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