[Arny Krueger]

"Dick Pierce" wrote in message

Arny Krueger wrote:
"Randy Yates" wrote in message
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On 03/02/2011 09:37 PM, David Nebenzahl wrote:

On 3/2/2011 5:09 PM Dick Pierce spake thus:


Arny Krueger wrote:


"Sergey Kubushyn" wrote in message


Music is _NOT_ a pure sinusoidal waves and there are
other things like attack, shape etc.

Actually, every music wave form can be entirely
represented as a collection of enveloped sine wave.

Not even "enveloped" sine waves: simply sine waves.


Yes. Just what is an "enveloped" sine wave anyway, pray
tell?


Amplitude-modulated.


Right.

I would like to hear how one simulates say piano notes
by means of just linear mixing of continuous sine waves.

Are you saying that it's not possible? Here, take
my shovel, dig up Mr. Fourier, tell him it's not
possible.

Take ANY amplitude-modulated waveform. Take it's
Fourier transform. The result is some collection of
continuous sine waves, n'est ce pas?

Right - the needed memory jog - an amplitude modulated carrier has a certain
spectrum. It picks up sidebands that are related to the modulating
frequency.

Let's look at a simple case: a 1 kHz wave modulated by
a 100 Hz envelope. That's three sine components, whose
relative amplitudes are dependent upon the amount of
modulation: one sitting at 900 Hz, one at 1000 Hz, and
one at 1100 Hz. Y'know, sidebands, and all that?

Yup.

Take a more complex waveform with a more complex envelope,
and it's merely an extension of the same thing.
Yup.

I asked a question, you answered it. I'm embarassed to say that I once knew
the answer but the fog of other battles, and all that.

Thank you.