[Kevin Aylward[_4_]]

"Scott Dorsey" wrote in message ...

William Sommerwerck wrote:
If you can represent a cycle function analytically -- that is, as a
mathematical expression -- then you can extract the Fourier coefficients
simply by multiplying the function by the sine and cosine of the desired
harmonic, then integrating. I assume Fourier had figured this out, because
it's pretty basic stuff once you recognize what's going on.

Yes! But Fourier never tried to apply this to any real-world applications,

This depends on your definition of applying to real world problems. I would
say that the general understanding is that Fourier specifically invented the
technique to solve real physical heat conduction and vibration problems, all
of which are meaningless in the virtual world. Fourier was apparently
working on actual physical problems, not abstract methods to solve
differential equations just for the sake of solving them. The understanding
was that Fourier got results that agreed with experiments, but that at the
time, were considered mathematically dubious. As others have already noted,
the mathematical justifications for the physical results came later.

Kevin Aylward B.Sc.
www.kevinaylward.co.uk

[William Sommerwerck]

Every spectrum analyzer is [sic] a form of Fourier analysis.

No so. Spectrum analyzers are for random or non-repetitive
signals, and do not use Fourier analysis.

Gee, you have never seen the spectrum of a sine wave on
a spectrum analyzer?

Simply because a device analyzes the spectral content of a signal, doesn't
mean it uses Fourier analysis. Instead of arguing about it, look it up.

[Mark]

On Dec 23, 10:03*am, "William Sommerwerck"
wrote:
Every spectrum analyzer is [sic] a form of Fourier analysis.

No so. Spectrum analyzers are for random or non-repetitive
signals, and do not use Fourier analysis.

Gee, you have never seen the spectrum of a sine wave on
a spectrum analyzer?

Simply because a device analyzes the spectral content of a signal, doesn't
mean it uses Fourier analysis. Instead of arguing about it, look it up.

Semantics about the word USES..

An HP8591 __USES__ swept filters to perform a Fourier analysis i.e.
convert a time domain signal to the frequency domain.

RTA software __USES__ an FFT algorithm to perform a Fourier analysis
i.e. convert a time domain signal to the frequency domain.

Spectral analysis = Fourier analysis = conversion between time and
frequency domains regardless of the method used.

The Fourier transform is one particular method to do this
mathematically.

The Fast Fourier transform is one particularly efficeint method to do
this mathematically.


http://en.wikipedia.org/wiki/Fourier_analysis

Have a nice day.

Mark

[Scott Dorsey]

Mark wrote:

An HP8591 __USES__ swept filters to perform a Fourier analysis i.e.
convert a time domain signal to the frequency domain.

NOT all ways of converting a time domain signal to the frequency domain
are strictly speaking Fourier analysis.

RTA software __USES__ an FFT algorithm to perform a Fourier analysis
i.e. convert a time domain signal to the frequency domain.

And they both get the same value on a periodic input but different values
on aperiodic inputs. Consequently they are not performing the same function.

Spectral analysis =3D Fourier analysis =3D conversion between time and
frequency domains regardless of the method used.

Fourier analysis is one element of the set of spectral analyses.
--scott

--
"C'est un Nagra. C'est suisse, et tres, tres precis."

[dbd]

On Dec 22, 6:44*pm, (Scott Dorsey) wrote:
...


Yup, but I have also seen the spectrum of an aperiodic signal on a spectrum
analyzer coming up with something utterly unlike what a Fourier analysis
would.

The spectrum analyzer is swept-sine and consequently if a frequency
appears in the input at any time other than the moment when the window
is directly on that frequency, it will not appear on the display.

This is an absolute and total nightmare for people trying to look at
WiFi signals with a regular spectrum analyzer, for instance. *And it
is going to be a similar nightmare with the new "white space" devices
that will be sharing RF bandwidth with wireless mikes soon.
--scott
...

Spectrum analyzers come in (at least ) two flavors: swept or
(super)heterodyne and realtime or dynamic signal analyzers. A number
of manufacturers of the former also produced the later such as
Tektronix and HP. The realtime or dynamic analyzers implement Fourier
methods.

See the Tektronix App Note 2EW_16550_0. A quick Google locates a copy
at:

http://www.isotest.es/web/Soporte/Fo...%C3%B1ales.pdf

Also the Agilent App Note 243 or 5952-8898E available:

http://cp.literature.agilent.com/lit...5952-8898E.pdf

Each of there references discusses both types of spectrum analyzer.

