Instantaneous Frequency

Consider the chirp signal

$$x(t)=\cos(2\pi(at^2+bt)).$$

1.

Determine values for a and b, such that the instantaneous frequency of x(t) will start at 0 Hz and end at 12000 Hz over the time interval $0\leq t \leq 10$ seconds.

2.

Plot the instaneous frequency versus time over the interval $0\leq t \leq 10$ seconds.

3.

Now assume that this chirp signal is sampled at rate f_s=8000 Hz. Plot the instaneous normalized (digital) frequency of the sampled signal versus time over the interval $0\leq t \leq 10$ seconds.