Exercises

1. A sound has fundamental 440. How could it be ring modulated to give a tone at 110 Hz with only odd partials? How could you then fill in the even ones if you wanted to?

2. What carrier and modulation frequencies would you give a two-operator FM instrument to give frequencies of 618, 1000, and 2618 Hz? (This is a prominent feature of Chowning's Stria [DJ85].)

3. Suppose you wanted to make FM yet more complicated by modulating the modulating oscillator, as in:
   
   $$\cos( \omega_c n + a \cos( \omega_m n + b \cos( \omega_p n )))$$
   
   
   How would the spectrum differ from that of the simple two-modulator example (section 5.5.7)?

4. A sinusoid at a frequency $\omega$ is ring modulated by another sinusoid at exactly the same frequency. At what phase differences will the DC component of the result disappear?