Dale B. Dalrymple

[Scott Dorsey]

dbd wrote:
Spectrum analyzers come in (at least ) two flavors: swept or
(super)heterodyne and realtime or dynamic signal analyzers. A number
of manufacturers of the former also produced the later such as
Tektronix and HP. The realtime or dynamic analyzers implement Fourier
methods.

Normally we call those DSAs or FFT analyzers to distinguish them from
regular swept spectrum analyzers.
--scott

--
"C'est un Nagra. C'est suisse, et tres, tres precis."

[Don Pearce[_3_]]

On 23 Dec 2010 13:07:23 -0500, (Scott Dorsey) wrote:

dbd wrote:
Spectrum analyzers come in (at least ) two flavors: swept or
(super)heterodyne and realtime or dynamic signal analyzers. A number
of manufacturers of the former also produced the later such as
Tektronix and HP. The realtime or dynamic analyzers implement Fourier
methods.

Normally we call those DSAs or FFT analyzers to distinguish them from
regular swept spectrum analyzers.
--scott

And of course swept analyzers are realtime instruments.

d

[William Sommerwerck]

An HP8591 __USES__ swept filters to perform a Fourier analysis
i.e. convert a time domain signal to the frequency domain.

Wrong, wrong, wrong, wrong, wrong.

A conversion from the time domain to the frequency domain is not, per se, a
Fourier analysis. Some forms are; all are not.


Spectral analysis = Fourier analysis = conversion between time and
frequency domains regardless of the method used.

WRONG, WRONG, WRONG. See above.

[Doug McDonald[_4_]]

On 12/22/2010 7:43 PM, William Sommerwerck wrote:
Every spectrum analyzer is [sic] a form of Fourier analysis.

No so. Spectrum analyzers are for random or non-repetitive signals, and do
not use Fourier analysis.



Not necessarily so.

You can use short Fourier transforms for such purposes, and some
spectrum analyzers do so. What you can't do is use a single Fourier
transform over the who audio bandwidth and expect optimal time
resolution of the various channels at all frequencies.

Doug McDonald

[dbd]

On Dec 23, 10:07*am, (Scott Dorsey) wrote:
dbd wrote:
Spectrum analyzers come in (at least ) two flavors: swept or
(super)heterodyne and realtime or dynamic signal analyzers. A number
of manufacturers of the former also produced the later such as
Tektronix and HP. The realtime or dynamic analyzers implement Fourier
methods.

Normally we call those DSAs or FFT analyzers to distinguish them from
regular swept spectrum analyzers.
--scott

The documentation shows that instrumentation manufacturers have long
made regular use of "spectrum analyzer" for all types. In the 1950's
the only spectrum analyzers may have been swept. Today the question of
which type is more common would produce a different idea of "regular".

Dale B. Dalrymple

[Scott Dorsey]

Doug McDonald wrote:
You can use short Fourier transforms for such purposes, and some
spectrum analyzers do so. What you can't do is use a single Fourier
transform over the who audio bandwidth and expect optimal time
resolution of the various channels at all frequencies.

In the old days before Fourier analyzers, there were a couple solutions.
One was to have a box with dozens of parallel filters, and live with the
fairly wide bands that resulted. (This method is something I blame for
much of the horrible equalization in the seventies.)

The other, and the one that Bell Labs used for speech analysis, was to
make a tape loop and play a short sample back over and over, thereby
taking an aperiodic signal and making it periodic.
--scott
--
"C'est un Nagra. C'est suisse, et tres, tres precis."

[Mark]

Also the Agilent App Note 243 or 5952-8898E available:

http://cp.literature.agilent.com/lit...5952-8898E.pdf

Each of there references discusses both types of spectrum analyzer.


Yes I understand how the various types of spectrum analyzers operate.
Trust me, I do.

A prisim is an example a spectrum analyzer that operates on light.

And these devices ALL perform Fourier analysis even though they use
different methods.

The decomposition of a waveform into it's various sinusoidal
components is the defintion of Fourier analysis.

See page 7 of the paper you cited above:

http://cp.literature.agilent.com/lit...5952-8898E.pdf

"It was shown over one hundred years ago by Baron Jean Baptiste
Fourier
that any waveform that exists in the real world can be generated by
adding up sine waves."

The decompostion of a waveform into it's sinusoidal components is
Fourier analysis regardless of method. If you disagree, it is a
matter of semantics and nothing more then that, so lets leave it at
that.

Mark

[Arny Krueger]

"Scott Dorsey" wrote in message

Mark wrote:

An HP8591 __USES__ swept filters to perform a Fourier
analysis i.e. convert a time domain signal to the
frequency domain.

NOT all ways of converting a time domain signal to the
frequency domain
are strictly speaking Fourier analysis.

