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In the above equation, the frequency is no longer a constant, rather it is of time-varying nature with initial frequency given by.

The time-varying frequency in Hertz is given by

The first derivative of the phase, which is the instantaneous angular frequency becomes a function of time, which is given by Therefore, the equation for chirp signal takes the following form, Instead of having the phase linear in time, let’s change the phase to quadratic form and thus non-linear. The time derivative of instantaneous phase is equal to the angular frequency of the sinusoid – which in case is a constant in the above equation. Where is the instantaneous phase of the sinusoid and it is linear in time. This can be written as a function of instantaneous phase

The equation for generating a sinusoidal (cosine here) signal with amplitude A, angular frequency and initial phase is Modifying the equation of a sinusoid to generate a chirp signal is a better approach. This method introduces discontinuities in the chirp signal due to the mismatch in the phases of each such segments. One approach to generate a chirp signal is to concatenate a series of segments of sine waves each with increasing(or decreasing) frequency in order. The frequency of the chirp signal can vary from low to high frequency (up-chirp) or from high to low frequency (low-chirp).Ĭhirp signals/signatures are encountered in many applications ranging from radar, sonar, spread spectrum, optical communication, image processing, doppler effect, motion of a pendulum, as gravitation waves, manifestation as Frequency Modulation (FM), echo location etc.Ī linear chirp signal sweeps the frequency from low to high frequency (or vice-versa) linearly. A signal that varies in frequency over time is called “chirp”. Obtaining a signal with time-varying frequency is of main focus here.