What Is a Linear Stage?

Linearity is one of the properties of convolution operations, that is, let a and b be arbitrary constants. For functions f (z, y), h (x, y) and g (x, y),

Convolution is an important tool for the analysis of linear time-invariant systems. Convolution is used in the design of many filters. The definition of the linear convolution operation is given below. With discrete signals x (n) and y (n), the linear convolution is:

.

Different from the linear correlation operation:

In the convolution operation, y (n) must first be refolded to obtain y (-n).

m> 0 means right shift of y (-n) sequence, m <0 means left shift, different m gets different

value. The rest is the same as the related calculation. The concise representation of the linear convolution operation is:

.

In the formula

Represents a linear winder operator.

make

versus

Compared,

Then

.

Therefore, the sequence point length of the linear convolution operation result is also the length of the sequence x (n) plus the length of y (n) minus one.

Reorder

Where k = mn, then n = mk,

Get

.

Therefore, the convolution operation exchange does not affect the result. ^[2]