RTA software __USES__ an FFT algorithm to perform a
Fourier analysis i.e. convert a time domain signal to
the frequency domain.

And they both get the same value on a periodic input but
different values
on aperiodic inputs. Consequently they are not
performing the same function.

Spectral analysis =3D Fourier analysis =3D conversion
between time and frequency domains regardless of the
method used.

Fourier analysis is one element of the set of spectral
analyses. --scott

There have also long been audio spectrum analyzers that were based on banks
of narrow-band filters. This methodology was used in analog SS RTAs
starting back in the 1970s. Ivie, Rane, Gold Line, Audio Control, and
others sold them. Some were rack mounted and some were hand held.

In the 1960s I maintained military equipment that used this methodology to
analyze the spectrum of audio from Doppler radars. The tuned filters were
implemented with vacuum tube amplfiers and L-C networks. There were over 30
bands. The equipment was about the size of a good-sized kitchen oven, and
produced similar amounts of heat. This particular piece of equipment was
replaced by a minicomputer running FFT software in the 1970s.

[Scott Dorsey]

Arny Krueger wrote:

There have also long been audio spectrum analyzers that were based on banks
of narrow-band filters. This methodology was used in analog SS RTAs
starting back in the 1970s. Ivie, Rane, Gold Line, Audio Control, and
others sold them. Some were rack mounted and some were hand held.

This is an RTA, realtime analyzer. It's not a spectrum analyzer, it is
a realtime analyzer because, unlike a spectrum analyzer, it displays
frequency vs. amplitude plots in real time.

In the 1960s I maintained military equipment that used this methodology to
analyze the spectrum of audio from Doppler radars. The tuned filters were
implemented with vacuum tube amplfiers and L-C networks. There were over 30
bands. The equipment was about the size of a good-sized kitchen oven, and
produced similar amounts of heat. This particular piece of equipment was
replaced by a minicomputer running FFT software in the 1970s.

Yup. Today the Watkins-Johnson folks make sigint systems that take
the RF input and knock down a 20 Mhz wide chunk of it into a 45 Mhz IF
signal, then digitize the whole damn thing at some crazy rate and tear it
up into narrow bands with FFTs in hardware. No oversampling and no
anti-aliasing filter save the IF filtration so strong signals nearby can
cause birdies.
--scott
--
"C'est un Nagra. C'est suisse, et tres, tres precis."

[William Sommerwerck]

The decomposition of a waveform into its various sinusoidal
components is the defintion of Fourier analysis.

That is not correct. It is the decomposition of the waveform into its
sinusoidal /harmonic/ components. Noise is made of sinusoidal components,
but they are not harmonically related, and their decomposition /is not/
Fourier analysis.

You really need to stop arguing for a bit, and look into this. You are quite
wrong.

[William Sommerwerck]

Today the Watkins-Johnson folks make sigint systems
that take the RF input and knock down a 20 Mhz wide
chunk of it into a 45 Mhz IF signal, then digitize the whole
damn thing at some crazy rate and tear it up into narrow
bands with FFTs in hardware.

I believe that's incorrect.

I own the Sony DSP FM tuner, I doubt there's even one bit of FFT in its
algorithms. One does not need FFT to implement a bandpass filter. I don't
even see the connection.

[david correia]

In article ,
Nomen Nescio wrote:

"...When I see you flo tin' down the gutter
I'll give you uh bottle uh wine
Put me on the white hook
Back in the fat rack
Shad rack ee shack
The sumptin' hoop the sumptin' hoop
The blimp the blimp
The drazy hoops the drazy hoops
They're camp they're camp
Tits tits the blimp the blimp
The mother ship the mother ship
The brothers hid under their hood..."



Think the first time I heard it was on one them Warner Bros mail in a
buck or 2 compilation albums. You couldn't help but wonder as his voice
targeted your brain - what the **** is that!?



David Correia
www.Celebrationsound.com

[Scott Dorsey]

William Sommerwerck wrote:
Today the Watkins-Johnson folks make sigint systems
that take the RF input and knock down a 20 Mhz wide
chunk of it into a 45 Mhz IF signal, then digitize the whole
damn thing at some crazy rate and tear it up into narrow
bands with FFTs in hardware.

I believe that's incorrect.

I own the Sony DSP FM tuner, I doubt there's even one bit of FFT in its
algorithms. One does not need FFT to implement a bandpass filter. I don't
even see the connection.

Your Sony tuner probably just does some filtering and detection in
the digital domain, as well as probably reconstituting and decoding
IBOC FM digital subcarriers.

