Chirp Equation: Solving Waveform Frequency Changes

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A sinusoidal chirp can be represented by an equation that reflects changes in frequency over time. A linear chirp is expressed as A Sin(a t^2), where frequency increases linearly. For a chirp with a frequency that decreases by a fixed fraction, an exponential decay model is used, indicating a half-life for frequency reduction. This type of chirp produces distinctive sound effects reminiscent of space-blaster noises. Understanding these equations is essential for accurately modeling waveform frequency changes.
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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 A Sin(a t^2) because its frequency at 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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