
Bret_E_Cahill@yahoo.com> wrote:

Taking a time derivative after an FFT would be easy on SPICE if you
had some curve that would FFT into a ramp: Just multiply the function
by the ramp.

Not sure what you are ultimately trying to do, but note that
you can obtain the FFT of the time derivative by taking the
FFT of the raw waveform and applying a +6 dB/octave
"envelope" to that... essentially, you just tilt the
spectrum up at a 6 dB/octave slope.

This turns out to be very handy for measuring frequency
response of a system. Classically, one can apply an impulse
to the system and take the FFT to get the frequency
response. But an impulse is pretty narrow (one sample, in a
digital system), so it doesn't have much energy. A step
response, on the other hand, has a whole lot more. Since
the derivatve of a step is an impulse, you can get the
frequency response by applying a step, taking the FFT, and
tilting it. This is so handy that I built this feature into
my Daqarta software. See "Frequency Response Measurement -
Step Response" at<http://www.daqarta.com/dw_0a0s.htm>.



Are you windowing the data before taking the DFT? Could get ugly otherwise.

No, in this case it's important to *not* window the data.
A window function (at least, any of the standard ones) has a
gradual onset and offset, for the specific purpose of
eliminating transients at the start/end of the FFT frame.
But here it is the onset that we are specifically interested
in. The transient response should be complete (for all
practical purposes) before the end of the frame, or else you
need more samples in the frame.

In general, you never want to window a transient or noise,
only a continous wave. The FFT analysis presumes a
continuous wave, such that every frame is an identical copy
that can be spliced seamlessly head to tail. A real-world
continuous wave that does not contain an exact integer
number of cycles in the FFT frame will have a discontinuity
where the next frame is spliced, which results in "spectral
leakage" that appears as "skirts" on what would otherwise be
a single line in the spectrum. The window function provides
a gradual onset and offset to smooth out this discontinuity,
greatly reducing the spectral leakage.

Interested readers may want to check out my "Gut Level
Fourier Transforms" series at
<http://www.daqarta.com/author.htm>.
In particular, see Part 5 "Dumping Spectral Leakage Out a
Window" <http://www.daqarta.com/eex05.htm>

Best regards,


Bob Masta

DAQARTA v6.00
Data AcQuisition And Real-Time Analysis
www.daqarta.com
Scope, Spectrum, Spectrogram, Sound Level Meter
Frequency Counter, FREE Signal Generator
Pitch Track, Pitch-to-MIDI
Science with your sound card!