It doesn't need to provide a wide panadaptor display to show the
operator the realtime spectrum of all possible threats, and it doesn't
need to identify multiple signal sources using the same frequency either.
It also doesn't need to do pattern matching of the source spectrum and
correlate it against a database of possible threat sources. (Although
that might be great to help you identify unknown songs on the radio.)
Modern sigint receivers are a lot more sophisticated today than simple
communications receivers.
--scott





--
"C'est un Nagra. C'est suisse, et tres, tres precis."

[Arny Krueger]

"William Sommerwerck" wrote in
message

Today the Watkins-Johnson folks make sigint systems
that take the RF input and knock down a 20 Mhz wide
chunk of it into a 45 Mhz IF signal, then digitize the
whole damn thing at some crazy rate and tear it up into
narrow bands with FFTs in hardware.

I believe that's incorrect.

I believe that Scott is correct, but you have to realize that he is talking
about a special-purpose analytical device, not a classic communications
receiver.

I own the Sony DSP FM tuner, I doubt there's even one bit
of FFT in its algorithms.

Yes, this device does use digital filtering, but there seems no need for th
simulated filter banks that FFT analysis is used to create.

One does not need FFT to
implement a bandpass filter. I don't even see the
connection.

I agree with your analysis here, too. I don't see any need for a FFT in a
communications receiver, except perhaps as an extra-fancy tuning indicator.

[Scott Dorsey]

Arny Krueger wrote:

I agree with your analysis here, too. I don't see any need for a FFT in a
communications receiver, except perhaps as an extra-fancy tuning indicator.

There's a big need for extra-fancy tuning indicators for a lot of
applications. I have an old Heatkit SB-620 panadaptor display on my
ham receiver at home; it's just an ordinary if somewhat drifty spectrum
analyzer that displays the receiver IF using a swept oscillator of
somewhat doubtful linearity. It's fine for identifying signals
way down in the noise while rapidly scanning the bands, though, which
is what it's for.

At work I have a radio with an AOR SDU-5500 analyzer on it, which _is_
a real FFT and can not only display the IF spectrum in realtime but it
can do an accurate waterfall plot of time vs. frequency vs. amplitude.
This is an absolute necessity today for tracking down intermittent
interference to wireless mikes, because there are so many RF sources today
that just squit an occasional burst and don't get seen on a regular
spectrum analyzer.

There is an _enormous_ need for these things, and as RF interference
problems get worse, as people move more critical systems to unlicensed
shared ISM bands, and as consumer electronics manufacturers continue to
disregard Part 15 requirements and turn the whole RF spectrum into a
dumping ground, the need will be greater every day.
--scott
--
"C'est un Nagra. C'est suisse, et tres, tres precis."

[dbd]

On Dec 23, 3:40*pm, "William Sommerwerck"
wrote:
Today the Watkins-Johnson folks make sigint systems
that take the RF input and knock down a 20 Mhz wide
chunk of it into a 45 Mhz IF signal, then digitize the whole
damn thing at some crazy rate and tear it up into narrow
bands with FFTs in hardware.

I believe that's incorrect.

I own the Sony DSP FM tuner, I doubt there's even one bit of FFT in its
algorithms. One does not need FFT to implement a bandpass filter. I don't
even see the connection.

A Sony DSP FM tuner only needs 1 channel, not a full bank so the FFT
provides no speed advantage.

The definition of the calculated FFT coefficients is equivalent to a
bank of narrowband filters with the center frequencies translated to
DC. You can't do an FFT without calculating a bank of filters, what
you do with the coefficients is up to the user. The algorithm works
the same whether the signal fed to it consists of stationary sinusoids
or noise. The coefficients are better for determining the parameters
of the sinusoids than for determining the parameters of a noise
process, but the analysis is still a Fourier analysis.

Dale B. Dalrymple

[William Sommerwerck]

A prisim [sic] is an example a spectrum analyzer
that operates on light.
And these devices ALL perform Fourier analysis even
though they use different methods.

A prism? Do you understand how a prism works? Of course not!

[Mark]

On Dec 23, 6:35*pm, "William Sommerwerck"
wrote:
The decomposition of a waveform into its various sinusoidal
components is the defintion of Fourier analysis.

That is not correct. It is the decomposition of the waveform into its
sinusoidal /harmonic/ components. Noise is made of sinusoidal components,
but they are not harmonically related, and their decomposition /is not/
Fourier analysis.

You really need to stop arguing for a bit, and look into this. You are quite
wrong.

it seems like you are saying that you believe that one cannot perform
a Fourier analysis of noise,

there is no point in continuing this..

