The final system you will work with is called the digital sinusoidal oscillator. The system function of a digital oscillator is given by: H(z) = A sin w0/1 - (2 cosw0)z - 1 + z-2
H(w) = A sin w0/1-(2 cos wo)e-jw +e-2jw
where A is some gain constant. Verify for yourself that the poles of the above system are at etjw on the unit circle). The inverse z-transform for this system can be shown to be:
h[n] = A sin((n +1)wo) u[n]
If you excite this system with an impulse function (i. e.,x[n] = 8[n]), the output y[n] will simply be equal to h[n]. Therefore:
• y[0] = A sin (wo),
• y[1] = A sin (2 wo),
• y[2] = A sin (3 wo), etc.
(a) Plot the pole zero locations corresponding to H(2), assuming A = 1 and w0 = π/4.
(b) Assuming A = 1 and w0 = π/4, generate the sequence {y[n]} for 0 < n < 49. Plot y[n] as a function of n. Enable the 'marker' option and mark the data points on the plot using a marker type and size of your choice.