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How would you describe this signal? It's like a sinusoid but as if its frequency was constantly increasing: could you write down a mathematical description? Thanks. And no, this is not homework...

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Frequency is more likely decreasing (period is getting longer). This is a sweep sine signal or as some people used to call it - chirp tone. No point in rewriting the literature, so here are some links with very good explanation for both linear and exponential frequency change.

For linear sweep you get:

$$s(t)=\sin\left(\omega_1t+\frac{\omega_2-\omega_1}{T}\cdot \frac{t^2}{2}\right) $$

where:

$\omega_1 $, $\omega_2$ - initial and final angular frequency respectively

$T$ - sweep duration.

Meng Q., et al. - Impulse Response Measurement With Sine Sweeps and Amplitude Modulation Schemes

Farina A. - Advancements in impulse response measurements by sine sweeps

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    $\begingroup$ You will also see it referred to as a Linear Frequency Modulated (LFM) pulse. It is commonly used in Radar and Sonar systems to increase the bandwidth and improve the resulting resolution. $\endgroup$
    – David
    Jul 16, 2014 at 12:52

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