Mark

[William Sommerwerck]

I own the Sony DSP FM tuner, I doubt there's even one bit
of FFT in its algorithms. One does not need FFT to implement
a bandpass filter. I don't even see the connection.

A Sony DSP FM tuner only needs 1 channel, not a full bank
so the FFT provides no speed advantage.

It wouldn't even need FFT if 20 channels were needed!


The definition of the calculated FFT coefficients is equivalent to a
bank of narrowband filters with the center frequencies translated to
DC. You can't do an FFT without calculating a bank of filters, what
you do with the coefficients is up to the user.

An utter misconception of what's goingon.

The algorithm works
the same whether the signal fed to it consists of stationary sinusoids
or noise. The coefficients are better for determining the parameters
of the sinusoids than for determining the parameters of a noise
process, but the analysis is still a Fourier analysis.

AAARRRGGGHHH!

It is amazing how people can utterly pervert the meaning of facts, then
insist they're right.

I get the feeling I'm arguing with people who think a Polaroid integral
print needs to be flapped to develop properly.

[Doug McDonald[_7_]]

On 12/23/2010 6:41 PM, Scott Dorsey wrote:
William wrote:
Today the Watkins-Johnson folks make sigint systems
that take the RF input and knock down a 20 Mhz wide
chunk of it into a 45 Mhz IF signal, then digitize the whole
damn thing at some crazy rate and tear it up into narrow
bands with FFTs in hardware.

I believe that's incorrect.

I own the Sony DSP FM tuner, I doubt there's even one bit of FFT in its
algorithms. One does not need FFT to implement a bandpass filter. I don't
even see the connection.

Your Sony tuner probably just does some filtering and detection in
the digital domain, as well as probably reconstituting and decoding
IBOC FM digital subcarriers.

It doesn't need to provide a wide panadaptor display to show the
operator the realtime spectrum of all possible threats, and it doesn't
need to identify multiple signal sources using the same frequency either.
It also doesn't need to do pattern matching of the source spectrum and
correlate it against a database of possible threat sources. (Although
that might be great to help you identify unknown songs on the radio.)
Modern sigint receivers are a lot more sophisticated today than simple
communications receivers.


IBOC receivers are complicated software. IBOC is COFDM, and
receivers use FFT to decode it.

It may, however, not use FFT to decode plain FM.

Doug McDonald

[Arny Krueger]

"William Sommerwerck" wrote in
message

A prisim [sic] is an example a spectrum analyzer
that operates on light.
And these devices ALL perform Fourier analysis even
though they use different methods.

A prism? Do you understand how a prism works? Of course
not!

It turns out that the behavior of lenses and prisms can be analyzed using
spatial Fourier transforms and FFTs. One of the rather non-obvious things
that can be accomplished this way is refocusing an unfocused picture.

http://sharp.bu.edu/~slehar/fourier/fourier.html

[Arny Krueger]

"William Sommerwerck" wrote in
message
I own the Sony DSP FM tuner, I doubt there's even one
bit of FFT in its algorithms. One does not need FFT to
implement a bandpass filter. I don't even see the
connection.

A Sony DSP FM tuner only needs 1 channel, not a full bank
so the FFT provides no speed advantage.

It wouldn't even need FFT if 20 channels were needed!

Which is not to say that there is no way to use FFT technology do it.

If I was going to build a receiver to monitor the entire FM band in a
certain locality, I might use a FFT-based receiver to do so.

The definition of the calculated FFT coefficients is
equivalent to a bank of narrowband filters with the
center frequencies translated to DC. You can't do an FFT
without calculating a bank of filters, what you do with
the coefficients is up to the user.

An utter misconception of what's goingon.

FFT technology can be used to implement filters with more-or-less arbitrary
bandpass characteristics. FFT-based filters are commonly used in audio
production. For example Adobe Audition has two FFT-based filters, one that
implements the user's arbitrarily drawn frequency response curve and another
that implments the user's arbitrarily drawn phase response curve.

[Arny Krueger]

"Scott Dorsey" wrote in message

Arny Krueger wrote:

I agree with your analysis here, too. I don't see any
need for a FFT in a communications receiver, except
perhaps as an extra-fancy tuning indicator.

There's a big need for extra-fancy tuning indicators for
a lot of applications. I have an old Heatkit SB-620
panadaptor display on my
ham receiver at home; it's just an ordinary if somewhat
drifty spectrum analyzer that displays the receiver IF
using a swept oscillator of somewhat doubtful linearity.
It's fine for identifying signals
way down in the noise while rapidly scanning the bands,
though, which
is what it's for.

