On Tue, 20 Feb 2007 23:03:10 -0500, "Arny Krueger"
wrote:


I don't know what Jenn said, but I do know that you don't
know either.

Paul, you keep missing the meaning of words that I wrote

Shouldn't that be "words that I've written"? There could be an
inherent explanation here.

On Tue, 20 Feb 2007 14:04:19 GMT, (Bob Masta)
wrote:

On Mon, 19 Feb 2007 10:34:50 -0800, Richard Clark
wrote:

On Mon, 19 Feb 2007 14:06:30 GMT, (Bob Masta)
wrote:

FFT size is 1024 points, so you won't be able to use
this for tuning your guitar, if that's what you had in mind.

Hi Bob,

Why not? 1024 points (bins) has enough resolution to shake out every
note on a Hawaiian slide guitar. The only care is selecting the
sampling rate and most FFT packages should be able to resolve
exceedingly fine.


The problem is that the line resolution of an FFT is the sample
rate divided by the number of time points. So with 44100 Hz
sample rate and 1024 points you get a bit over 43 Hz per line.
So the first non-DC spectral line would be 43 Hz, which is about
a low F on a bass guitar, and the very next line would be the F
an octave above that... you'd miss an entire octave!

Hi Bob,

What you describe here, and that which followed, is a problem of
either hardware (I design my own) or a perception of Fourier
techniques that is constrained to common applications.

The trick is one that is encountered quite commonly with RF designers
(and those Hams that actually practice the craft instead of being
appliance operators) - it is called mixing. Or to describe it with
more precision (as an audio crowd has a restricted meaning for the
term "mixing") heterodyning or modulating/demodulating. Simply put,
the data channel is pre-processed by multiplying it with a reference
cosine before being passed onto the FFT. (Although this sounds like
windowing, it is not.) Of course, the output of the FFT has to have
its units recast. In the old days, this was called "zooming" or an
arbitrary view of a single frequency encompassed by a span of far
higher resolution than that obtained from a simple transform. I would
quickly point out that the simple transform is still performed (same
bin interval, same bin count), but it has been augmented.

This technique, plus a waterfall display, is useful in tracing down
mechanical problems in journals, bearing races (with bearing run-out
or ball defect) and bad gear meshes. It also relates to Hank's desire
to test individual construction components in the guitar as all of
these problems relate to a subtle data inflection that can be
destructive in machinery, or discordant in music. The zoom feature
can reveal these defects with remarkable resolution. As I said, the
FFT as originally described can differentiate every note of an
Hawaiian slide guitar. Perhaps I should have added the proviso:
provided you use a synchronized tracking generator for mixing.
However, given this can be done digitally (no one needs a hardware
oscillator), no change in hardware is necessary. All the data that is
needed is already there.

www.daqarta.com
by the way, this seems to be a dead link. (later) I take that back,
but it took a lot of retries over the span of an hour.

Further, it seems you have a lot of what I mention above covered in
your pages, by parts, but none of them encompass the whole of
"zooming."

And for your page on windowing, drop me an email if you would like to
see some pascal routines embodying some very tight windows. These
came from my time with HP whose chief engineer soon after departed for
a chair at some eastern university.

73's
Richard Clark, KB7QHC

On Wed, 21 Feb 2007 23:47:39 -0800, Richard Clark
wrote:

On Tue, 20 Feb 2007 14:04:19 GMT, (Bob Masta)
wrote:

On Mon, 19 Feb 2007 10:34:50 -0800, Richard Clark
wrote:

On Mon, 19 Feb 2007 14:06:30 GMT, (Bob Masta)
wrote:

FFT size is 1024 points, so you won't be able to use
this for tuning your guitar, if that's what you had in mind.

Hi Bob,

Why not? 1024 points (bins) has enough resolution to shake out every
note on a Hawaiian slide guitar. The only care is selecting the
sampling rate and most FFT packages should be able to resolve
exceedingly fine.


The problem is that the line resolution of an FFT is the sample
rate divided by the number of time points. So with 44100 Hz
sample rate and 1024 points you get a bit over 43 Hz per line.
So the first non-DC spectral line would be 43 Hz, which is about
a low F on a bass guitar, and the very next line would be the F
an octave above that... you'd miss an entire octave!

Hi Bob,

What you describe here, and that which followed, is a problem of
either hardware (I design my own) or a perception of Fourier
techniques that is constrained to common applications.

The trick is one that is encountered quite commonly with RF designers
(and those Hams that actually practice the craft instead of being
appliance operators) - it is called mixing. Or to describe it with
more precision (as an audio crowd has a restricted meaning for the
term "mixing") heterodyning or modulating/demodulating. Simply put,
the data channel is pre-processed by multiplying it with a reference
cosine before being passed onto the FFT. (Although this sounds like
windowing, it is not.) Of course, the output of the FFT has to have
its units recast. In the old days, this was called "zooming" or an
arbitrary view of a single frequency encompassed by a span of far
higher resolution than that obtained from a simple transform. I would
quickly point out that the simple transform is still performed (same
bin interval, same bin count), but it has been augmented.

