- #1
woohs1216
- 2
- 0
Hello
I don't quiet understand how the integration in the picture works...
I must have forgotten something...
Can anyone explain what is used?
Convolution is a mathematical operation that combines two functions to produce a third function. It is commonly used in signal processing to represent the output of a linear, time-invariant system in response to an input signal.
The time scaling property of convolution states that if a function is scaled by a factor of α, then the convolution of that function with another function will also be scaled by the same factor α.
The time scaling property of convolution can be proven using the definition of convolution and the properties of integrals. By substituting the scaled function into the convolution formula and using the change of variable method, it can be shown that the result is indeed scaled by the same factor α.
The time scaling property is important in signal processing because it allows us to analyze the effects of changing the scale of a signal. This can be useful in applications such as filtering and noise reduction.
While the time scaling property holds true in most cases, there are some situations where it may not apply. For example, if the function being scaled is not continuous, the time scaling property may not hold. Additionally, if the function being scaled is not absolutely integrable, the convolution may not exist.