At work I have a radio with an AOR SDU-5500 analyzer on
it, which _is_
a real FFT and can not only display the IF spectrum in
realtime but it can do an accurate waterfall plot of time
vs. frequency vs. amplitude. This is an absolute
necessity today for tracking down intermittent
interference to wireless mikes, because there are so many
RF sources today that just squit an occasional burst and
don't get seen on a regular spectrum analyzer.

There is an _enormous_ need for these things, and as RF
interference problems get worse, as people move more
critical systems to unlicensed shared ISM bands, and as
consumer electronics manufacturers continue to disregard
Part 15 requirements and turn the whole RF spectrum into
a dumping ground, the need will be greater every day.
--scott

Here's a modern, FFT-based approach to the same thing:

http://www.dxzone.com/cgi-bin/dir/jump2.cgi?ID=9270


"DL4YHF's Amateur Radio Softwa
Audio Spectrum Analyzer ("Spectrum Lab"

"This program started as a simple FFT program running under DOS a long time
ago, but it is now a specialized audio analyzer, filter, frequency
converter, hum filter, data logger etc (see history at the bottom of this
page). You can download it from this site. Or look into the manual though
the manual included in the archive will be more up-to-date."

[William Sommerwerck]

You really need to stop arguing for a bit, and look into this.
You are quite wrong.

it seems like you are saying that you believe that one cannot
perform a Fourier analysis of noise...

Uh... Noise does not generally have a harmonic structure.


there is no point in continuing this.

Of course not. You might discover you were wrong.

[William Sommerwerck]

"Arny Krueger" wrote in message
...
"William Sommerwerck" wrote in
message

A prisim [sic] is an example a spectrum analyzer
that operates on light.
And these devices ALL perform Fourier analysis even
though they use different methods.

A prism? Do you understand how a prism works? Of course
not!

It turns out that the behavior of lenses and prisms can be analyzed using
spatial Fourier transforms and FFTs. One of the rather non-obvious things
that can be accomplished this way is refocusing an unfocused picture.
http://sharp.bu.edu/~slehar/fourier/fourier.html

Arny, there is nothing whatever on this page about prisms. NOTHING.

I would be really curious to understand how optical dispersion can be
modeled as a cyclic function.

[Don Pearce[_3_]]

On Thu, 23 Dec 2010 22:41:07 -0500, "Arny Krueger"
wrote:

"William Sommerwerck" wrote in
message
I own the Sony DSP FM tuner, I doubt there's even one
bit of FFT in its algorithms. One does not need FFT to
implement a bandpass filter. I don't even see the
connection.

A Sony DSP FM tuner only needs 1 channel, not a full bank
so the FFT provides no speed advantage.

It wouldn't even need FFT if 20 channels were needed!

Which is not to say that there is no way to use FFT technology do it.

If I was going to build a receiver to monitor the entire FM band in a
certain locality, I might use a FFT-based receiver to do so.

The definition of the calculated FFT coefficients is
equivalent to a bank of narrowband filters with the
center frequencies translated to DC. You can't do an FFT
without calculating a bank of filters, what you do with
the coefficients is up to the user.

An utter misconception of what's goingon.

FFT technology can be used to implement filters with more-or-less arbitrary
bandpass characteristics. FFT-based filters are commonly used in audio
production. For example Adobe Audition has two FFT-based filters, one that
implements the user's arbitrarily drawn frequency response curve and another
that implments the user's arbitrarily drawn phase response curve.


The question here is what gets FFT'd. I suspect that in the Audition
filters, the drawn curve is FFT'd into the time domain, then
convolution is used against the actual signal. Mathematically and
time-wise that would make much more sense than chopping the signal
into chunks, FFTing, multiplying by the filter function and IFFTing
back to time domain many, many times.

d

[dbd]

On Dec 23, 5:10*pm, "William Sommerwerck"
wrote:
...

The definition of the calculated FFT coefficients is equivalent to a
bank of narrowband filters with the center frequencies translated to
DC. You can't do an FFT without calculating a bank of filters, what
you do with the coefficients is up to the user.

An utter misconception of what's goingon.

I think you are simply ignorant of what is going on and the
applications and established practices. Filterbanks arejust another
useful valid interpretation of the DFT/FFT algorithm:

https://ccrma.stanford.edu/~jos/sasp...er_Bank_I.html

The algorithm works
the same whether the signal fed to it consists of stationary sinusoids
or noise. The coefficients are better for determining the parameters
of the sinusoids than for determining the parameters of a noise
process, but the analysis is still a Fourier analysis.

AAARRRGGGHHH!

Noise measurement is one of the classic applications of the DFT:

https://ccrma.stanford.edu/~jos/st/P...stimation.html


It is amazing how people can utterly pervert the meaning of facts, then
insist they're right.
...

