Echo Shaping Using Sums of Damped Complex Sinusoids

Feedback delay lines are the basis of myriad audio effects and reverberation schemes. The feedback delay line, by itself, is limited to producing an infinite sequence of exponentially decaying echoes. We introduce a new type of linear time-invariant echo effect whose impulse response is a generalized sum of damped complex sinusoids. This permits echo responses to be shaped as simple sinusoids, Fourier-based waveforms, and many other complex, possibly nonperiodic, patterns that would not be feasible with other existing methods. Additionally, because the response is complex-valued, it can be used to produce auto-panning echo effects with many kinds of spatial trajectories. The effect is computationally efficient and straightforward to implement, as it only requires a parallel combination of feedback delay lines.