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...

enter image description here


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:

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


$\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

| improve this answer | |
  • 1
    $\begingroup$ 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 '14 at 12:52

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.