It's sad that you find such useful applications of the facts so
painful and confusing.

Dale B. Dalrymple

[William Sommerwerck]

The definition of the calculated FFT coefficients is equivalent to a
bank of narrowband filters with the center frequencies translated to
DC. You can't do an FFT without calculating a bank of filters, what
you do with the coefficients is up to the user.

An utter misconception of what's going on.

I think you are simply ignorant of what is going on and the
applications and established practices. Filterbanks arejust another
useful valid interpretation of the DFT/FFT algorithm:

https://ccrma.stanford.edu/~jos/sasp...er_Bank_I.html

The algorithm works
the same whether the signal fed to it consists of stationary sinusoids
or noise. The coefficients are better for determining the parameters
of the sinusoids than for determining the parameters of a noise
process, but the analysis is still a Fourier analysis.

AAARRRGGGHHH!

Noise measurement is one of the classic applications of the DFT:

https://ccrma.stanford.edu/~jos/st/P...stimation.html


It is amazing how people can utterly pervert the meaning of facts, then
insist they're right.
...

It's sad that you find such useful applications of the facts so
painful and confusing.


I still say you don't understand what the Fourier transform is all about.
However, I can see how one might analyze a /time-limited/ noise signal.

[William Sommerwerck]

"William Sommerwerck" wrote in message
...
You really need to stop arguing for a bit, and look into this.
You are quite wrong.

it seems like you are saying that you believe that one cannot
perform a Fourier analysis of noise...

Uh... Noise does not generally have a harmonic structure.


there is no point in continuing this.

Of course not. You might discover you were wrong.


I partially retract what I said above.

[Kevin Aylward[_4_]]

The decomposition of a waveform into it's various sinusoidal
components is the defintion of Fourier analysis.

See page 7 of the paper you cited above:

http://cp.literature.agilent.com/lit...5952-8898E.pdf

"It was shown over one hundred years ago by Baron Jean Baptiste Fourier
that any waveform that exists in the real world can be generated by adding
up sine waves."

Technically, Fourier didn't actually prove that certain functions, under
certain conditions, could be expanded in a sine/cosine series. The proof
under what conditions such an orthogonal expansion is valid only came later
by others. Fourier is associated with using the technique to solve heat
conduction and vibration problems, but he was by no means the first to use
sine/cosine expansions of functions.

Secondly, it is not true that any waveform has a Fourier sine/cosine series
expansion. In general, only waveforms that are repetitive may be expanded in
such a manner. All real world signals are non repetitive, and can only be
approximated by repetitive waveforms. Non repetitive waveforms can be
analysed by Fourier Integral Transform methods.

Thirdly, there is a fundamental limit in knowing a signal's time domain
description and frequency domain description. It can be shown that sigma_T X
sigma_F 1/2. This means, that it is impossible to have complete knowledge
of both a signals time response and frequency response together.

Kevin Aylward B.Sc.
www.kevinaylward.co.uk

[Kevin Aylward[_4_]]

"Mark" wrote in message
...

On Dec 23, 6:35 pm, "William Sommerwerck"
wrote:
The decomposition of a waveform into its various sinusoidal
components is the defintion of Fourier analysis.

That is not correct. It is the decomposition of the waveform into its
sinusoidal /harmonic/ components. Noise is made of sinusoidal components,
but they are not harmonically related, and their decomposition /is not/
Fourier analysis.

You really need to stop arguing for a bit, and look into this. You are
quite
wrong.

Not really.

it seems like you are saying that you believe that one cannot perform a
Fourier analysis of noise,
there is no point in continuing this..

Depends on your definition of "Fourier analysis". In general, noise is not
periodic, therefore cannot be expanded in a Fourier sine/cosine series. Only
repetitive functions can be expanded as a Fourier sine/cosine series.

Noise may be analysed by Fourier Integral Transforms. Its very debatable
whether this is included under the term "Fourier Analysis". Technically,
generalising from a a discrete system to an continuous system can be very
problematic, mathematically.


Kevin Aylward B.Sc.
www.kevinaylward.co.uk

[Don Pearce[_3_]]

On Fri, 24 Dec 2010 12:58:50 -0000, "Kevin Aylward"
wrote:

"Mark" wrote in message
...

On Dec 23, 6:35 pm, "William Sommerwerck"
wrote:
The decomposition of a waveform into its various sinusoidal
components is the defintion of Fourier analysis.

That is not correct. It is the decomposition of the waveform into its
sinusoidal /harmonic/ components. Noise is made of sinusoidal components,
but they are not harmonically related, and their decomposition /is not/
Fourier analysis.

