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.
