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Wed Mar 27 00:44:59 EDT 2013

Phasor path

Init: p_0
Desired at end of period: f_1
p_1  = ^exp(-j f_1)  # approx, but make sure unit norm
p_01 = p_1 * p_0'    # complex conjugate, to get angle difference

p_01^(1/(2^n))       # p_01 is expected to be small, so this should be fairly accurate

Computing the log can be split into 2 parts: first part with
normalization, second part as division.

Eventually, the algorithm will converge, as long as there is no
positive feedback.  I.e. we should *underestimate* the magnitude of
p_01^(1/(2^n)).

The approximation of the complex exponential can a simple second order
approximation, together with normalization and successive squaring.

If accurate frequencies are necessary, they could be computed using
another feedback loop, i.e. a PLL.

A second level is possible here too: since the normalization step is
part of the computation, it will might be added to the compensation.
I.e. given an approximation of exp(-jw) that produces unit norm
estimates, construct a map of w'->w to compensate for the phase
non-linearity.



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