On the performance of chain codes for quantization of line drawings

Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...

In a three-phase circuit, line loss is an indicator of energy dissipated as heat due to the resistance of transmission lines. To address this, incorporating transformers into the system—a step-up transformer at the source and a step-down transformer at the load—is a strategic solution. Two three-phase transformers are introduced to improve this.
With a step-up transformer at the source, the voltage is increased, thereby reducing the current in the transmission lines since power loss in...

Transmission-line series resistance and shunt conductance cause three primary effects: attenuation, distortion, and power losses.
Attenuation
When constant series resistance and shunt conductance are present, voltage and current equations are modified. The propagation constant indicates that voltage and current waves consist of both forward and backward traveling components. These waves attenuate as they propagate, with the attenuation factor related to the resistance and conductance. In a...

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...

Complex numbers, represented in Cartesian coordinates, can also be visualized as vectors. These vectors can be expressed in polar form, emphasizing their magnitude and angle. When a complex number is input into a function, the output is another complex number, highlighting the function's zero point from which the vector representation can originate.
Consider a function defined as the product of the complex factors in the numerator divided by the product of the complex factors in the denominator.

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.