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September 19th, 2010, 07:20 AM   #1
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Sine wave question

Hello, My name is Driehoek and I'm new to this forum.
To learn the math involved I'm programming a software synthesizer. I can't find the answer for one problem though:

Let's say I have a function that desribes a sine-wave making one rotation per unit:

[color=#FF0000]f(x) = (sin (x * pi * 2))[/color]

I then want a wave that rotates 4 times per unit, I simply do:

[color=#FF0000]h(x) = f(x * 4)[/color]

My problem comes if I want to shift the frequency of the wave from i.e. 4 to 0:
First I thought I'd make just a function describing the shift:

[color=#FF0000]g(x) = 4 - x[/color]
and then simply plug it into the wave function:
[color=#FF0000]h(x) = f(x * g(x))[/color]

The result of this is an undesired one however (the frequency goes down and then up again) this
is presumably because "x * g(x)" describes an inverted parabola.

...so finally the question, can somebody hint me, answer me or explain me how to create a sine wave slowly shifting from
one frequency to another? This a been troubling me for over a week.

I Thank you,
Driehoek
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September 19th, 2010, 09:47 AM   #2
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Re: Sine wave question

I think I solved it myself:

h(x) = f((x * a * (d - x)) + (x * b * x) / d)

where:
a is the starting frequency,
b is the ending frequency and
d is the duration of the wave.
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