Instantaneous Frequency

Listen to the chirp with a linear frequency movement versus time

This sound is synthesized via the formula:

x(t) = cos( 2pi(mt+f)t )

The frequency that will be heard is determined by taking the derivative of the quantity 2pi(mt+f)t which is the argument of the cosine. If we start with cos(P(t)), the derivative must divided by 2pi to get the frequency in Hertz.

fi(t) = (1/2pi) dP(t)/dt

Therefore, if m=5,000 and f=100, the frequency can be calculated to be

fi(t) = 2m + f = 10,000 t + 100 (Hertz)

The following example shows a comparison of the plot of the chirp to constant frequency sinusoids for reference.