RainmanTime
Super Moderator
Understanding how to manipulate Time (or frequency) will require some basic understandings of control and instrumentation theory with respect to how inputs are transformed into outputs over given periods of Time (frequency). Before one can even understand non-linear control theory, one should become familiar with the ten linear control responses that are part of classical control systems instruction. They are:
1) A Summing Function
The system output equals the algebraic sum of its inputs.
2) An Averaging Function
The system output equals the algebraic sum of its inputs divided by the number of inputs.
3) A Difference Function
The system output equals the algebraic difference between its inputs.
4) A Proportional Function
The system output is directly proportional to its input.
5) An Integral Function
The system output varys with both magnitude and duration of its input. The output is proportional to the time integral of the input.
6) A Derivative Function
The system output is proportional to the time rate of change (derivative) of the input.
7) A Multiplying Function
The system output equals the product of the inputs.
8) A Dividing Function
The system output equals the quotient of the inputs.
9) A Root Extraction Function
The system output equals some root (square root, cube root, 3/2 root) of the inputs.
10) An Exponential Function
The system output equals the input raised to some power.
These ten linear elements form a foundation upon which the study and understanding of much more complex system responses can be approached. If you wanted to add a category 11, it would consist of any and all responses that are some form of non-linear representation of the inputs.
It is in these, the non-linear responses, where we have already seen amazing improvements in system energy efficiency. And it is in these that we will come to learn how to engineer the Massive SpaceTime metric (matrix).
RMT
1) A Summing Function
The system output equals the algebraic sum of its inputs.
2) An Averaging Function
The system output equals the algebraic sum of its inputs divided by the number of inputs.
3) A Difference Function
The system output equals the algebraic difference between its inputs.
4) A Proportional Function
The system output is directly proportional to its input.
5) An Integral Function
The system output varys with both magnitude and duration of its input. The output is proportional to the time integral of the input.
6) A Derivative Function
The system output is proportional to the time rate of change (derivative) of the input.
7) A Multiplying Function
The system output equals the product of the inputs.
8) A Dividing Function
The system output equals the quotient of the inputs.
9) A Root Extraction Function
The system output equals some root (square root, cube root, 3/2 root) of the inputs.
10) An Exponential Function
The system output equals the input raised to some power.
These ten linear elements form a foundation upon which the study and understanding of much more complex system responses can be approached. If you wanted to add a category 11, it would consist of any and all responses that are some form of non-linear representation of the inputs.
It is in these, the non-linear responses, where we have already seen amazing improvements in system energy efficiency. And it is in these that we will come to learn how to engineer the Massive SpaceTime metric (matrix).
RMT