Comparison between the ordinary Coefficient Differential Equations of order n and the differential equations is prone to errors (d' y (T)/dt corresponds to Y [n-1]? )

Linear Constant-coefficient Difference Equations

Here is a place that is easy to "confusing". Let's take a closer look at the two equations, and add the "1.109 formula (the above formula in the figure) in the book ), the corresponding discrete time equation is the following equation"

We will find that there is a feeling that "since it is corresponding, Here d' y (T)/dt does not correspond to Y [n-1] (when k = 1 )"

In this way, I am deeply confused...

I think, "How can the first derivative of the continuous field be equal to the offset of the discrete field ?" Cannot understand

In essence, this thinking is wrong.

In a misunderstanding, these two equations have different objects. The former is a model created to portray the continuous field, and the latter is in the discrete field.

This equation is true because it depicts the relationship between input and output. For the attention system, the corresponding coefficient can always be found, the linear combination of the derivatives of each order of the input signal can be equal to the linear combination of the derivatives of each order of the output signal.

Input --> | system | --> output

For discrete systems, the output of the LTI system is only related to the input or output (with feedback,

The following formula is used to describe the relationship.

When the system has feedback, K is not equal to 1, and the right side serves as a combination of the system's separate input.

For example

Y [N] = Y [n-1] + X [N];

This system describes the output of the current system. Y [N] depends on the output of the system at the previous time plus the input of the current system (this guy is a positive feedback ).

X [N] --- (+) --> | system | ---> Y [N]

^ -------------------- |

The system description equation is slightly deformed, and Y [] and X [] are separated on the left and right sides of the equation.

Y [N]-y [n-1] = x [N];

Therefore, they only describe different systems. They all try to use known system input and output to create a model for describing the system.

In a continuous system, the order of the system will affect the input and output, so the differential is used,

In a discrete system, the offset of the system input/output may affect the system output, so the system offset is used.

Do not get confused by comparison between "D 'y (T)/dt corresponding to Y [n-1 ]"

Comparison between the ordinary Coefficient Differential Equations of order n and the differential equations is prone to errors (d' y (T)/dt corresponds to Y [n-1]? )