This technique, plus a waterfall display, is useful in tracing down
mechanical problems in journals, bearing races (with bearing run-out
or ball defect) and bad gear meshes. It also relates to Hank's desire
to test individual construction components in the guitar as all of
these problems relate to a subtle data inflection that can be
destructive in machinery, or discordant in music. The zoom feature
can reveal these defects with remarkable resolution. As I said, the
FFT as originally described can differentiate every note of an
Hawaiian slide guitar. Perhaps I should have added the proviso:
provided you use a synchronized tracking generator for mixing.
However, given this can be done digitally (no one needs a hardware
oscillator), no change in hardware is necessary. All the data that is
needed is already there.

www.daqarta.com
by the way, this seems to be a dead link. (later) I take that back,
but it took a lot of retries over the span of an hour.

Further, it seems you have a lot of what I mention above covered in
your pages, by parts, but none of them encompass the whole of
"zooming."

And for your page on windowing, drop me an email if you would like to
see some pascal routines embodying some very tight windows. These
came from my time with HP whose chief engineer soon after departed for
a chair at some eastern university.

73's
Richard Clark, KB7QHC

Richard:

Thanks for your detailed post. I am aware of the "zoom"
approach, but have not implemented it yet. The cosine
multiplication down to baseband is the easy part; the part
that has put me off is the pesky decimating filter.

For others reading this, the basic idea of the zoom FFT is that
if you want to "zoom in on" some frequency region at
higher resolution, you multiply the incoming signal by the
center of the desired range. From that old high school
trig formula for the product of sinusoids, you get a bunch of
sum and difference components. So the center of the
target band ends up at 0 Hz since you multiplied it by a
sinusoid at the center frequency, and all the rest of
the original spectrum is now spreading out on either
side of 0. Now, if you low-pass filter this mess you can
re-sample it at a much lower frequency. The filter has
to be set so there is nothing of significance above half
of the new sample rate, just as for the orignal ADC (or
you get aliasing errors).

Then you take an FFT of the same size (1024 or whatever)
samples, but at the new lower sample rate. If the new rate is
1/100 of the original, the resolution of the spectrum is improved
x100. Another way to think about this is that if you only wanted
to zoom in on the low end of the spectrum, you wouldn't need to
do the cosine multiply, filter, or resampling... you could just reduce
the base sample rate to 1/100 (if your sound card permitted, and had
its anti-alias filters set for that) and get exactly the same results.

Note that this gives exactly the same resolution as an FFT that is
x100 larger, where you only get to see 1/100 of the whole spectrum.
Also note that an x100 increase in resolution takes x100 increase
in sample time, so you must insure that the signal is stable over that
interval or you will get spectral peak smearing... there is no free
lunch here! This is no problem for Richard's examples of bearings
and gear meshes, but I'd expect troubles with most music since
it is so dynamic.

Anyway, back to my original lament: The low-pass filtering and
resampling would be quite inefficient if done by conventional
approaches, but there are apparently some elegant solutions
that do both functions in one block, reusing it over and over
to get successive halvings of the sample rate. My problem is
that I have only seen this described in theoretical terms with
simple block diagrams, leaving the exact coefficients, etc, as
"an excercise for the reader". Searching the Web I find that
others are apparently as left out in the cold by this as I am,
and there is no example code, hints, or tips to be found.

So, until this particular reader either gets struck by a flash
of insight or takes the time to read up on this enough to
get a whole lot smarter, the zoom FFT is on a back burner.

(Richard, I'll Email you about those window routines...
many thanks for the offer!)

Best regards,





Bob Masta

D A Q A R T A
Data AcQuisition And Real-Time Analysis
www.daqarta.com
Scope, Spectrum, Spectrogram, Signal Generator
Science with your sound card!

On Thu, 22 Feb 2007 14:19:22 GMT, (Bob Masta)
wrote:

My problem is
that I have only seen this described in theoretical terms with
simple block diagrams, leaving the exact coefficients, etc, as
"an excercise for the reader".

Hi Bob,

What you want to resource here are the printed materials available
(then) from the manufacturers of analyzers in the time span of 1980 to
1986 or so. Those would include Analog Devices or Hewlett Packard,
both of which had superb application notes that went to considerable
detail. The academic treatments of that era were mostly semester
based fluff introducing concepts, and not many at that. Industry was
the best source for actually grasping the concepts and implementing
the details. Soon after this period saw the introduction of DSP which
is a silicon processor equivalent of the IIR or FIR math (resource
Texas Instruments from that slightly later era for this discussion).

You did quite well in describing the "zoom" process. This hallmark of
the Real Time Audio Analyzers designed by HP 20 years ago was a long
time in coming. They had a 16 member design team working with a
million lines of Pascal code. It took them 5 years to develop the
product in contrast to the HP design cycle of 18 months. They also
had to design their own Pascal compiler.

I would recommend for reading those works from the Program Manager
Nick Pendergrass (Google: "nick pendergrass" fft).

73's
Richard Clark, KB7QHC