Oscillator-Bank Resynthesis

In classic oscillator-based additive synthesis, the (possibly modified) amplitude and frequency envelopes are used to control a bank of summing sinusoidal oscillators:

$$\begin{eqnarray*} {\hat x}(n) & \isdef & {1\over N} \sum_{k=-N/2+1}^{N/2-1} {\h... ...2\over N}\sum_{k=0}^{N/2-1}{\hat A}_k(n)\cos(\hat{\Theta }_k(n)) \end{eqnarray*}$$