Exercises

1. What input to a fourth-power transfer function gives an output of -12 dB, if an input of 1 outputs 0 dB?
2. An envelope generator rises from zero to a peak value during its attack segment. How many decibels less than the peak has the output reached halfway into the attack, assuming linear output? Fourth-power output?
3. What power-law transfer function (i.e. what choice of $n$ for the function $f(x) = {x^n}$) would you use if you wish the halfway-point value to be -12 decibels?
4. Suppose you wish to cross-fade two signals, i.e., to ramp one signal in and simultaneously another one out. If they have equal power and are uncorrelated, a linear cross-fade would result in a drop of 3 decibels halfway though the cross-fade. What power law would you use to maintain constant power throughout the cross-fade?
5. A three-note chord, lasting 1.5 seconds, is played starting once every second. How many voices would be needed to synthesize this without cutting off any notes?
6. Suppose a synthesis patch gives output between $-1$ and $1$. While a note is playing, a new note is started using the ``rampdown" voice-stealing technique. What is the maximum output?