You really need to stop arguing for a bit, and look into this. You are
quite
wrong.

Not really.

it seems like you are saying that you believe that one cannot perform a
Fourier analysis of noise,
there is no point in continuing this..

Depends on your definition of "Fourier analysis". In general, noise is not
periodic, therefore cannot be expanded in a Fourier sine/cosine series. Only
repetitive functions can be expanded as a Fourier sine/cosine series.

Noise may be analysed by Fourier Integral Transforms. Its very debatable
whether this is included under the term "Fourier Analysis". Technically,
generalising from a a discrete system to an continuous system can be very
problematic, mathematically.


Kevin Aylward B.Sc.
www.kevinaylward.co.uk

You can certainly perform a Fourier analysis and get a result out. But
you do need to be aware of what it is you are looking at. What you are
seeing is the spectrum that would result if the noise were not random,
but an endless perfect repetition of the entire sample being analysed.
Given the right circumstances and signals, the result is correct. Get
things wrong and the result is nonsense, mitigated to an arbitrary
degree by selecting a suitable windowing function - a more or less
desperate attempt to make the cut ends join up neatly.

d

[Arny Krueger]

"William Sommerwerck" wrote in
message
"Arny Krueger" wrote in message
...
"William Sommerwerck" wrote
in
message

A prisim [sic] is an example a spectrum analyzer
that operates on light.
And these devices ALL perform Fourier analysis even
though they use different methods.

A prism? Do you understand how a prism works? Of course
not!

It turns out that the behavior of lenses and prisms can
be analyzed using spatial Fourier transforms and FFTs.
One of the rather non-obvious things that can be
accomplished this way is refocusing an unfocused
picture.

http://sharp.bu.edu/~slehar/fourier/fourier.html

Arny, there is nothing whatever on this page about
prisms. NOTHING.

See the information about lenses?

A lens is a special case of the general class of items called prisms.
Fresnel lenses are even made out of prisms. Prisms and lenses both work on
the principle of refraction.

I would be really curious to understand how optical
dispersion can be modeled as a cyclic function.

I gave you a starting point, but the more general starting point is google.

[Arny Krueger]

"Don Pearce" wrote in message

On Thu, 23 Dec 2010 22:41:07 -0500, "Arny Krueger"
wrote:

FFT technology can be used to implement filters with
more-or-less arbitrary bandpass characteristics.
FFT-based filters are commonly used in audio
production. For example Adobe Audition has two
FFT-based filters, one that implements the user's
arbitrarily drawn frequency response curve and another
that implments the user's arbitrarily drawn phase
response curve.

The question here is what gets FFT'd.

Windowed sets of data.

I suspect that in
the Audition filters, the drawn curve is FFT'd into the
time domain, then convolution is used against the actual
signal.

Very little seems to be known about how Audition does much of anything at
that level of detail.

Mathematically and time-wise that would make much
more sense than chopping the signal into chunks, FFTing,
multiplying by the filter function and IFFTing back to
time domain many, many times.

Given that windowing and FFT size are known to be part of the processing,
the second method seems to be the more likely.

[Don Pearce[_3_]]

On Fri, 24 Dec 2010 10:11:07 -0500, "Arny Krueger"
wrote:

"Don Pearce" wrote in message

On Thu, 23 Dec 2010 22:41:07 -0500, "Arny Krueger"
wrote:

FFT technology can be used to implement filters with
more-or-less arbitrary bandpass characteristics.
FFT-based filters are commonly used in audio
production. For example Adobe Audition has two
FFT-based filters, one that implements the user's
arbitrarily drawn frequency response curve and another
that implments the user's arbitrarily drawn phase
response curve.

The question here is what gets FFT'd.

Windowed sets of data.

I suspect that in
the Audition filters, the drawn curve is FFT'd into the
time domain, then convolution is used against the actual
signal.

Very little seems to be known about how Audition does much of anything at
that level of detail.

Mathematically and time-wise that would make much
more sense than chopping the signal into chunks, FFTing,
multiplying by the filter function and IFFTing back to
time domain many, many times.

Given that windowing and FFT size are known to be part of the processing,
the second method seems to be the more likely.




Windowing is no good with audio when you have to turn it back into
time domain. You end up with amplitude modulation of the finished
waveform that way. I suspect that the filter response is IFFT'd then
convolved with the audio on the fly. That would use least processing,
and minimize latency in real-time filtering.

Of course the Audition FFT filter comes with the problem that
amplitude and phase responses are not related, so you can't get back
to where you started later using minimum phase networks.

d