Why Does Changing Intervals and Arguments Affect Convolution Integrals?

In summary, the conversation discusses the confusion about changing the interval and cutting in half the argument inside an integral. The reason for changing the integration limits is because of convolving two pulses that are only defined from -1 to +1.
  • #1
nhrock3
415
0
5fqj5l.jpg

cant understand the red arrow transition
i changes the intervals and i cuts half of the arguent inside the integral
i can't see why
?

regarding the interval change
the H function is 1 in a certain interval
so if they change the integrval then its no longer H inside
because we have taken the '1' part of the H
??

regarding the cutting in half the argument inside the integral
i have no idea
 
Last edited:
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  • #2
sorry wrong forum
 
  • #3
The reason the integration limits change is because you're convolving two pulses that are only defined from -1 to +1, so the convolution is just 0 for all intervals other than -1 to +1.
 

FAQ: Why Does Changing Intervals and Arguments Affect Convolution Integrals?

1. What is a convolution integral?

A convolution integral is a mathematical operation that combines two functions to create a new function. It is often used in signal processing and image processing to describe how a signal or image is affected by a system or filter.

2. How is a convolution integral calculated?

A convolution integral is calculated by multiplying two functions, one of which is reversed and shifted, and then integrating the product over a specific range. This process is repeated for different values of the shifting variable to create a new function.

3. What is the significance of a convolution integral in science?

Convolution integrals have many applications in science, particularly in signal processing, image processing, and solving differential equations. They help us understand how signals and systems interact and how to model complex systems.

4. Can you provide an example of a convolution integral in real life?

An example of a convolution integral in real life is the process of filtering a sound signal. The sound signal is the input function, and the filter is the second function. The convolution integral of these two functions will create the output sound signal that has been modified by the filter.

5. Are there any limitations to using convolution integrals?

One limitation of using convolution integrals is that they can be computationally expensive, especially for complex functions. Additionally, they assume that the system or filter is linear and time-invariant, which may not always be the case in real-world scenarios.

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