Transfer functions are mathematical representations of the relationship between the input and output of a system. They are commonly used in control systems engineering to analyze and design systems.

The transfer function of a system can be obtained from a signal flow graph. A signal flow graph is a graphical representation of a system that shows the flow of signals through different components or blocks of the system. It consists of nodes (representing variables or signals) and directed edges (representing the flow of signals between nodes).

A signal flow graph can be used to represent the interconnection between different components or blocks of a system. Each block or component in the signal flow graph is associated with a transfer function. The transfer function of the entire system can be obtained by combining the transfer functions of the individual blocks or components according to the interconnections shown in the signal flow graph.

In a signal flow graph, the transfer function of a block or component is obtained by considering the output of the block as a ratio of the sum of the inputs to the block. This is based on the principle of superposition, which states that the response of a linear system to a sum of inputs is equal to the sum of the responses to each individual input.

The transfer function can also be obtained from an analogous table, which is a tabular representation of the interconnections between different components or blocks of a system. The analogous table specifies the transfer function of each block or component and the interconnections between them.

However, the transfer function cannot be directly obtained from the output-input ratio or the standard block system. The output-input ratio represents the relationship between the output and input variables of a system, but it does not provide the mathematical representation of this relationship in the form of a transfer function. Similarly, the standard block system is a graphical representation of a system, but it does not explicitly specify the transfer functions of the individual blocks or components.

Therefore, the correct answer is option 'A' - Signal flow graph.