"Franz Heymann" <notfranz.heymann@btopenworld.com> wrote in message
news:c7rgo5$aqg$2@titan.btinternet.com...

"Paul" <nospam@nospam.com> wrote in message
news:40a0deb8$0$3035$61fed72c@news.rcn.com...

What's the most basic process for Fourier analysis? I'm

to

program a pitch recognition application. I haven't found any

mathematical

information that i could digest since I'm not well versed with

mathematical

cryptic symbols. Let's say i have a sine wave generated with

formula

f(x)=sin (x)*sin(x*2)

How would I got about determining its actual frequency using

Fourier?

You should not tinker with Fourier transforms for the same reason

should not tinker with the controls of an aircraft. You need to

the apropriate maths to unserstand what Fourier analysis actually

before asking how to do a Fourier analysis in baboon mode.

Enlighten me, i'm not a math major.

Sam Wormley <swormley1@mchsi.com> wrote in message news:<40A0F104.D6A3C706@mchsi.com>...

Paul wrote:

What's the most basic process for Fourier analysis? I'm attempting to
program a pitch recognition application. I haven't found any mathematical
information that i could digest since I'm not well versed with mathematical
cryptic symbols. Let's say i have a sine wave generated with this formula

f(x)=sin (x)*sin(x*2)

How would I got about determining its actual frequency using Fourier?

Fast Fourier Transform
http://www.library.cornell.edu/nr/bookfpdf.html
http://www.library.cornell.edu/nr/bookcpdf.html

Nice links. Do you know of any that explain how to calculate
correlation coefficients for non-linear multidimensional curve
fitting?

Paul Cardinale

John Popelish <jpopelish@rica.net> wrote in message news:<40A0F193.47DF3BB9@rica.net>...

Fourier analysis is an approximate method for finding the spectrum of
any real waveform, because it assumes that the waveform being analyzed
is periodic and that the sample interval contains an integer number of
cycles of that periodic waveform. Most real waveforms do not meet
those assumptions.

The analysis computes the amplitudes and phases of all harmonics that
have integer numbers of cycles that fit in the sample interval. For
instance, if you select a 1 second sample of an arbitrary waveform and
apply fourier analysis, you get a result that specifies the amplitude
and phase of a DC component (0 cycles per period), a 1 Hz component (1
cycle per period), a 2 Hz component (2 cycles per period), etc.
Obviously, if the waveform being sampled was 1.5 Hz, it would be
misinterpreted as a combination of other frequencies, because an
integer number of cycles did not fit, exactly in the sample period and
the analysis has no way to describe 1.5 Hz or any other frequency
that is not a harmonic of 1 Hz.
There would be a lot of high harmonics present in the result because
of the discontinuity where the end of the 1 second second sample meets
the beginning of that same sample in the assumed periodic repetition
of the sample. There is a whole science of fading the waveform on at
the beginning of the sample period and fading it out at the end
(called windowing), to reduce this discontinuity and the resulting
false harmonics. But it doesn't help with the fact that a 1 second
sample period produces only harmonics of 1 Hz.

Way interesting.

The human auditory sensory apparatus presumably ... well, most
certainly ... does some windowing. The entire idea of hearing the
frequency spectrum as a function of time (e.g. "music") depends on it.
Somehow the smoothing/aliasing problem seems to be a non-problem.

Any thoughts on a mathematical analysis of the VFFT of the auditory
system? Obviously, effectively (and all good buzz words) the window is
suitably fuzzy, continuously weighted, and probably frequency
dependent. Signal analysis types would drool for an algorithm like
that.