In this problem, we will become familiar with the sinusoidal trajectories. Use the audio file ch9aud2.wav. Consider a frame size of $N=512$ samples, no overlap between frames, and $K=10$ sinusoids. Write a MATLAB program to implement the sinusoidal A-by-S algorithm [Geor90]. For each frame, $i$, compute the amplitudes $A_i^k$, the frequencies $\omega_i^k$, and the phases, $\phi_i^k$ of the $k$-th sinusoid.
a. Give a contour plot of the frequencies, $\omega_i^k$ versus the frame number, $i=1,2, \ldots, N_f$, associated with each of the 10 sinusoids.
b. Now assume a $50 \%$ overlap and repeat the above step. Comment on the smoothness and continuity of the frequency trajectories when frames are overlapped $50 \%$.