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Exercises

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

  2. A sinusoid with frequency 400 and unit peak amplitude is squared. What are the amplitudes and frequencies of the new signal's components?

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

  4. Two sinusoids with frequency 300 and 400 Hertz and peak amplitude one (so RMS amplitude $\approx$0.707) are multiplied. What is the RMS amplitude of the product?

  5. Suppose you wanted to make FM yet more complicated by modulating the modulating oscillator, as in:

    \begin{displaymath}
\cos( \omega_c n + a \cos( \omega_m n + b \cos( \omega_p n )))
\end{displaymath}

    How, qualitatively speaking, would the spectrum differ from that of the simple two-modulator example (Section 5.5)?

  6. 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?


next up previous contents index
Next: Designer spectra Up: Modulation Previous: Phase modulation and FM   Contents   Index
Miller Puckette 2006-09-24