FPGA Central

Pete,

I meant very simple thing. Realness together with assumption about
analytical behavior at very low frequency can be used to roughly
estimate if we have or have not enough data points close to DC.

Theoretically, there are two scenarios. First, the dependence can be
thought as a function analytical in vicinity of s=0.
Then, real part must approximate to a constant level as low order even
polynomial in f: R(f) = S0 + S2*f^2 + ... and imaginary part as odd
polynomial: I(f) = S1*f + S3*f^3 + ... If low frequency data points
exhibit such behavior, and we see that real part approximates to a
constant level (S0) while imaginary turns into a straight line pointing
to the origin I(f) = S1*f, then we have enough confidence in predicting
what should be at f=0.

If the function we represent has no derivative in s=0 [example: s^(1/N),
in particular, sqrt(s) used in skin effect description], we don't
observe such behavior, regardless of how close we are to DC. This case
is difficult to differentiate from when the underlying function is
analytical but the low frequency portion is missing. Fortunately, these
are not frequent cases for measured models.

Thanks,
Vladimir


>7) I'm not sure what Vladimir was talking about regarding realness from
>s-parameter data. Whenever you inverse transform to get
>back to the time domain, you enforce realness by producing the negative
>frequency data as the complex conjugate of the positive
>frequency data provided. Vladimir, if you can explain this further,
I'd be
>interested to know what you're thinking.


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