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In DACs, it is a measure of the deviation between the ideal output value and the actual measured output value for a certain input code. In ADCs, it is the deviation between the ideal input threshold value and the measured threshold level of a certain output code. This measurement is performed after offset and gain errors have been compensated. [1]
Lur'e problem block diagram. An early nonlinear feedback system analysis problem was formulated by A. I. Lur'e.Control systems described by the Lur'e problem have a forward path that is linear and time-invariant, and a feedback path that contains a memory-less, possibly time-varying, static nonlinearity.
Differential non-linearity is a measure of the worst-case deviation from the ideal 1 LSB step. For example, a DAC with a 1.5 LSB output change for a 1 LSB digital code change exhibits 1⁄2 LSB differential non-linearity. Differential non-linearity may be expressed in fractional bits or as a percentage of full scale.
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
The advantage of this technique is that it results in a simplification of the mathematics; the differential equations that represent the system are replaced by algebraic equations in the frequency domain which is much simpler to solve. However, frequency domain techniques can only be used with linear systems, as mentioned above.
The concept of gamma can be applied to any nonlinear relationship. For the power-law relationship =, the curve on a log–log plot is a straight line, with slope everywhere equal to gamma (slope is represented here by the derivative operator):
Fixed-pattern noise (FPN) is the term given to a particular noise pattern on digital imaging sensors often noticeable during longer exposure shots where particular pixels are susceptible to giving brighter intensities above the average intensity.
The homotopy analysis method (HAM) has also been reported for obtaining approximate solutions of the Duffing equation, also for strong nonlinearity. [ 4 ] [ 5 ] In the special case of the undamped ( δ = 0 {\displaystyle \delta =0} ) and undriven ( γ = 0 {\displaystyle \gamma =0} ) Duffing equation, an exact solution can be obtained using ...