Sentence examples for by a logarithmic operator from inspiring English sources

Next this range is mapped to the full real axis by a logarithmic operator according to ρ = log 10 1 − z 1 + z. (7).

It will then be shown that the Laplace-domain logarithmic operator arises naturally as an order distribution, thereby providing a method for constructing a logarithmic operator either in the time or frequency domain.

For erasure recovery, we showed how to find the inverse of a matrix using a simple algorithm by exploiting the logarithmic operator of the elements of the Vandermonde matrix and converting the operations to simple modulo- additions.

By applying the logarithmic operator to each element of and removing the common factor, we get the required shifts (monomials order representation) as follows: (13).

This now provides a definition and an approximation, for the logarithmic operator at low frequencies 1 ln ( s ) ≡ lim Q → 0 Q s Q - 1, ∣ s ∣ < 1, (33).

A two-sided incomplete Laplace-domain logarithmic operator can also be defined as F ( s ) = ∫ b a s q d q X ( s ) (36).

From Equation 16, it can be seen that the reciprocal Laplace-domain logarithmic operator can be represented by the sum of all fractional-order derivatives at low frequencies (large time).

From Equation 12, it can be seen that the reciprocal Laplace-domain logarithmic operator can be represented by the sum of all fractional-order integrals at high frequencies, ω > 1.

It is motivated by the appearance of logarithmic operators in a variety of fractional-order systems and order-distributions.

An incomplete Laplace-domain logarithmic operator can be defined as F ( s ) = ∫ - ∞ a s q d q X ( s ), (34).

The measurement signal is quantized by a logarithmic quantizer.