Wed Mar 27 00:44:59 EDT 2013
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
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