Equation for a Chirp

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Can anyone give me a general equation for a sinusoidal chirp.

I want to calculate a waveform where the frequency drops a given fraction over a given number of cycles.
 
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A chirp is a sinusoidal signal whose frequency changes with time.

For example, a linear chirp has the form [tex] A Sin(a t^2) [/tex] because its frequency [tex] at [/tex] is a linear function of time.

A chirp for which the frequency decreased by a fixed fraction per time would involve exponential decay i.e. the frequency would have a half life. These chirps sound like space-blaster sound effects.
 

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