Traditional View of the Time and Frequency Domains as Independent
Fourier Transform / Inverse Transform Connects Each Domain
At the Micro-Sound Level, Time and Frequency are Interdependent and Linked by an Uncertainty Principle
Analogy to Heisenberg Uncertainty Principle
Position <----> Speed (rate of change of position)
Time <-----> Frequency (rate of change of phase)
The extremes of the Time and Frequency Domains
Discrete Frequency -----> Infinite Time Discrete Time (impulse) -------> Infinite Bandwidth
Gabor (1946-47) showed that between these extremes, a Gaussian shaped grain has a Gaussian shaped spectrum
Techniques that link the Time and Frequency Domains
with the rule that a change in the time domain results in a change in the frequency domain audio rate fusion <---> 50 ms/20 Hz threshold <---> discrete events
FOF Synthesis (formant waveform)
FOG synthesis (formant grains)
VOSIM (voice simulation)
Curtis Roads' techniques (pulsar, glisson, wavelet, trainlet synthesis, etc)
All are examples of complex systems with emergent form
